How do you factor $f (x) = x^{2} + 8 x + 16$ $f(x)=x^2+8x+16$ ?

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Answer 1 · 2018-06-27T18:39:41

${(x + 4)}^{2}$ $(x+4)^2$

We need a pair of numbers that add to make $8$ $8$ and multiply to make $16$ $16$ :

List the factors of $16$ $16$ :

$16 and 1$ $16 and 1$

$\Rightarrow 16 + 1 = 17$ $rArr 16+1=17$

$8 and 2$ $8 and 2$

$\Rightarrow 8 + 2 = 10$ $rArr 8+2=10$

$4 and 4$ $4 and 4$

$\Rightarrow 4 + 4 = 8$ $rArr 4+4=8$

$therefore$ we place these in brackets:

$rArr (x+4)(x+4)$

Which can be written as:

$(x+4)^2$

How do you factor f(x)=x^2+8x+16f(x)=x2+8x+16f(x)=x^2+8x+16?