Question

Common factor in a quadratic polynomial x 2 +8x+15 and x 2 +3x-10 is ?/

Answer 1

x 2 +8x+15 and x 2 +3x-10 = x 2 +8x+15 = x^2+5x+3x+15= x(x+5)+3(x+5) = (x+5)(x+3) ,.....eq 1 = x^2+3x-10= x^2+5x-2x-10= x(x+5)-2(x+5) = (x-2)(x+5) Common factor is (x+5)

Answer 2

Given,

Two quadratic equations x²+8x+15 and x²+3x-10.

To find,

The common factor of two equations

Solution,

• Splitting the middle term of the equation  x²+8x+15 we get,

     ⇒  x²+8x+15

     ⇒  x²+3x+5x+15

Taking x common in  x² and 3x and 5 common in 5x + 15,

    ⇒  x(x+3) + 5(x+3)

    ⇒  (x+3)(x+5)

So x+3 and x+5 are factors of equation x²+8x+15.

• Now, we have to find the common factors of equation x²+3x-10,

    ⇒  x²+3x-10

    ⇒  x²+5x-2x+10

Taking x common in  x² and 5x, and 2common in  -2x and 10.

    ⇒ x(x+5) -2(x+5)

    ⇒  (x-2)(x+5)

So x-2 and x+5 are factors of equation x²+3x-10.

So (x+5) is a common factor in two quadratic equations x²+8x+15 and x²+3x-10.