Question

What must be subtracted from 16x³ – 8x² + 4x + 7 so that the resulting expression has 2x + 1 as a factor?

Answer 1

Let the number to be subtracted from the given polynomial be k

Let f(x) = 16x³ – 8x² + 4x + 7 – k

It is given that (2x + 1) is a factor of f(x).

∴ `f(-1/2) = 0`

`=> 16(-1/2)^3 - 8(-1/2)^2 + 4(-1/2)+7 - k = 0`

`=> -16 xx 1/8 - 8 xx 1/4 -4 xx 1/2 + 7 - k = 0`

`=>` –2 – 2 – 2 + 7 – k = 0

`=>` – 6 + 7 – K = 0

`=>` 1 – k = 0

`=>` k = 1

Thus, 1 should be subtracted from the given polynomial.