Question

What must be added to p(x)=8^4+14^3-2x^2+8x-12 so that 4x^2+3x-2 is a factor of p(x) ?

Answer 1

Answer:

Step-by-step explanation:

8x^2 - 15x + 10 should be added to p(x)

So that 4x^2 + 3x - 2 is the factor

Answer 2

Correct question will be :

What must be added to p(x) = 8 x⁴ + 14 x³ - 2 x² + 8 x - 12  so that 4 x²+ 3 x-2 is a factor of p(x) ?

Answer:

15 x - 14

Explanation:

Let k be added to 8 x⁴ + 14 x³ - 2 x² + 8 x - 12 .

Then the polynomial will become :

8 x⁴ + 14 x³ - 2 x² + 8 x - 12 + k

Now if we divide the given polynomial with the factor we will get the remainder as k and hence we should divide the polynomial with the factor of the expression .

The given factor is 4 x² + 3 x - 2 and hence we have :

4 x² + 3 x - 2 is the factor of 8 x⁴ + 14 x³ - 2 x² + 8 x - 12 + k .

We know that :

f ( x ) = q ( x ) × g ( x ) + r ( x ) where q ( x ) is the quotient .

r ( x ) is the remainder .

Obtain the remainder by dividing the polynomials .

4x²+3 x-2) 8 x⁴+ 14 x³- 2 x²+8 x-12( 2x²-2x-1

                 8 x⁴ +6 x³- 4 x²

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

                         8 x³ + 2x²+ 8 x

                         8 x³ + 6x² - 4x

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

                                     - 4 x²+12 x- 12

                                     - 4 x² - 3 x + 2

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

                                               15 x - 14

The value to be added is 15 x - 14 .