How do you write $w^{2} + 18 w + 77$ $w^2+18w+77$ in factored form?

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How do you write $w^{2} + 18 w + 77$ $w^2+18w+77$ in factored form?

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Answer 1 · 2015-09-17T16:49:39

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

Explanation:

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

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

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

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 77 = 77$ $N_1*N_2 = a*c = 1*77 =77$
AND
$N_{1} + N_{2} = b = 18$ $N_1 +N_2 = b = 18$

After trying out a few numbers we get $N_{1} = 7$ $N_1 = 7$ and $N_{2} = 11$ $N_2 =11$
$11 \cdot 7 = 77$ $11*7 =77$ , and $11 + 7 = 18$ $11+7= 18$

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

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

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

Answer 2 · 2015-09-17T18:23:49

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

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)

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How do you write $w^{2} + 18 w + 77$ $w^2+18w+77$ in factored form?

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How do you write w2+18w+77w^2+18w+77 in factored form?

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How do you write $w^{2} + 18 w + 77$ $w^2+18w+77$ in factored form?