If P(x) = 2x^3-9x^2+x+12. Find P(2)
Answers
Answered by
1
The factor theorem states that a polynomial f(x) has a factor (x−a) if and only if f(a)=0
Let p(x)=x+2x
3
−9x
2
+12 and g(x)=2x−3
g(x)=2x−3=0 gives x=
2
3
g(x) will be factor of p(x) if p(
2
3
)=0 (Factor theorem)
Now, p(
2
3
)=
2
3
+2(
2
3
)
3
−9(
2
3
)
2
+12=
2
3
+2(
8
27
)−9(
4
9
)+12
=
2
3
+
4
27
−
4
81
+12=
4
6+27−81+48
=
4
0
=0
Since, p(
2
3
)=0, so g(x) is a factor of p(x).
p = 3/2
Hope it helps you ☺️❤️
Answered by
1
Answer:
P(2) = -6
Step-by-step explanation:
Given
P(x) = 2x^3-9x^2+x+12
Now P(2)
P(2) = 2(2)^3-9(2)^2+2+12
P(2) = 2(8)-9(4)+2+12
P(2) = 16-36+2+12
P(2) = 30-36
P(2) = -6
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