Question 11 Mark
Determine the degree of the following polynomial:
–10
Answer-10 is a non-zero constant. A non-zero constant term is always regarded as having degree 0.
View full question & answer→Question 21 Mark
Determine the degree of following polynomial:
2x - 1
AnswerSince the highest power of x is 1, the degree of the polynomial 2x - 1 is 1.
View full question & answer→Question 31 Mark
Classify the following polynomials as polynomials in one variable, two variables etc. $x^2 - 2xy + y^2 + 1$
Answer$x^2 - 2xy + y^2 + 1$ is a polynomial in three variable.
View full question & answer→Question 41 Mark
Factorise: $2x^2 - 7x - 15$
Answer$2x^2 - 7x - 15 = 2x^2 - 10x + 3x - 15$
$= 2x(x - 5) + 3(x - 5) $
$= (2x + 3)(x - 5) [$by splitting middle term$]$
View full question & answer→Question 51 Mark
Verify whether the following are True or False:
$\frac{-4}{5}$ is a zero of 4 - 5y
AnswerFalseSolution:
Because zero of 4 - 5y is $\frac{4}{5}.$ $\big[\therefore$ 4 - 5y = 0 ⇒ y = $\frac{4}{5}\big]$
View full question & answer→Question 61 Mark
Which of the following expression are polynomials?
$\frac{1}{5\text{x}^{-2}}+5\text{x}+7$
AnswerPolynomial, because the exponent of the variable of $\frac{1}{5\text{x}^{-2}}+5\text{x}+7=\frac{1}{5}\text{x}^2+5\text{x}+7,$ is a which is whole number.
View full question & answer→Question 71 Mark
Verify whether the following are True or False:$ -3$ is a zero of $y^2 + y - 6$
AnswerNow,$y^2 + y - 6 = y^2 + 3y - 2y - 6 [$by splitting middle term$]$
$=y(y + 3) - 2(y + 3)$
$=(y - 2)(y + 3)$
Hence, zeroes of $y^2 + y - 6$ are $2$ and $-3.$
View full question & answer→Question 81 Mark
Write the coefficient of $x^2$ in the following: $(2x - 5)(2x^2 - 3x + 1)$
AnswerLet $p(x) = (2x - 5)(2x^2 - 3x + 1)$
$= 2x(2x^2 -3x + 1) - 5(2x^2 - 3x + 1)$
$= 4x^3 - 6x^2 + 2x - 10x^2 + 15x - 5$
$= 4x^3 - 16x^2 + 17x - 5$
Hence, the cofficient of $x^2$ in $p(x)$ is $-16.$
View full question & answer→Question 91 Mark
Classify the following polynomials as polynomials in one variable, two variables etc. $x^2 + x + 1$
Answer$x^2 + x + 1$ is a polynomial in one variable.
View full question & answer→Question 101 Mark
Factorise: $84 - 2r - 2r^2$
Answer$84 - 2r - 2r^2$
$= -2(r^2 + r - 42)$
$= -2(r^2 + 7r - 6r -42)$
$= -2[r(r + 7) - 6(r + 7)]$
$= -2(r - 6)(r + 7) = 2(6 - r)(r + 7)$
View full question & answer→Question 111 Mark
Factorise the following: $4x^2 + 20x + 25$
Answer$4x^2 + 20x + 25 = (2x)^2 + 2 \times 2x \times 5 + (5)^2$
$= (2x + 5)^2 [$Using identity, $a^2 + 2ab + b^2 = (a + b)^2]$
View full question & answer→Question 121 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial: $3x^3$
AnswerPolynomial $3x^3$ is a cubic polynomial, because maximum exponent of $x$ is $3.$
View full question & answer→Question 131 Mark
Determine the degree of the following polynomial: $x^3 - 9x + 3x^5$
AnswerSince the highest power of $x$ is $5,$ the degree of the polynomial $x^3 - 9x + 3x^5$ is $5$.
View full question & answer→Question 141 Mark
Give an example of a polynomial, which is:
Monomial of degree 1
Answer3x is monomial of degree 1.
View full question & answer→Question 151 Mark
Find the zeroes of the polynomial in following:
h(y) = 2y
AnswerGiven, polynomial is
h(y) = 2y
For zero of polynomial, put h(y) = 0
2y = 0
Hence, zero of polynomial is 0.
View full question & answer→Question 161 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial: $2 - x^2 + x^3$
AnswerPolynomial $2 - x^2 + x^3$ is a cubic polynomial, because maximum exponent of $x$ is $3$.
View full question & answer→Question 171 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial:
$5\text{t}-\sqrt{7}$
AnswerPolynomial $5\text{t}-\sqrt{7}$ is a linear polynomial, because maximum exponent of t is 1.
