Division of a Polynomial by a Polynomial

Q.

Use the Factor Theorem to determine whether $\text{g(x)}$ is a factor of $\text{p(x)}$ in the following case: ${\text{p(x) = x}}^3+3x^2+3x+1$, $\text{g(x) = x + 2}$

Q. Divide $10x^4+17x^3-62x^2+30x-3$ by $2x^2+7x-1$
[4 MARKS]

Q.

Evaluate the product $103\times 107$ without multiplying directly

Q.

Use remainder theorem to factorize the polynomial $2x^3+3x^2-9x-10$.

Q.

Factorize the following expressions:

$4a^2+12ab+9b^2-8a-12b$

Q.

x⁴−2x³+2x²+x+4 by x²+x+1

Q.

Factorise the expression and divide them as directed: $(m^2-14m-32)÷(m+2)$

Q.

Divide 48 ÷ 6.

Q. Question 23

On dividing $p(4p^2-16)$ by $4p(p-2)$, we get
a) $2p+4$
b) $2p-4$
c) $p+2$
d) $p-2$

Q.

Divide the given polynomial by the given monomial: $(3y^8-4y^6+5y^4)÷y^4$

Q.

Find the value of 'a', if $x+2$ is a factor of $4x^4+2x^3-3x^2+8x+5a$.

Q.

Verify division algorithm i.e., Dividend = Divisor $\times$ Quotient + Remainder, in each of the following. Also, write the quotient and remainder :

$\begin{array}{ccc}\left(i\right)& 14x^2+13x-15& 7x-4\\ \left(ii\right)& 15z^2-20z^2+13z-12& 3z-6\\ \left(iii\right)& 6y^5-28y^3+3y^2+30y-9& 2y^2-6\\ \left(iv\right)& 34x-22x^3-12x^4-10x^2-75& 3x+7\\ \left(v\right)& 15y^4-16y^3+9y^2-\frac{10}{3}y+6& 3y-2\\ \left(vi\right)& 4y^3+8y+8y^2+7& 2y^2-y+1\\ \left(vii\right)& 6y^5+4y^4+4y^3+7y^2+27y+6& 2y^3+1\end{array}$

Q.

Divide $15y^4+16y^3+\frac{10}{3}y-9y^2-6$ by 3y - 2. Write down the co-efficients of the terms in the quotient.

Q.

$x^5+x^4+x^3+x^2+x+1$ by $x^3+1$

Q.

Divide $x^4-y^4$ by $x^2-y^2$.

Q.

Factorise the expression and divide them as directed: $12xy\left(9x^2-16y^2\right)÷4xy\left(3x+4y\right)$.

Q. Question 5(vii)
Factorise the expressions and divide them as directed
$39y^3(50y^2-98)÷26y^2(5y+7)$

Q.

$14x^2-53x+45by7x-9$

Q. $8^y=64$.find the value of y

Q.

Single choice question:
If p(x) = g(x) × q(x) + r(x), p(x) and g(x) are any two polynomials with g(x) $\ne$ 0, then we can find polynomials q(x) and r(x) by division algorithm.We should stop the division process when

1. r(x) = 0

2. degree of r(x) < degree of g(x)

3. None of these

4. Either A or B

Q. Question 5(v)
Factorise the expressions and divide them as directed
$5pq(p^2-q^2)÷2p(p+q)$

Q.

$3x^3+4x^2+5x+18byx+2$

Q. Question 5(iii)
Factorise the expressions and divide them as directed
$(5p^2-25p+20)÷(p-1)$

Q.

Factorize $3x^2-(3\sqrt{3}-1)x-\sqrt{3}$ and verify relationship between the zeroes and the coefficients. [2 MARKS]

Q.

$ac{x}^2+(bc+ad)x+bdby(ax+b)$

Q.

$3y^4-3y^3-4y^2-4yby{y}^2-2y$

Q. Question 5(ii)
Factorise the expressions and divide them as directed
$(m^2-14m-32)÷(m+2)$

Q.

$6x^3+11x^2-39x-65by3x^2+13x+13$

Q.

When $x^5-5x^4+9x^3-6x^2-16x+13$ is divided by $x^2-3x+a$, the quotient and remainder are $x^3-2x^2+x+1$ and $-15x+11$, respectively. Find the value of $a$.

Q. Question 5(v)
Factorise the expressions and divide them as directed
$5pq(p^2-q^2)÷2p(p+q)$