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Given the polynomial function .
MATHEMATICS · Multi-part · AoPS · Mathematics · Polynomials · Polynomials
Problem
Given the polynomial function
f
(
x
)
=
3
x
3
−
5
x
2
+
2
x
−
7
f(x)=3x^{3}-5x^{2}+2x-7
f
(
x
)
=
3
x
3
−
5
x
2
+
2
x
−
7
. (a) Calculate
f
(
−
2
)
f(-2)
f
(
−
2
)
and
f
(
1
2
)
f\!\left(\dfrac{1}{2}\right)
f
(
2
1
)
. (b) Using the results from part (a), find the value of
f
(
−
2
)
−
2
f
(
1
2
)
f(-2)-2f\!\left(\dfrac{1}{2}\right)
f
(
−
2
)
−
2
f
(
2
1
)
. (c) Verify whether
x
=
−
2
x=-2
x
=
−
2
is a zero of the function
f
f
f
. Show complete working.
Related theory
Polynomials
Algebraic expansions
Algebra
Zeroes of a polynomial
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