Factor and Remainder Theorems

Edexcel IAL WMA12/01/P2/Jan 2021/Q01 (The Factor Theorem)

f(x) = x4 + ax3 - 3x2 + bx + 5 

where a and b are constants.​​ 

When f(x) is divided by (x + 1), the remainder is 4​​ 

• Show that a + b = −1​​ 

(2)​​ 

When​​ f(x)​​ is divided by​​ (x-2),​​ the remainder is −23​​ 

• Find the value of a and the value of b.​​ 

(4)

SOLUTION​​ 

a-​​ 

f-1=4

-14+a-13-3-12+b-1+5=4

1-a-3-b+5=4

-a-b+3=4

-a-b=1

a+b=-1 

b-​​ 

f2= -23

24+a23-322+b2+5=-23

16+8a-12+2b+5=-23

8a+2b+9=-23

8a+2b=-32

4a+b=-16

a+b=-1     -1

4a+b=-16     -2

2-1

3a=-15

a=-153

a=-5

a+b=-1

b=-1-a

b=-1--5

b=4