Question 11 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
$r(x)=3 x^3+4 x^2+5 x-7$
Answer$r(x)=3 x^3+4 x^2+5 x-7$ since the degree is $3,$ it is a cubic polynomial.
View full question & answer→Question 21 Mark
Write the coefficients of $x^2$ in the following:
$9-12 x+x^3$
Answer$9-12 x+x^3$ the coefficient is $0.$
View full question & answer→Question 31 Mark
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 41 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 51 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $3x - 2$
Answer$3x - 2$ it is a linear polynomial as its degree is $1.$
View full question & answer→Question 61 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials: $3y$
Answer$3y$ it is a linear polynomial as its degree is $1.$
View full question & answer→Question 71 Mark
The following expression are polynomials in one variable and which are not? State the reasons for your answer.
$3 x^2-4 x+15$
Answer$3 x^2-4 x+15$ it is a polynomial of x.
View full question & answer→Question 81 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
$2 x+x^2$
Answer$2 x+x^2$ it is a quadratic polynomial as its degree is $2.$
View full question & answer→Question 91 Mark
Write the degrees of the following polynomials:
$0$
AnswerDegree is highest power in the polynomial
$0$ the degree of $0$ is not defined
View full question & answer→Question 101 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $q(x) = 4x + 3$
Answer$q(x) = 4x + 3$ since the degree is $1,$ it is a linear polynomial.
View full question & answer→Question 111 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 121 Mark
Write the coefficients of $x^2$ in the following:
$17-2 x+7 x^2$
Answer$17-2 x+7 x^2$ the coefficient is $7.$
View full question & answer→Question 131 Mark
Identify the polynomials in the following:
$f(x)=4 x^3-x^2-3 x+7$
Answer$f(x)=4 x^3-x^2-3 x+7$ it is a polynomial.
View full question & answer→Question 141 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 151 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
$p(x)=2 x^2-x+4$
Answer$p(x)=2 x^2-x+4$ since the degree is $2,$ it is a quadratic polynomial.
View full question & answer→Question 161 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 171 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 181 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 191 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $f(x) = 0$
Answer$f(x) = 0$ as $0$ is constant , it is a constant variable
View full question & answer→Question 201 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 211 Mark
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
$7 t^4+4 t^2+3 t-2$
Answer$7 t^4+4 t^2+3 t-2$ - it is a bi-quadratic polynomial as its degree is $4$
View full question & answer→Question 221 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 231 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 241 Mark
Write the degrees of the following polynomials:
$7 x^3+4 x^2-3 x+12$
AnswerDegree is highest power in the polynomial $7 x^3+4 x^2-3 x+12$ the degree is $3$
View full question & answer→Question 251 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 261 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 271 Mark
Identify constant, linear, quadratic and cubic polynomial from the following polynomials: $g(x)=2 x^3-7 x+4$
Answer$g(x)=2 x^3-7 x+4$ since the degree is $3$, it is a cubic polynomial.
View full question & answer→Question 281 Mark
Write the degrees of the following polynomials:
$12-x+2 x^3$
AnswerDegree is highest power in the polynomial $12-x+2 x^3$ the degree is $3$
View full question & answer→Question 291 Mark
Classify the following polynomials as polynomials in one variables, two - variables etc:
$t^3-3 t^2+4 t-5$
Answer$t^3-3 t^2+4 t-5$ it is a polynomial in one variable t.
View full question & answer→Question 301 Mark
Find the remainder when $x^3+4 x^2+4 x-3$ is divided by $x$.
AnswerWhen the polynomial $f(x)=x^3+4 x^2+4 x-3$ 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 311 Mark
Define zero or root of a polynomial.
AnswerA real number a is a zero (or root) of the polynomial $f(x),$ if $f(a) = 0.$
View full question & answer→Question 321 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 331 Mark
Classify the following polynomials as polynomials in one variables, two - variables etc:
$x^2-x y+7 y^2$
Answer$x^2-x y+7 y^2$ it is a polynomial in two variables $x$ and $y.$
View full question & answer→Question 341 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 351 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 361 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 371 Mark
Classify the following polynomials as polynomials in one variables, two - variables etc:$ xy + yz + zx$
Answer$xy + yz + zx$ it is a polynomial in $3$ variables in $x , y$ and $z.$
View full question & answer→Question 381 Mark
Write the remainder when the polynomial $f(x)=x^3+x^2-3 x+2$ 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 391 Mark
Classify the following polynomials as polynomials in one variables, two - variables etc:
$x^2-2 t x+7 t^2-x+t$
Answer$x^2-2 t x+7 t^2-x+t$ it is a polynomial in two variables $x$ and $t.$
View full question & answer→Question 401 Mark
If $f(x)=x^4-2 x^3+3 x^2-a x-b$ when divided by $x-1$, the remainder is 6 , then find the value of $a+b$
View full question & answer→Question 411 Mark
If $x+1$ is a factor of $x^3+a$, then write the value of $a$.
View full question & answer→Question 421 Mark
Find the remainder when $x^3+4 x^2+4 x-3$ is divided by $x$.
View full question & answer→Question 431 Mark
Write the remainder when the polynomial $f(x)=x^3+x^2-3 x+2$ is divided by $x+1$.
View full question & answer→Question 441 Mark
If $x=\frac{1}{2}$ is a zero of the polynomial $f(x)=8 x^3+a x^2-4 x+2$, find the value of $a$.
View full question & answer→Question 451 Mark
Define zero or root of a polynomial.