Identify four common factors of 2x^2+4x

Question

Choose the correct answer below.

(a) 1, 2, 2x, 2x^2

(b) 2 ,2x, 4x, x^2

(c) 2, x ,2x, x^2

(d) 1, 2, x, 2x

Answer 1

A common factor is an expression which will divide evenly into each term of  the original expression.

Original:  2x² + 4x

Look at answer (a). Can 1 divide into each term?  Yes

                             Can 2 divide into each term? Yes, 2(x² + 2x)

                             Can 2x divide into each term?  Yes, 2x(x + 2)

                             Can 2x² divide into each term? NO.

Look at answer (b). We know that 2 and 2x can divide into each term.

                             Can 4x divide into eacn term? NO.

Look at answer (c). We know that 2 and 2x can divide into each term.

                             Can x divide into each term? Yes, x(2x + 4)

                             Can x² divide into each term? NO.

Look at answer (d). We already know from (a), (b), and (c), that 1, 2, x, and 2x can divide into each term.

                             All four are common factors.