Question

A.
If the polynomial P(x)= x3 + ax2+bx+1 has a remainder 5 when divided by
x-1 and a remainder 7 when divided by x-2, find the values of a and b.

B.
Prove that 2x-1 is a factor of P(x) = 2x3+ 3x2-8x+3, and factorise P(x)
completely

Answer A : a= -4, b= 7
B : P(x)=(2x-1)(x+3)(x-1)
NEED FULL WORKING.
THANK YOU​

Answer 1

Step-by-step explanation:

A.

If the polynomial P(x)= x3 + ax2+bx+1 has a remainder 5 when divided by

x-1 and a remainder 7 when divided by x-2, find the values of a and b.

B.

Prove that 2x-1 is a factor of P(x) = 2x3+ 3x2-8x+3, and factorise P(x)

completely

Answer A : a= -4, b= 7

B : P(x)=(2x-1)(x+3)(x-1)

NEED FULL WORKING.

THANK YOU

please mark me as brainliest

Answer 2

Answer:

Thus a=-4, b=7

Step-by-step explanation:

A. P(x)= x³ + ax²+bx+1

has a remainder 5 when divided by

x-1

Let x-1=0 then x=1

r=p(1)=5

(1)³+a(1)²+b(1)+1=5

1+a+b+1=5

a+b=3.............(1)

p[(x) has a remainder 7 when divided by x-2

So r=p(2)=7

(2)³+a(2)²++b(2)+1=7

8+4a+2b+1=7

4a+2b=-2

2a+b=-1...........(2)

subtracting (1) from(2)

a=-4

from(1)

-4+b=3

b=7

Thus a=-4, b=7