Question

Check whether the polynomial q(t) = 4t3 + 4t2 – t - 1 is a multiple of 2t+1.


please tell me the Ans​

Answer 1

Answer:

The polynomial 4t³ + 4t² - t - 1 is a multiple of 2t + 1.

Step-by-step explanation:

Polynomial = 4t³ + 4t² - t - 1

To check = Whether 2t + 1 is a factor of the given polynomial

$\sf{\longrightarrow{2t + 1 = 0}}$

$\sf{\longrightarrow} \: 2t = -1$

$\sf{\longrightarrow} \: t = {\dfrac{ - 1}{2}}$

By Remainder theorem:

$\sf{\longrightarrow} \: q(t) = 4 {t}^{3} + 4 {t}^{2} - t - 1$

$\sf{\longrightarrow} \: q\left( \dfrac{ - 1}{2}\right) = 4 {\left( \dfrac{ - 1}{2}\right)}^{3} + 4 {\left( \dfrac{ - 1}{2}\right)}^{2} - \left( \dfrac{ - 1}{2}\right) - 1$

$\sf{\longrightarrow} \:4 {\left( \dfrac{ - 1}{8}\right)} + 4 {\left( \dfrac{1}{4}\right)} - \left( \dfrac{ - 1}{2}\right) - 1$

$\sf{\longrightarrow} \: {\dfrac{ - 1}{2}} + 1 + \dfrac{ 1}{2}- 1$

$\sf{\longrightarrow} \:1 - 1$

$\sf{\longrightarrow} \:0$

The Remainder is 0.

Therefore, the polynomial 4t³ + 4t² - t - 1 is a multiple of 2t + 1.

Answer 2

Answer:

4t³ + 4t² – t – 1 is a multiple of 2t + 1.

For explanation kindly refer the attachment.