Factorisation Using Synthetic Division

Q.

Factorise $x^2-4x-5$

Q.

Select the option that contains the factor of $4x^3+4x^2-x-1$

1. 2x-1

2. 2x+1

3. x-1

4. x-4

Q. Find the factors of the polynomial $(x^3+12x^2+48x+64)$
using synthetic division.

1. $(x-4{)}^3$
2. $(x+4{)}^3$
3. $2(x+2{)}^3$
4. $(x+2{)}^3$

Q. If $(x-1)$ is one of the factors of the polynomial $(x^3-5x^2+8x-4),$ then find the other factors using synthetic division.

1. $(x+1{)}^2$
2. $(x-3{)}^2$
3. $(x-2)(x-3)$
4. $(x-2{)}^2$

Q.

Using factor theorem factorize $x^3-6x^2+3x+10$.

Q.

Factor the quadratic expression $p^2-5p-14$ completely.

Q. Factorise: $2x^3-10x^2-4x+24$
using synthetic division.

1. $2(x+2)(x-3)(x-4)$
2. $(x+2)(x-3)(x-4)$
3. $2(x-2)(x-3)(x-4)$
4. $2(x+2)(x-3)(x+4)$

Q. Find the quotient the and remainder of the following division:

Q. If $(x-2)(x+a)(x-b)$ is the factorised form of the polynomial $(x^3-2x^2-9x+18),$ then find the values of $a$ and $b.$

1. $a=3b=-3$
2. $a=-3b=3$
3. $a=-3b=-3$
4. $a=3b=3$

Q. If $(x-2)(x+a)(x-b)$ is the factorised form of the polynomial $(x^3-2x^2-9x+18),$ then find the values of $a$ and $b.$

1. $a=3$
   $b=-3$
2. $a=-3$
   $b=3$
3. $a=3$
   $b=3$
4. $a=-3$
   $=-3$

Q.

Factor the quadratic expression $m^2-9m+8$ completely.

Q. The factors of $x^3-7x+6$ are

1. (x-1), (x-2), (x+3)
2. (x+1), (x+2), (x+3)
3. (x-1), (x-2), (x-3)
4. (x-1), (x+2), (x+3)

Q.

Find the values of $\mathrm{a}$ and $\mathrm{b}$ so that the polynomial ${\mathrm{x}}^3-{\mathrm{ax}}^2-13\mathrm{x}+\mathrm{b}$ has $(\mathrm{x}-1)$ and $(\mathrm{x}+3)$ as factors.

Q.

What is the factorized form of (2+14x)?

1. 2(1+7x)

2. 2(x +7)

3. (x + 7)

4. 2x + 7