Question 11 Mark
Write the degrees of the following polynomials:
0
AnswerDegree is highest power in the polynomial
0 the degree of 0 is not defined
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Write the coefficients of $x^2 $in the following: $17 - 2x + 7x^2$
Answer$17 - 2x + 7x^2$ the coefficient is $7.$
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Write the coefficients of $x^2$ in the following: $9 - 12x + x^3$
Answer$9 - 12x + x^3$ the coefficient is $0$.
View full question & answer→Question 41 Mark
Write the remainder when the polynomial $f(x) = x^3 + x^2 - 3x + 2$ is divided by $x + 1.$
AnswerWhen the polynomial $f(x),$ divided by $(x + 1)$ the remainder will be
f$(-1) = (-1)^3 + (-1)^2 - 3(-1) + 2$
$= -1 + 1 + 3 + 2$
$= 5$
Thus, the reminder $= 5$
View full question & answer→Question 51 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $p(x) = 2x^2 - x + 4$
Answer$p(x) = 2x^2 - x + 4$ since the degree is $2,$ it is a quadratic polynomial.
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Define zero or root of a polynomial.
AnswerA real number a is a zero (or root) of the polynomial f(x), if f(a) = 0.
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Identify the polynomials in the following:
$\text{p(x)}=\frac{2}{3}\text{x}^2-\frac{7}{4}\text{x}+9$
Answer$\text{p(x)}=\frac{2}{3}\text{x}^2-\frac{7}{4}\text{x}+9$ it is a polynomial as it has positive integers as exponents.
View full question & answer→Question 81 Mark
Identify the polynomials in the following:
$\text{f(x)}=2+\frac{3}{\text{x}}+4\text{x}$
Answer$\text{f(x)}=2+\frac{3}{\text{x}}+4\text{x}$ it is not a polynomial since the exponent of $\frac{3}{\text{x}}$ is a negative integer.
View full question & answer→Question 91 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer.
$\text{y}^2+2\sqrt{3}$
Answer$\text{y}^2+2\sqrt{3}$ it is a polynomial of y.
View full question & answer→Question 101 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer.
$3\sqrt{\text{x}}+\sqrt{2}\text{x}$
Answer$3\sqrt{\text{x}}+\sqrt{2}\text{x}$ it is not a polynomial since the exponent of $3\sqrt{\text{x}}$ is not a positive term.
View full question & answer→Question 111 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer.
$\text{x}-\frac{4}{\text{x}}$
Answer$\text{x}-\frac{4}{\text{x}}$ it is not a polynomial since the exponent of $-\frac{4}{\text{x}}$ is not a positive term.
View full question & answer→Question 121 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $r(x) = 3x^3 + 4x^2 + 5x - 7$
Answer$r(x) = 3x^3 + 4x^2 + 5x - 7$ since the degree is $3,$ it is a cubic polynomial.
View full question & answer→Question 131 Mark
Identify the polynomials in the following:
$\text{g(x)}=2\text{x}^3-3\text{x}^2+\sqrt{\text{x}}-1$
Answer$\text{g(x)}=2\text{x}^3-3\text{x}^2+\sqrt{\text{x}}-1$ it is not a polynomial since the exponent of $\sqrt{\text{x}}$ is a negative integer.
View full question & answer→Question 141 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
$\text{h(x)}=-3\text{x}+\frac{1}{2}$
Answer$\text{h(x)}=-3\text{x}+\frac{1}{2}$ since the degree is 1, it is a linear polynomial.
View full question & answer→Question 151 Mark
Classify the following polynomials as polynomials in one variables, two - variables etc:
xy + yz + zx
Answerxy + yz + zx it is a polynomial in 3 variables in x , y and z.
View full question & answer→Question 161 Mark
Classify the following polynomials as polynomials in one variables, two $-$ variables etc: $x^2 - 2tx + 7t^2 - x + t$
Answer$x^2 - 2tx + 7t^2 - x + t$ it is a polynomial in two variables $x$ and $t.$
View full question & answer→Question 171 Mark
Identify the polynomials in the following:
$\text{h(x)}=\text{x}^4-\text{x}^\frac{3}{2} +\text{x}-1$
Answer$\text{h(x)}=\text{x}^4-\text{x}^\frac{3}{2} +\text{x}-1$ it is not a polynomial since the exponent of $-\text{x}^\frac{3}{2}$ is a negative integer.
