How do you factor the expression #10x^2-3x-1 #?

2 Answers
Dec 13, 2015

Answer:

#(5x+1)(2x-1)#

Explanation:

Look for a pair of numbers whose PRODUCT is the product of the first and last numbers #(-10)# and sum is the middle number #(-3)#.

The two numbers that meet these criteria are #-5# and #2#.

Rewrite the #-3x# term in the expression as #-5x+2x#.

#10x^2-5x+2x-1#

Factor by grouping.

#(10x^2-5x)+(2x-1)#

#5x(2x-1)+1(2x-1)#

#(5x+1)(2x-1)#

Dec 13, 2015

Answer:

Split the middle term (-3x) into two separate terms . Then, use grouping to complete the factoring.

Explanation:

Split the middle term into two separate terms so that the sum is still #-3# however, you want the product of the two new terms to equal #(10)(-1)=-10#. For this problem use #2# and #-5#

Here is the new expression ...

#10x^2+2x-5x-1#

Use grouping ...

#(10x^2+2x)-(5x+1)#

#2x(5x+1)-(5x+1)#

#(2x-1)(5x+1)#

hope that helped