View full question & answer→Question 181 Mark
Factorise: $x^2 + 9x + 18$
Answer$x^2 + 9x + 18 = x^2 + 6x + 3x + 18$
$= x(x + 6) + 3(x + 6) $
$= (x + 3)(x + 6) [$by splitting middle term$]$
View full question & answer→Question 191 Mark
Using suitable identity, evaluate the following: $999^2$
Answer$(999)^2 = (1000 - 1)^2 = (1000)^2 - 2 \times (1000) \times 1 + 1^2$
$= 1000000 - 2000 + 1$
$= 998001$
View full question & answer→Question 201 Mark
Classify the following polynomials as polynomials in one variable, two variables etc. $y^3 - 5y$
Answer$y^3 - 5y$ is a polynomial in one variable.
View full question & answer→Question 211 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial: $1 + x + x^2$
AnswerPolynomial $1 + x + x^2$ is a quadratic polynomial, because maximum exponent of $x$ is $2$.
View full question & answer→Question 221 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial:
2 + x
AnswerPolynomial 2 + x is a linear polynomial, because maximum exponent of x is 1.
View full question & answer→Question 231 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial:
$\sqrt{2}\text{x}-1$
AnswerPolynomial $\sqrt{2}\text{x}-1$ is a linear polynomial, because maximum exponent of x is 1.
View full question & answer→Question 241 Mark
Which of the following expression are polynomials?
8
AnswerPolynomial, because the exponent of the variable of 8 or 8x° is 0 which is a whole number.
View full question & answer→Question 251 Mark
Write the coefficient of $x^2$ in the following: $\frac{\pi}{6}\text{x}+\text{x}^2-1$
AnswerThe coefficient of $x^{2 }$ in $\frac{\pi}{6}\text{x}+\text{x}^2-1$ is $1$.
View full question & answer→Question 261 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial: $y^3 - y$
AnswerPolynomial $y^3 - y$ is a cubic polynomial, because maximum exponent of $y$ is $3.$
View full question & answer→Question 271 Mark
Classify the following polynomials as polynomials in one variable, two variables etc.
xy + yz + zx
Answerxy + yz + zx is a polynomial in three variable.
View full question & answer→Question 281 Mark
Which of the following expression are polynomials?
$\frac{1}{7}\text{a}^3-\frac{2}{\sqrt{3}}\text{a}^2+4\text{a}-7$
AnswerPolyonimial, because the exponent of the variable of $\frac{1}{7}\text{a}^3-\frac{2}{\sqrt{3}}\text{a}^2+4\text{a}-7$ is a whole number.
View full question & answer→Question 291 Mark
Factorise: $6x^2 + 7x - 3$
Answer$6x^2+ 7x - 3 = 6x^2 + 9x - 2x - 3$
$= 3x(2x + 3) -1(2x + 3) $
$= (3x - 1)(2x + 3) [$by splitting middle term$]$
View full question & answer→Question 301 Mark
Which of the following expression are polynomials? $\frac{1}{\text{x}+1}$
AnswerNot Polynomial, as the polynomial is expressed as $a_{0 }+ a_1x + a_2x +...a_nx^n,$ where $a_{0,} a_{1,} a_{2,..., }a_{n}$are constants. Now $\text{f(x)}=\frac{\text{p(x)}}{\text{q(x)}}$ is arational expression where $\text{q(x)}\neq0, p(x)$ and $q(x)$ are polyonimials. Hence$,_{ }\frac{1}{\text{x}+1}_{ }$is a rational expression but not a polyonimial.
View full question & answer→Question 311 Mark
Find the zeroes of the polynomial in following:
g(x) = 3 - 6x
AnswerGiven, polynomial is
g(x) = 3 - 6x
For zero of polynomial, put g(x) = 0
3 - 6x = 0 ⇒ 6x = 3
$\Rightarrow\text{x}=\frac{1}{2}$
Hence, zero of polynomial is $\text{x}=\frac{1}{2}.$
View full question & answer→Question 321 Mark
Verify whether the following are True or False: $0$ and $2$ are the zeroes of $t^2 - 2$
AnswerNow, $t^2 - 2t = t(t - 2)$ Hence, zeroes of $t^2 - 2t$ are $0$ and $2$.
View full question & answer→Question 331 Mark
Which of the following expression are polynomials?
$\frac{1}{2\text{x}}$
AnswerNot polyonimial, because the exponent of the variable of is $\frac{1}{2\text{x}}$ or $\frac{1}{2}\text{x}^{-1}$ is -1 which is not a whole number.
View full question & answer→Question 341 Mark
Which of the following expression are polynomials?
$\frac{(\text{x}-2)(\text{x}-4)}{\text{x}}$
AnswerNot Polynomial, because the exponent of the variable of $\frac{(\text{x}-2)(\text{x}-4)}{\text{x}}=\frac{\text{x}^2-6\text{x}+8}{\text{x}}=\text{x}-6+8\text{x}^{-1}$ is -1 which is not whole number.
View full question & answer→Question 351 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial$: 4 - 5y^2$
AnswerPolynomial $4 - 5y^2$ is a quadratic polynomial, because maximum exponent of $y$ is $2$.
