Question

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

Answer 1

Hey buddy here is the answer

Answer 2

2x-3 must be deducted from x⁴ + 2x³ – 13x² –12x + 21

Step-by-step explanation:

Polynomial  f(x) = x⁴ + 2x³ – 13x² –12x + 21

To be divisible by x² – 4x + 3.

Let's find the quotient and remainder.

x⁴ + 2x³ – 13x² –12x + 21 / x² – 4x + 3 = x² +6x + 8

x⁴ - 4x³ + 3x²

     6x³ -16x² -12x +21

     6x³ -24x² +18x

         +8x²  -30x + 21

         +8x²  -32x + 24

               + 2x -3

So the quotient is x² +6x + 8. There is a remainder of 2x-3.

So 2x-3 must be deducted from x⁴ + 2x³ – 13x² –12x + 21 to make it divisible by x² – 4x + 3.