Question

what must be subtracted from 16x^3 - 8x^2 + 4x+7 so that the resulting expression has 2x+1 as a factor?

30 points question and will mark brainliest to correct answer.​

Answer 1

Here's the ans have a great day

Answer 2

Answer:

Hence, 1 must be subtracted from $16x^3 - 8x^2 + 4x+7$.

Step-by-step explanation:

In context to questions asked ,

From the given polynomial what Must Be Subtracted from $16x^3 - 8x^2 + 4x+7$,

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

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

Let, $f(y)=16 x^{3}-8 x^{2}+4 x+7-k$

$\therefore f\left(-\frac{1}{2}\right)=0$

Simplifying it further, we get

$\Rightarrow 16\left(-\frac{1}{2}\right)^{3}-8\left(-\frac{1}{2}\right)^{2}+4\left(-\frac{1}{2}\right)+7-k=0$

$\Rightarrow-16 \times \frac{1}{8}-8 \times \frac{1}{4}-4 \times \frac{1}{2}+7-k=0$

$\Rightarrow-2-2-2+7-k=0$

$\Rightarrow-6+7-k=0$

$\Rightarrow 1-k=0$

$\Rightarrow k=1$

Thus, $1$ should be subtracted from the given polynomial