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

2 Answers
Sep 17, 2015

Answer:

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

Explanation:

#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 #aw^2 + bw + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 1*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*7 =77#, and #11+7= 18#

#w^2+18w+77 = w^2+11w +7w+77#

#w^2+11w +7w+77 = w(w+11) + 7(w+11)#

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

Sep 17, 2015

Answer:

Factor #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)