View full question & answer→Question 181 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
f(x) = 0
Answerf(x) = 0 as 0 is constant , it is a constant variable
View full question & answer→Question 191 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
q(x) = 4x + 3
Answerq(x) = 4x + 3 since the degree is 1, it is a linear polynomial.
View full question & answer→Question 201 Mark
Find the remainder when $x^3 + 4x^2 + 4x - 3$ is divided by $x.$
AnswerWhen the polynomial $f(x) = x^3 + 4x^2 + 4x - 3$ is, divided by $x$ the remainder will be.
$f(0) = (0)^3 + 4(0)^2 + 4(0) - 3$
$= -3$
Thus, the reminder $= -3$
View full question & answer→Question 211 Mark
Write the degrees of the following polynomials: $7x^3 + 4x^2 - 3x + 12$
AnswerDegree is highest power in the polynomial $7x^3 + 4x^2 - 3x + 12$ the degree is $3$
View full question & answer→Question 221 Mark
Classify the following polynomials as polynomials in one variables, two $-$ variables etc:
$x^2 - xy + 7y^2$
Answer$x^2 - xy + 7y^2$ it is a polynomial in two variables $x$ and $y.$
View full question & answer→Question 231 Mark
Write the coefficients of $x^2$ in the following: $\frac{\pi}{6}\text{x}^2-3\text{x}+4$
Answer$\frac{\pi}{6}\text{x}^2-3\text{x}+4$ the coefficient is $\frac{\pi}{6}$
View full question & answer→Question 241 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
3x - 2
Answer3x - 2 it is a linear polynomial as its degree is 1.
View full question & answer→Question 251 Mark
Write the degrees of the following polynomials:
$5\text{x}-\sqrt{2}$
AnswerDegree is highest power in the polynomial
$5\text{x}-\sqrt{2}$ the degree is 1
View full question & answer→Question 261 Mark
Identify the polynomials in the following:
$\text{q(x)}=2\text{x}^2-3\text{x}+\frac{4}{\text{x}}+2$
Answer$\text{q(x)}=2\text{x}^2-3\text{x}+\frac{4}{\text{x}}+2$ it is not a polynomial since the exponent of $\frac{4}{\text{x}}$ is a negative integer.
View full question & answer→Question 271 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
3y
Answer3y it is a linear polynomial as its degree is 1.
View full question & answer→Question 281 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer. $x^{12} + y^2 + t^{50}$
Answer$x^{12} + y^2 + t^{50}$ it is a three variable polynomial which variables of $x, y, t$
View full question & answer→Question 291 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $t^2 + 1$
Answer$t^2 + 1 -$ it is a quadratic polynomial as its degree is $2$
View full question & answer→Question 301 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $x + x^2 + 4$
Answer$x + x^2 + 4$ it is a quadratic polynomial as its degree is $2.$
View full question & answer→Question 311 Mark
Identify the polynomials in the following: $f(x) = 4x^3 - x^2 - 3x + 7$
Answer$f(x) = 4x^3 - x^2 - 3x + 7$ it is a polynomial.
View full question & answer→Question 321 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $7t^4 + 4t^2 + 3t - 2$
Answer$7t^4 + 4t^2 + 3t - 2 -$ it is a bi$-$quadratic polynomial as its degree is $4$
View full question & answer→Question 331 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $2x + x^2$
Answer$2x + x^{2 }$ it is a quadratic polynomial as its degree is $2.$
View full question & answer→Question 341 Mark
Write the coefficients of $x^2$ in the following: $\sqrt{3}\text{x}-7$
Answer$\sqrt{3}\text{x}-7$ the coefficient is $0$.
View full question & answer→Question 351 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $g(x) = 2x^3 - 7x + 4$
Answer$g(x) = 2x^3 - 7x + 4$ since the degree is $3$, it is a cubic polynomial.
View full question & answer→Question 361 Mark
Write the degrees of the following polynomials: $12 - x + 2x^3$
AnswerDegree is highest power in the polynomial $12 - x + 2x^3$ the degree is $3$
View full question & answer→Question 371 Mark
Classify the following polynomials as polynomials in one variables, two $- $ variables etc: $t^3 - 3t^2 + 4t - 5$
Answer$t^3 - 3t^2 + 4t - 5$ it is a polynomial in one variable $t.$
View full question & answer→Question 381 Mark
Write the degrees of the following polynomials:
7
AnswerDegree is highest power in the polynomial
7 the degree is 0
View full question & answer→Question 391 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer. $3x^2 - 4x + 15$
Answer$3x^2 - 4x + 15$ it is a polynomial of $x.$
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