Question

if x square -x-6 and x square+3x-18 have a common factor (x-a) then find the value of a​

Answer 1

Answer:

Value of a: (3)

Step-by-step explanation:

Step 1: Factorise x²-x-6:

⇒x²-x-6

= x²-3x+2x-6

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

= (x+2)(x-3)

Step 2: Factorise x²+3x+18:

⇒ x²+3x+18

= x²+6x-3x-18

= x(x+6)-3(x+6)

=(x+6)(x-3)

Step 3: Identify common factors between the factors of the two polynomials:

The common factor is (x-3)

Step 4: Equate:

x-a = x-3

-a = -3

a=3.

Hence a=3.

Hope this helps!