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 − 9xy + 14y²

Accepted Answer

Perform factories ation and they give an expression or categorize it as a prime time, Amiel also perform a check using the foil method where we have the expression H squared -17 Hk plus 66 K sq. Now we notice we have a coefficient of one R H squared. We can then break this down into a product rather of two factors H plus A K and H plus B K or we define A and B. Now we know a plus B will be equal to the coefficient of our middle term -17. Let's go ahead and find eight times. Now A is the coefficient on our first term, what B is the coefficient on our final term? 66, We get 66. Now I want to find the factors of 66 and see which two will add up to negative all foot 66. We have 1 66 negative 1 2, 33 negative two And -33. That's a -66. There. Finally, we have two more three and 22 negative three, negative And 11 6, -11 -6. They want to add these together and see which one is equal to negative 17. Here we get 67, negative 67 35 negative 35 25 negative 17 and negative 17. We then notice that we have negative 11 and negative six adding up to negative 17, you're gonna rewrite are factors as H Plus eight of 11. So we have H -11. Okay & H -6 K, we can't simplify anymore. So let's check this to make sure using the foil method. That is correct. So we will take eight minus 11 K multiply it with H minus six K. First multiply our first terms h times h gives us eight squared. Then we have the outside terms H times negative six K, it's minus six HK Native 11 K Times H is native 11 HK. Finally night 11 times native six, both with K plus 66 K square. Simplify them. Get X squared minus 17 HK plus 66 K squared, which corresponds to our original function. We can then tell that our answer H minus 11 K times H minus six K corresponds to answer A. 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 − 9xy + 14y²

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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