How do you factor completely: #5x^2 − 2x − 7#?

1 Answer
Jul 20, 2015

Answer:

#5x^2-2x-7=(5x-7)(x+1)#

Explanation:

#5x^2-2x-7# is a quadratic equation in the form #ax^2+bx+c#, in which #a=5, b=-2, and c=-7#.

This equation can be factored by the #a*c# method, also called splitting the middle, or factoring by grouping.

Multiply #a# times #c#.

#5*-7=-35#

Find two numbers that when multiplied equal #-35#, and when added equal the coefficient of the center term, #b=-2#.

The numbers #5# and #-7# meet the criteria.

Rewrite the equation, replacing #-2x# with the sum of #5x# and #-7x#.

#5x^2+5x-7x-7#

Group into two binomials.

#(5x^2+5x)-(7x-7)# =

Factor out the GCF from each group.

#5x(x+1)-7(x+1)#

Factor out the common term #(x+1)#.

#(5x-7)(x+1)#