I need to factor this trinomial,
but I can't figure it out.
2q²-9q-18
(2q+3)(q-6) , i just think of it was you know the 2q and q because of 2q^2. and you know the last two have to multiply to be 18
3 * 6 = 18
2 * 6 = 12
12 - 3 = 9
This can lead you to John's answer.
To factor the trinomial 2q² - 9q - 18, follow these steps:
Step 1: Make sure the trinomial is in standard form, with the highest power of the variable (in this case, q) as the first term.
Step 2: Look for two numbers that multiply to give the product of the first and last terms (2q² * -18) and add up to the coefficient of the middle term (-9q). In this case, the product is -36q², and we need to find two numbers that add up to -9q.
Step 3: Write down all the factor pairs of the product from step 2. In this case, the factor pairs of -36q² are:
-1q and 36q
1q and -36q
-2q and 18q
2q and -18q
-3q and 12q
3q and -12q
-4q and 9q
4q and -9q
-6q and 6q
Step 4: Determine which factor pair from step 3 adds up to the coefficient of the middle term (-9q). In this case, the factor pair -6q and 6q adds up to -9q.
Step 5: Rewrite the middle term (-9q) using the factor pair from step 4. In this case, -6q and 6q represent the factor pair, so -9q can be rewritten as -6q + 6q.
Step 6: Group the terms in pairs and factor by grouping.
2q² - 6q + 6q - 18
Step 7: Factor out the greatest common factor from each pair of terms.
2q(q - 3) + 6(q - 3)
Step 8: Factor out the common binomial factor from the resulting expression.
(q - 3)(2q + 6)
Hence, the factored form of the trinomial 2q² - 9q - 18 is (q - 3)(2q + 6).