Question

Check whether the polynomial q(t) = 4t^3 +4t^2-t-1 is a multiple of
2t + 1.​

Answer 1

Answer:

\begin{gathered}g(x) = 0 \\ = > 2t + 1 = 0 \\ = > 2t = - 1 \\ = > t = \frac{ - 1}{2}\end{gathered}g(x)=0=>2t+1=0=>2t=−1=>t=2−1 

Now,

\begin{gathered}q(t) = {4t}^{3} + {4t}^{2} - t \times 1 \\ \\ = > q(t) = 4 \times {( \frac{ - 1}{2} )}^{3} + 4 \times {( \frac{ - 1}{2} )}^{2} - (\frac{ - 1}{2} ) - 1 \\ = 4 \times \frac{ - 1}{8} + 4 \times \frac{1}{4} + \frac{1}{2} - 1 \\ = \frac{ - 1}{2} + 1 + \frac{1}{2} - 1 \\ = \frac{ - 1 + 2 + 1 - 2}{2} \\ = \frac{0}{2} \\ = 0\end{gathered}q(t)=4t3+4t2−t×1=>q(t)=4×(2−1)3+4×(2−1)2−(2−1)−1=4×8−1+4×41+21−1=2−1+1+21−1=2−1+2+1−2=20=0 

Yes, q( t ) is the multiple of 2t + 1.

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Answer 2

Answer:

Here's your answer!!Remainder= 0

Hence

q(t) is the multiple