QuestionFactor the trinomial.
Suggested tutorial: Learn ... Factor trinomials ...
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STEP 1
What is this asking?
We need to rewrite the trinomial as a product of simpler expressions.
Watch out!
The order of terms can be tricky!
Don't let it fool you.
Rearranging might make things clearer.
STEP 2
1. Rearrange the trinomial
2. Find the factors
3. Verify the factorization
STEP 3
Let's rearrange the trinomial in descending powers of to make it look more familiar.
This gives us .
This way, it looks more like the trinomials we're used to factoring!
STEP 4
Notice that we can think of as a quadratic in .
Let's think of as a single variable, say .
So, we have .
STEP 5
Now, we're looking for two numbers that multiply to **50** and add up to **15**.
Those numbers are **5** and **10**!
So, we can factor the quadratic as .
STEP 6
Remember, was standing in for .
So, substituting back, we get .
STEP 7
Let's double-check our work by expanding .
Using the distributive property (also known as FOIL), we get:
STEP 8
This matches our original (rearranged) trinomial, so we're good to go!
STEP 9
The factored form of the trinomial is .
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