Question

Factor the trinomial: 2x2 + 7x + 3
A. (2x - 1)(2x + 3)
B. (2x + 3)(x + 1)
C. (2x + 1)(x + 3)
D. (2x + 1)(2x + 3)

Answer 1

C

Answer 2

Explain. You can't just give the answer like that

There's two ways you could figure this out;
1) solve each of the factors
2) factor the trinomial normally

Answer 3

First one:
find two numbers which add up to 7 and multiply to make 6. Those are 6 and 1
Replace the middle term by those numbers:
2x^2 + (6 + 1)x + 3 = 0
2x^2 + 6x + x + 3 = 0
Now factor the two groups:
2x(x+3) + (x+3) = 0
Your factored equation is: (2x + 1)(x + 3) = 0 with solutions x=-1/2 and x=-3

For the second:
Move the right hand side to the left and simplify. You'll get:
6d^2 + 11d - 35 = 0
Now we need 2 numbers which add up to 11 and multiply to make -210. Those are 21 and -10. Now do the same steps as before:
6d^2 + (21 - 10)d - 35 = 0
6d^2 + 21d - 10d - 35 = 0
3d(2d + 7) - 5(2d + 7) = 0
Final equation: (3d - 5)(2d + 7) = 0
Solutions: d = 5/3 or -7/2

Answer 4

(2x + 1)(x + 3)
= 2x^2 + 6x +1x +3
=2x^2 + 7x + 3
DONE.