Question

What must be subtracted from f(x) = x4 + 2x3
- 13x2
-12x +21 so that the resulting
polynomial is exactly divisible by x2
- 4x + 3?

Answer 1

this may helps u ...........

Answer 2

Answer:

2x-3

Step-by-step explanation:

Given : Dividend = $x^{4} +2x^{3} -13x^{2} -12x+21$

Divisor = $x^{2} - 4x+3$

Solution :

Since we know that :

$Dividend = divisor * quotient +remainder$

$x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*x^{2} + (6x^{3}-16x^{2}-12x+21)$

$x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x) + (8x^{2}-30x+21)$

$x^{4} +2x^{3} -13x^{2} -12x+21 = (x^{2} - 4x+3)*(x^{2}+6x+8) + (2x-3)$

Since the remainder is  2x-3

So, 2x-3 must be subtracted from   $x^{4} +2x^{3} -13x^{2} -12x+21$  so that the resulting  polynomial is exactly divisible by $x^{2} - 4x+3$