How do you factor the expression $x^{2} + 5 x + 4$ $x^2 + 5x + 4$ ?

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Answer 1 · 2016-04-26T21:15:26

$x^{2} + 5 x + 4 = (x + 4) (x + 1)$ $x^2+5x+4 = (x+4)(x+1)$

Find a pair of factors of $4$ $4$ with sum $5$ $5$ .

The pair $4, 1$ $4, 1$ works.

Hence:

$x^{2} + 5 x + 4 = (x + 4) (x + 1)$ $x^2+5x+4 = (x+4)(x+1)$

In general note that:

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

So if you are given a polynomial to factor in the form:

$x^{2} + p x + q$ $x^2+px+q$

then you can try finding a pair of factors of $q$ $q$ with sum $p$ $p$ .

If you can find $a, b$ $a, b$ such that $a + b = p$ $a+b = p$ and $a b = q$ $ab = q$ , then:

$x^{2} + p x + q = (x + a) (x + b)$ $x^2+px+q = (x+a)(x+b)$

How do you factor the expression x2+5x+4x^2 + 5x + 4?