# Verify (2x-3) is factor of the polynomial 2x³-9x²+x+12

2
by Deleted account

2015-09-30T16:26:14+05:30

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We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12

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.
2015-09-30T16:44:03+05:30

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x^2 - 3x - 4

2x-3 divided  2x^3 - 9x^2 + x + 12
2x^3 - 3x^2
-        +
________________
-6x^2 + x
-6x^2 + 9x
+       -
________________
- 8x + 12
-8x + 12
+        -
______________________
0

therefore, its a factor of given equation

^ means exponent power
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