Log in to add a comment

## Answers

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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

=

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**.

The Brainliest Answer!

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

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

wer

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

wer