Can you help me factor the trinomials step by step in this problem?
12q ² + 34 q - 28
Here's another method that you can use to factor some quadratic trinomials of the form
ax
2 + bx + c
Note that after removing a common factor of 2, as JeffM did in his approach, you have 2(6q
2 + 17q - 14)
What is inside the parentheses is a quadratic trinomial of this form:
ax
2 + bx + c
6q
2 + 17q - 14
Step 1: multiply a*c. 6*(-14) is -84
Step 2: look for two factors of this product (-84) which add up to "b" in the original expression, which in this case is +17
-4*21 = -84, and -4 + 21 = +17
Step 3: Use the numbers you found in step 2 to rewrite the middle term. We'll rewrite +17q as -4q + 21q:
6q
2 - 4q + 21q - 14
Step 4: Factor by grouping the first two terms together and the last two terms together, and then remove a common factor from each group:
(6q
2 - 4q) + (21q - 14)
2q (3q - 2) + 7 (3q - 2)
Now, (3q - 2) is a common factor. Remove it, and you have
(3q - 2)(2q + 7)
remember that you originally removed a common factor of 2; this needs to be included in the "final answer":
2 (3q - 2)(2q + 7)