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.a² − 18ab + 45b²

Accepted Answer

Perform factory ization in the given expression or categorize it as a prime trim Amiel also perform a check using the foil method where our equation Q squared minus 24 PQ plus 1, 19 P squared can be written as a product of two different factors Q plus A P times Q plus BP. Now we want to find what are A and B are, we know based on our quadratic six that A plus B will equal. Our middle term Are -24. Let's go ahead and find a be super confined factors that will add up to A B R A is a number on our Q square. That coefficient is just one coefficient on the P squared is in 1 19. So A B is 1 19, not one to find two factors that will add up to negative 24 of 19. Well, 1 19 has factors one times 1, 19, negative, one times negative 1, 19, seven times 17 and negative seven times negative 17. We want to factors that will add up to negative 24. If we notice We will have negative -17, equal negative 24, we can then rewrite our factored form. We have Q minus seven P times Q minus 17 P. These are factors. Let's go and check to make sure that these are correct. Well, we foil, which means we will take these two factors and multiply them together. Q times Q gives us Q squared as our first, our outer Q times like the 17 P is minus 17 P Q, there are seven P times Q is minus seven P Q. And finally 97 P times 9 to 17 P is plus 19 P square. We get Q squared minus 24 PQ plus 19 P squared. After simplifying, which means I answer to our problem for response with 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.a² − 18ab + 45b²

Key Concepts

Factoring Trinomials

Prime Trinomials

FOIL Method

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