Question

without actual division,prove that (x-2) is a factor of the polynomial 3x^3-13x^2+8x+12.Also factorise it completely​

Answer 1

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Answer 2

Answer:

If (x-2) is a factor of p(x)

p(x) = 0

p(2) = 3x^3 - 13x^2 + 8x + 12

3(2)^3 - 13(2)^2 + 8(2) + 12

3 x 8 - 13 x 4 + 16 + 12

24 - 52 + 16 + 12

52 - 52 = 0

Hence, (x-2) is a factor of p(x)

x-2 ) 3x^3 - 13x^2 + 8x + 12( 3x^2 -7x^2 - 6

3x^3 - 6x^2

(-) (+)

-----------------------------------------

- 7x^2 + 8x + 12

- 7x^2 + 14x

(+) (-)

-----------------------------------------

-6x + 12

-6x + 12

(+) (-)

-----------------------------------------

0

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Step-by-step explanation:

Now, (x-2) (3x^2 - 7x - 6)

(x-2) {3x^2 - ( 9 - 2 ) x - 6}

(x-2) { 3x^2 -9x + 2x - 6}

(x-2) {3x (x- 3) + 2 ( x - 3 )}

(x-2) (3x+2) (x - 3)