How do you factor $x^{3} + 11 x^{2} + 28 x$ $x^3 + 11x^2 + 28x$ ?

Question

3389 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-17T11:24:22

$x^{3} + 11 x^{2} + 28 x = x (x^{2} + 11 x + 28) = x (x + 7) (x + 4)$ $x^3+11x^2+28x = x(x^2+11x+28) = x(x+7)(x+4)$

First identify the greatest common factor of all the terms, which is $x$ $x$ and separate that out as a factor:

$x^{3} + 11 x^{2} + 28 x = x (x^{2} + 11 x + 28)$ $x^3+11x^2+28x = x(x^2+11x+28)$

The remaining quadratic factor must have factors of the form:

$(x + a)$ $(x+a)$ , $(x + b)$ $(x+b)$ , with $a + b = 11$ $a+b = 11$ and $a \cdot b = 28$ $a * b = 28$ ,

since $(x + a) (x + b) = x^{2} + (a + b) x + a b$ $(x+a)(x+b) = x^2+(a+b)x+ab$

The pair $7, 4$ $7, 4$ works.

Hence:

$x^{2} + 11 x + 28 = (x + 7) (x + 4)$ $x^2+11x+28 = (x+7)(x+4)$

and

$x^{3} + 11 x^{2} + 28 x = x (x^{2} + 11 x + 28) = x (x + 7) (x + 4)$ $x^3+11x^2+28x = x(x^2+11x+28) = x(x+7)(x+4)$

How do you factor x^3 + 11x^2 + 28xx3+11x2+28xx^3 + 11x^2 + 28x?