View full question & answer→Question 361 Mark
Determine the degree of the following polynomial$: y^3(1 - y^4)$
Answer$y^3(1 - y^4) = y^3 - y^7$ Since the highest power of $x$ is $7,$ the degree of the polynomial is $7.$
View full question & answer→Question 371 Mark
Verify whether the following are True or False:
$-\frac{1}{3}$ is a zero of 3x + 1
AnswerTrueSolution:
Because zero of 3x + 1 is $-\frac{1}{3}$. $\big[\therefore$ 3x + 1 = 0 ⇒ x = $-\frac{1}{3}\big]$
View full question & answer→Question 381 Mark
Find the zeroes of the polynomial in following:
q(x) = 2x - 7
AnswerGiven, polynomial is
q(x) = 2x - 7
For zero of polynomial, put q(x) = 0
2x - 7 = 0 ⇒ 2x = 7
$\Rightarrow\text{x}=\frac{7}{2}$
Hence, zero of polynomial is $\text{x}=\frac{7}{2}.$
View full question & answer→Question 391 Mark
Which of the following expression are polynomials?
$1-\sqrt{5\text{x}}$
AnswerNot Polynomial, because the exponent of the variable of $1-\sqrt{5\text{x}}$ or $1-\sqrt{5\text{x}}^{\frac{1}{2}}$ is $\frac{1}{2}$ which is not a whole number.
View full question & answer→Question 401 Mark
Verify whether the following are True or False:
-3 is a zero of x - 3
AnswerFalseSolution:
Because zero of x - 3 is 3. [$\therefore$ x - 3 = 0 ⇒ x = 3]
View full question & answer→Question 411 Mark
Factorise the following: $9y^2 - 66yz + 121z^2$
Answer$9y^2 - 66yz + 121z^2 = (3y)^2 - 2 \times 3y \times 11z + (11z)^2$
$= (3y - 11z)^2 [$Using identity, $a^2 - 2ab + b^2 = (a - b)^2]$
View full question & answer→Question 421 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial $: t^2$
AnswerPolynomial $t^2$ is a quadratic polynomial, because maximum exponent of $t$ is $2$.
View full question & answer→Question 431 Mark
Write the coefficient of $x^2$ in the following: $3x - 5$
AnswerThe coefficient of $x^{2 }$ in $3x - 5$ is $0$.
View full question & answer→Question 441 Mark
Write the coefficient of $x^2$ in the following: $(x - 1)(3x - 4)$
AnswerLet $p(x) = (x - 1)(3x - 4)$
$= 3x^2 - 7x + 4$
$= 3x^2 - 4x - 3x + 4$
Hence, the cofficient of $x^2$ in $p(x)$ is $3$.
View full question & answer→Question 451 Mark
Find $p(0), p(1), p(-2)$ for the following polynomial: $p(x) = 10x - 4x^2 - 3$
AnswerGiven, polynomial is
$p(x) = 10x - 4x^2 - 3$
On putting $x = 0, 1$ and $-2,$ respectively in $Eq. (i),$
we get $p(0) = 10(0) - 4(0)^2 - 3 $
$= 0 - 0 - 3 $
$= -3$
$p(1) = 10(1) - 4(1)^2 - 3$
$= 10 - 4 - 3 = 10 - 7 = 3$
and $p(-2) =10(-2) - 4(-2)^2 - 3$
$= -20 - 4 \times 4 - 3 = -20 - 16 - 3= -39$
Hence, the values of $p(0), p(1)$ and $p(-2)$ are respectively, $-3, 3$ and $-39$.
View full question & answer→Question 461 Mark
Give an example of a polynomial, which is: Trinomial of degree $2$
Answer$5x^2 + 3x - 1$ is a trinomial of degree $2.$
View full question & answer→Question 471 Mark
Find the zeroes of the polynomial in following:
p(x) = x - 4
AnswerGiven, polynomial is
p(x) = x - 4
For zero of polynomial, put p(x) = x - 4 = 0
⇒ x = 4
Hence, zero of polynomial is 4.
View full question & answer→Question 481 Mark
Classify the following as a constant, linear, quadratic and cubic polynomial:3
AnswerPolynomial 3 is a constant polynomial, because the exponent of variable is 0.
View full question & answer→Question 491 Mark
Find p(0), p(1), p(-2) for the following polynomial:
p(y) = (y + 2)(y - 2)
AnswerGiven, polynomial is p(y) = (y + 2)(y - 2)
On putting y = 0, 1 and -2, respectively in Eq. (i),
We get p(0) = (0 + 2)(0 - 2)= -4
p(1) = (1 + 2)(1 - 2)
= 3 × (-1) = -3
and p(-2) = (-2 + 2)(-2 - 2)
= 0(-4) = 0
Hence, the values of p(0), p(1) and p(-2) are respectively, -4, -3 and 0.
View full question & answer→Question 501 Mark
Factorise the following: $1 - 64a^3 - 12a + 48a^2$
Answer$1 - 64a^3 - 12a + 48a^2 = (1)^3 - (4a)^3 - 3 \times 1^2 \times 4a + 3 \times 1 \times (4a)^2$
$[$Using identity, $(a - b)^3 = a^3 - b^3 + 3a(-b)(a - b)]$
$= (1 - 4a)^3 $
$= (1 - 4a)(1 - 4a)(1 - 4a)$
View full question & answer→