Common factor in quadratic polynomials $x^{2} + 8 x + 15$ and $x^{2} + 3 x - 10$ is

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Solution

Given $x^{2} + 8 x + 15$
$= x^{2} + 5 x + 3 x + 15$
$= x (x + 5) + 3 (x + 5)$
$= (x + 5) (x + 3)$
Similar way, $x^{2} + 3 x - 10$
$= x^{2} + (5 - 2) x - 10$
$= x^{2} + 5 x - 2 x - 10$
$= x (x + 5) - 2 (x + 5)$
$= (x + 5) (x - 2)$
Hence, the common factor in quadratic polynomials $x^{2} + 8 x + 15$ and $x^{2} + 3 x - 10$ is $(x + 5) .$

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Common factor in quadratic polynomials x2+8x+15 and x2+3x−10 is

Given x2+8x+15=x2+5x+3x+15 =x(x+5)+3(x+5)=(x+5)(x+3)Similar way, x2+3x−10=x2+(5−2)x−10=x2+5x−2x−10=x(x+5)−2(x+5)=(x+5)(x−2)Hence, the common factor in quadratic polynomials x2+8x+15 and x2+3x−10 is (x+5).

Common factor in quadratic polynomials $x^{2} + 8 x + 15$ and $x^{2} + 3 x - 10$ is