If (x + 2) and (3x - 1) are factors of 6x³ + x² - 19x + 6, find the third factor.

Correct Answer is : 2x−32x - 32x−3

Correct Answer is : 2x−32x - 32x−3

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WAEC Further Mathematics 2014 Paper

Question : 9

Total: 40

(x + 2)

(3x - 1)

6x^{3} + x^{2} - 19x + 6

, find the third factor.

Solution:

Concept:

If two factors of a polynomial are known, divide the polynomial by their product to obtain the third factor.

Explanation:

First find the product of the two given factors:

(x+2)(3x-1) = 3x^{2} + 5x - 2

Now divide

6x^{3} + x^{2} - 19x + 6

3x^{2} + 5x - 2

First term:

6x^{3} \div 3x^{2} = 2x

Multiply:

2x(3x^{2} + 5x - 2) = 6x^{3} + 10x^{2} - 4x

Subtract:

(6x^{3} + x^{2} - 19x + 6) - (6x^{3} + 10x^{2} - 4x) = -9x^{2} - 15x + 6

Next term:

-9x^{2} \div 3x^{2} = -3

Multiply:

-3(3x^{2} + 5x - 2) = -9x^{2} - 15x + 6

Subtract:

-9x^{2} - 15x + 6 - (-9x^{2} - 15x + 6) = 0

So the quotient is

2x - 3

Answer:

The third factor is

2x - 3

Correct option: A.

2x - 3

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