Check whether the polynomial f(x) = 4x³+4x²-x-1 is a multiple of (2x+1)
Answers
Answered by
3
Answer:
According to factor theorem, when f(x) is divided by (2x+1), f(
2
−1
)=0
f(x)=4x
3
+4x
2
−x−1
f(
2
−1
)=4(
2
−1
)
3
+4(
2
−1
)
2
−(
2
−1
)−1
=4×
8
−1
+4×
4
1
+
2
1
−1
=
2
−1
+1+
2
1
−1=0
∵f(
2
−1
)=0,(2x+1) is a factor of the polynomial.
Answered by
1
Answer:
hay!!
Dear friend -
☺☺Hear is ur solution ☺☺
2x+1=0
\begin{gathered}x = - \frac{1}{2} \\ \end{gathered}
x=−
2
1
Now, p
\begin{gathered}( - \frac{1}{2}) = 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) = 0\end{gathered}
(−
2
1
)=4×(−
2
1
)
3
+4×(−
2
1
)
2
−(
2
−1
)−1
=4×(−
8
1
)+4×
4
1
+
2
1
−1
=(−
2
1
+1+
2
1
−1)=0
so, when p(x) is divided by (2x+1),the reminder is 0.This shows that (2x+1) is a factor of p(x).
Hence, p(x) is multiple of (2x+1)
I hope it's help you
Similar questions