I need to factor this trinomial,
but I can't figure it out.
2q²-9q-18
Please put the class not the grade in the Subject area.
Ahh, sorry, it's ninth grade math.
To factor the trinomial 2q² - 9q - 18, we can use the method known as "Factor by Grouping." This method involves breaking up the middle term, -9q, into two terms whose coefficients multiply to give -36 (the product of the coefficient of the quadratic term, 2, and the constant term, -18), and whose sum is equal to the coefficient of the linear term, -9.
Step 1: Multiply the coefficient of the quadratic term, 2, by the constant term, -18. The product is -36.
Step 2: Find two numbers whose product is -36 and whose sum is -9. In this case, the numbers are -12 and 3, since (-12) * 3 = -36 and (-12) + 3 = -9.
Step 3: Rewrite the middle term -9q as the sum of -12q and 3q:
2q² - 12q + 3q - 18
Step 4: Group the terms and factor by grouping:
(2q² - 12q) + (3q - 18)
Step 5: Factor out the greatest common factor from each group:
2q(q - 6) + 3(q - 6)
Step 6: Notice that (q - 6) is common to both terms. Factor it out:
(q - 6)(2q + 3)
Therefore, the factored form of the trinomial 2q² - 9q - 18 is (q - 6)(2q + 3).