9-4 Factoring Trinomials ax2 + bx + c

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Presentation transcript:

9-4 Factoring Trinomials ax2 + bx + c Objective #1: Factor trinomials of the form ax2 + bx + c (2x + 3)(x + 2) = **To factor quadratic trinomials of the form ax2 + bx + c, find two integers, m and n, whose sum is equal to b and whose product is equal to ac. Then use factoring by grouping to write in factored form. Ex 1: Factor ax2 + bx + c a) Factor 5x2 + 27x + 10 Identify a, b, and c Factors of 50 Sum Make an organized list of factors of 50 5x2 + 27x + 10 = 5x2 + mx + nx + 10 b) Factor 24x2 - 22x + 3 Factors of 72 Sum Make an organized list of factors of 72 24x2 - 22x + 3 = 24x2 + mx + nx + 3

Factor out the GCF using the DP Ex 2: Factor when a, b, and c have a common factor. Factor 4x2 + 24x + 32 Find the GCF of 4, 24, 32 Factor out the GCF using the DP STUDY TIP: Always check for a GCF before factoring a trinomial!!

Prime Polynomial--A polynomial that cannot be written as a product of two polynomials with integer coefficients. Ex 3: Determine whether a polynomial is prime Factor 3x2 + 7x - 5 GCF? Identify a, b, and c Factors of -15 Sum Make an organized list of factors of -15 STUDY TIP: Make sure you list all possible factors of mn, including positive and negative factors, before you decide if it's prime.

Objective #2: Solve equations of the form ax2 + bx + c = 0 Ex 4: Solve an equation by factoring Solve 18x2 - 19x - 8 = 3x2 - 5x Write in ax2 + bx + c = 0 form Factor left side Zero Product Property Solve each equation