Question

The polynomial x^3 + 4x^2 + ax – b has x - 1 as a factor and gives the remainder -6 when divided
by x + 1. Find the values of a and b. ​

NEED HELP PLS

Answer 1

Hey User,

Here is Your answer,

x-1=0

x=1

Put the value of x in given p(x)

Now,

$p(x)=x^3+4x^2+ax-b$

$p(1)=(1)^3+4(1)^2+a(1)-b$

$1+4+a-b=0$

$5+a-b=0$.............1

Now,

Atq---When divided by x+1 leaves tge remainder -6.

x+1=0

x=-1

$(-1)^3+4(-1)^2+a(-1)-b=-6$

$-1+4-a-b=-6$

$3-a-b=-6$...........2

Now

adding eq 1 and eq .2

$5+a-b+3-a-b=-6+0$

$8-2b=-6$

$-2b=-14$

$b=7$

Now put tha value of b in eq..1

$5+a-b=0$

$5+a-7=0$

$-2+a=0$

$a=2$

Hence, The value of a and b is 2 and 7 respwctively.

Thank you!

#BEBRAINLY.