In Exercises 1–30, factor each trinomial, or state that the trino...

Question

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.

x² − xy − 30y²

Accepted Answer

Perform factory ization in the given expression or categorize it as a prime time. Um You'll also perform a check using the foil method where we have our polynomial is Q squared minus 10 P Q -39 P sq. Now we notice here, the coefficient on our Q squared is one, we can then break down into two factors Q plus A P times Q plus B P. Now we need to solve for A and B. Well, we know A plus B will be equal to the coefficient of our middle term. In this case, that coefficient is -10. To find this, we're gonna multiply a and b together and find two factors of that number that will add up to be negative 10. So A which is the coefficient on our Q squared as one B is the coefficient on RP Squared which is -39. So when they find the factors of -39, We can say we have one 39, 1 of them is negative the other one negative. So one negative 39 we have three and 13, 3, negative 13, negative three positive 13. Now we want these two factors to some of them to equal negative tent. Let's add these together. Negative 1 39 gives us 1 -39, negative 38 three, negative 13, negative 10, negative three and positive 13 is 10. We see here, we wanna look at three and -13. We can then replace our A and B with our numbers. Now Q-plus three Q -13 p, we can't factor this anymore. So we can see that these are two factors corresponding to answer C. But let's check the foil method just to be safe. Foil method states that we can multiply both of these factors together by multiplying our first terms first. So Q times Q Q squared multiplying our outside terms. So Q times negative 13 P, that's negative 13 P Q three P times Q gives us plus three P Q finally three P times negative 13 P negative 39 P can then simplify to get Q squared minus 10 P Q minus 39 P squared, which corresponds to our original function. That makes sense to our problem as answers. See? Okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² − xy − 30y²

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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