Question

if f(x)=2x^4+ax^3+2x^2-3x+b is exactly divisible by x^2-1 find a and b

Answer 1

Heya !!!

Given that,

(X²-1) is a factor of the given polynomial.

P(X) = 2X⁴+AX³+2X²-3X+B

G(X) => X²-1

On dividing P(X) by G(X) we get,

X²-1 )2X⁴+AX³+2X²-3X+B( 2X² + AX + 2

*******2X⁴ ******-2X²

-------------------------------------

******0***+ AX³ + 4X² - 3X + B

***********+AX³ *********-AX + B

---------------------------------------------

************0******+ 4X² + X(A - 3) + B

********************+4X² *************-2

----------------------------------------------------

********************0******+ X(A-3) + (B+2)

Therefore,

Quotient = 2X²+AX+ 2

And,

Remainder = X(A-3) + (B+2)

Now,

Remainder = 0

X(A-3) + (B+2) = 0

X(A-3) + (B+2) = 0X + 0

A-3 = 0

A = 3

And,

(B+2) = 0

B = -2

Hence,

A = 3 and B = -2.

★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★

Answer 2

Hi,

Please see the attached file!


Thanks