Factoring Trinomials with a = 1 – Practice Problems

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Before you factor a trinomial, a polynomial with only three terms, write it in the standard form of ax² + bx + c. Then, take a look at the leading coefficient. If the leading coefficient, the coefficient to a, is equal to one, you can use the reverse FOIL method to factor the trinomial as two binomials: (x + m)(x + n) which is equal to x² + nx + mx + mn and the same as x² + x(m + n) + mn. Compare this polynomial to the standard form: ax² + bx + c, and you can see the sum of m and n is equal to b and the product of m and n is equal to c.

To figure out how to write the binomial pair, list the factors of c. Most likely the list is not that long. Next, determine which pair of factors will sum to b, and then use the two factors to write the two binomials: (x + m)(x + n). Always use FOIL to verify your answer because it’s easy to make careless mistakes, especially when negative numbers are used.

To help you understand this process, and make it easy for you to factor trinomials with the leading coefficient equal to one, sit back, relax, and enjoy watching this video - while you learn at the same time.

Understand the relationship between zeros and factors of polynomials.

CCSS.MATH.CONTENT.HSA.APR.B.2

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Exercises in this Practice Problem
Explain how Johnny Redbeard can factor the trinomial $x^2+6x-27$.
Find all possible factors of $-27$ and add them together to identify $m$ and $n$.
Assign each polynomial to its corresponding factorization.
Factor the given polynomials in order to open the treasure chests.
Describe the FOIL method for multiplying binomials.
Write each trinomial as a product of two binomials by factoring.