Question

If x^2-x-6 and x^2+3x-18 hacpve a common factor (x-a) then find the value of a.​

Answer 1

Q. 1) x^2 - x - 6. And 2) x^2 + 3x - 18

Factorise the two expressions
And u get

1) (x-3) (x+2). And 2) (x+6) (x-3)

Common factor is (x-3) so a= -3

Answer 2

a = 3

Explanation:

Factor both expressions

x² - x - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)

The factors are - 3 and + 2 , since

- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus

x² - x - 6 = (x - 3)(x + 2)

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x² + 3x - 18

consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)

The factors are + 6 and - 3 , since

6 × - 3 = - 18 and 6 - 3 = + 3 , thus

x² + 3x - 18 = (x + 6)(x - 3)

Both expressions have a common factor of (x - 3)

Compare with (x - a ), then a = 3