Question

examine if 2x-3 is factor of 2x³-9x²+x+12.

Answer 1

Heya HERE is your answer

2x-3)2x³ - 9x² +x +12( x²-6x
2x³ - 3x²
- 12x² +x
-12x² +18x
19x +12

No its not a factor

Answer 2

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.

HOPE IT HELPS YOU.
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