# How do you write w^2+18w+77 in factored form?

Sep 17, 2015

color(blue)((w+7)(w+11) is the factorised form of the expression.

#### Explanation:

${w}^{2} + 18 w + 77$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {w}^{2} + b w + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 77 = 77$
AND
${N}_{1} + {N}_{2} = b = 18$

After trying out a few numbers we get ${N}_{1} = 7$ and ${N}_{2} = 11$
$11 \cdot 7 = 77$, and $11 + 7 = 18$

${w}^{2} + 18 w + 77 = {w}^{2} + 11 w + 7 w + 77$

${w}^{2} + 11 w + 7 w + 77 = w \left(w + 11\right) + 7 \left(w + 11\right)$

=color(blue)((w+7)(w+11)

Sep 17, 2015

Factor ${w}^{2} + 18 w + 77$

Ans: y = (w + 7)(w + 11)

#### Explanation:

I use the new AC Method (Socratic Search) that is simpler and that avoids the lengthy factoring by grouping.
y = w^2 + 18w + 77 = (w + p)(w + q).
The 2 numbers p and q have same sign. Compose factor pairs of 77.--> (1, 77)(7, 11). This sum is 18 = b. Then, p = 1 and q = 77.
Factored form y = (w + 7)(w + 11)