2x-3 divided by x+2x³-9x²+12. can someone pls tell this-with steps. wrong answer wil be reported
Answers
Answer:
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).
Answer:
hope it will help you
Step-by-step explanation:
First equate 2x-3 to 0 and find value of x.
2x - 3 = 0
⇒ 2x = 3
⇒ x = 3/2
If x=3/2 is a root of the polynomial, then (2x-3) is a factor.
at x=3/2, value of polynomial is
2(3/2)³ - 9(3/2)² + 3/2 + 12
= 2×(27/8) - 9×(9/4) + 3/2 + 12
= 27/4 - 81/4 + 3/2 + 12
= (27 - 81 + 6 + 48)/4
= (81-81)/4
= 0
So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.