Factor the trinomial completely. $$2 x ^ { 2 } + 9 x + 4$$
A) $( 2 x + 1 ) ( x + 4 )$
B) $( 2 x - 1 ) ( x - 4 )$
C) $( 2 x + 2 ) ( x + 4 )$
D) $( x + 1 ) ( 2 x + 4 )$
E)not factorable

Question

Quizplus · Accepted Answer

To factor the trinomial, we need to find two binomials whose product gives us the original trinomial. We can start by thinking about which two binomials have 2x as their leading term, since that is the highest power of x in the trinomial. The two binomials with 2x as their leading term are (2x + ?) and (x + ?). We need to find the numbers to go in the blanks so that when we multiply the two binomials, we get 2x^2 + 9x + 4. We can find these numbers by thinking about the last term of the trinomial and looking for two numbers that multiply to 4. The only two numbers that multiply to 4 are 4 and 1 (or -4 and -1). Now we just need to figure out which combination of signs gives us the middle term of the trinomial, which is 9x. We can see that (2x + 1)(x + 4) gives us 2x^2 + 9x + 4 when we expand it using FOIL, so that is our answer.

Factor the Trinomial Completely 2x2+9x+42 x ^ { 2 } + 9 x + 42x2+9x+4

Factor the Trinomial Completely $2 x ^ { 2 } + 9 x + 4$