Question

Factorize the following to answer the code below. Letters may be used more than once.

Q3. Find remainder if x 3 – 3x 2 + 4x – 14 is divisible by x + 2.
Q4. Factorize x 3 – x 2 – 22x + 40

Answer 1

3.-42

Explanation:

3.

x+2=0,x=-2

f(-2)=(-2)³-3(-2)²+4(-2)-14=-8-12-8-14=-42

4.

x³-x²-22x+40

put x=2

2³-2²-22(2)+40

=8-4-44+40

=48-48

=0

x=2

so x-2 is one factor.

by synthetic division.

2 | 1 -1 -22 40

| 2 2 -40

_____________

1 1 -20 | 0

x²+x-20=0

x²+5x-4x-20

=x(x+5)-4(x+5)

=(x+5)(x-4)

x³-x²-22x+40=(x+5)(x-2)(x-4)