Factor completely write as product of two linear terms

Question

Factor completely 49x²+28x+4 write as product of two linear terms

Answer 1

When we're factoring, a good trick to use is to look for numbers that "multiply to c, add to b", where b and c are the coefficients in the standard form ax²+bx+c. It gets just slightly trickier when we have a coefficient for a as well, but not by much.

I like to start by writing out the two parenthesis that will hold my linear terms: ( )( )

Then, if I don't want to use the quadratic formula or anything like that, it's often quickest to just guess and check. Since the first terms have to multiply to 49x², I'm guessing they're probably 7x and 7x.

(7x )(7x )

The last terms have to multiply to 4, so I'm going to guess +2 and +2. Then I'll check with FOIL method (First, Outside, Inside, Last) to see if I get +28x as my middle term.

(7x+2)(7x+2) = 49x²+14x+14x+4 = 49x²+28x+4

It worked! So my factoring is done.

Answer 2

It the Binomial squared !!!

(7x + 2)(7x + 2)