How do you factor #-3a - 18+ a ^ { 2}#?

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Answer 1 · 2018-03-19T12:35:31

#color(green)(-3a - 18+ a ^ { 2}=(a-6)(a+3)#

Given:
#-3a - 18+ a ^ { 2}#

We must factor this quadratic expression.

Rewrite the given expression as:

#a ^ { 2}-3a - 18 " "# Expression.1

Split the middle term as : #color(blue)(-6, 3)#

Procedure used for splitting the middle term:

When we multiply #-6# and #3#, we get #-18# (this is equal to the the product of coefficient of #a^2# term and the constant.)

When we add #-6# and #3#, we get #-3# (This is equal to the coefficient of the middle term)

Hence, we can rewrite Expression.1 as

#a ^ { 2}-6a +3a- 18 " "#

#rArr a(a-6)+3(a-6)#

#rArr (a-6)(a+3)#

Hence,

#color(green)(-3a - 18+ a ^ { 2}=(a-6)(a+3)#

Hope it helps.