Factor each trinomial, if it cannot be factored, write prime.
2q²-9q-18 2*-18=36
2q²-3a-12a-18 1, -36
2, -18
3, -12
I can't get the rest of this problem,
thanks.
To factor the trinomial 2q²-9q-18, we can use the method of factoring by grouping.
Step 1: Multiply the coefficient of the quadratic term by the constant term. In this case, 2 * -18 = -36.
Step 2: Find two numbers that multiply to give the result from step 1 (-36), and add up to give the coefficient of the linear term (-9). In this case, the numbers are -12 and 3, because -12 * 3 = -36 and -12 + 3 = -9.
Step 3: Rewrite the middle term (-9q) as the sum of the two numbers found in step 2. This gives us: 2q² - 12q + 3q - 18.
Step 4: Group the terms together based on the two pairs obtained in step 3. We have: (2q² - 12q) + (3q - 18).
Step 5: Factor out the greatest common factor (GCF) from each group. In the first group, the GCF is 2q, and in the second group, the GCF is 3. Factoring them out, we get: 2q(q - 6) + 3(q - 6).
Step 6: Notice that we now have a common binomial factor, (q - 6), in both groups. Factor it out to obtain the final factored form: (2q + 3)(q - 6).
Therefore, the factored form of the trinomial 2q² - 9q - 18 is (2q + 3)(q - 6).