Sample QuestionsFactorization Of Polynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $x +1$ is a factor of the polynomial $2 x ^2+ kx$, then $k =$
Answer: D.
View full solution →If both $x - 2$ and $\text{x}-\frac{1}{2}$ are factor of $px^2 + 5x + r$, then
- ✓
$p = r$
- B
$p + r = 0$
- C
$2p + r = 0$
- D
$p + 2r = 0$
Answer: A.
View full solution →If $x-3$ is a factor of $x^2-a x-15$, then $a=$
Answer: A.
View full solution →If $x^3+6 x^2+4 x+k$ is exactly divisible by $x+2$, then $k$
Answer: C.
View full solution →If $x - a$ is a factor of $x^3 - 3x^2a + 2a^2x + b$, then the value of $b$ is:
Answer: A.
View full solution →Identify constant, linear, quadratic and cubic polynomial from the following polynomials:
$r(x)=3 x^3+4 x^2+5 x-7$
View full solution →Write the coefficients of $x^2$ in the following:
$9-12 x+x^3$
View full solution →Identify the polynomials in the following:$\text{p(x)}=\frac{2}{3}\text{x}^2-\frac{7}{4}\text{x}+9$
View full solution →Identify the polynomials in the following:$\text{f(x)}=2+\frac{3}{\text{x}}+4\text{x}$
View full solution →Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
3x - 2
What must be subtracted from $x^3-6 x^2-15 x+80$ so that the result is exactly divisible by $x^2+x-12 ?$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$f(x)=x^2, x=0$
View full solution →Find the remainder when $x^3+3 x^3+3 x+1$ is divided by:
x
View full solution →In the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
$f(x) = 3x^4 + 17x^3 + 9x^2 - 7x - 10; g(x) = x + 5$
View full solution →If $x + 1$ is a factor of $x^3 + a$, then write the value of a.
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:$\text{f(x)}=2\text{(x)}+1,\text{x}=\frac{1}{2}$
View full solution →Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
f(x) = $x^2 - 1, x = 1, -1$
View full solution →Find the value of a such that $(x - 4)$ is a factors of $5x^3 - 7x^2 - ax - 28.$
View full solution →Find the remainder when $x^3+3 x^3+3 x+1$ is divided by: $x+\pi$
View full solution →Factorize the following polynomials:
$4x^3 + 20x^2 + 33x + 18$ given that $2x + 3$ is a factor.
View full solution →In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division:
$f(x) = 9x^3 - 3x^2 + x - 5$, $\text{g(x)}=\text{x}-\frac{2}{3}$
View full solution →Find the value of a, if $x + 2$ is a factor of $4x^4 + 2x^3 - 3x^2 + 8x + 5a$.
View full solution →Using factor theorem, factorize the following polynomials:
$2y^3 + y^2 - 2y - 1$
View full solution →If $\text{x}=-\frac{1}{2}$ is zero of the polynomial $p(x) = 8x^3 - ax^2 - x + 2$, Find the value of a.
View full solution →In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division:
$f(x) = x^3 + 4x^2 - 3x + 10, g(x) = x + 4$
View full solution →Find the values of p and q so that$ x^4 + px^3 + 2x^3 - 3x + q$ is divisible by $(x^2 - 1).$
View full solution →Find the values of $a$ and $b$ so that $(x+1)$ and $(x-1)$ are factors of $x^4+a x^3-3 x^2+2 x+b$.
View full solution →Show that $(x+4),(x-3)$ and $(x-7)$ are factors of $x^3-6 x^2-19 x+84$.
View full solution →In the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the by actual division:
$f(x) = x^3 - 6x^2 + 2x - 4, g(x) = 1 - 2x$
View full solution →If polynomials $ax^3 + 3x^2 - 3$ and $2x^3 - 5x + a$ when divided by $(x - 4)$ leave the remainders as $R_1$ and $R_2$ respectively.
Find the values of a in each of the following cases, if
- $R_1 = R_2$
- $R_1 + R_2 = 0$
- $2R_1 − R_2 = 0$
View full solution →