Factoring Trinomials x2 + bx + c

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Presentation transcript:

Factoring Trinomials x2 + bx + c

Objectives Students will learn how to factor trinomials with the following pattern: x2 + bx + c

What does a factored trinomial look like? What are the factors of 27 that add to give you 12? 1 + 27 = 28 3 + 9 = 12 (x )(x ) + 3 + 9 Look at the trinomial. Are the signs positive, negative or both positive and negative. For example: x2 + 12x + 27 Both signs are positive meaning you are looking for factors of 27 that add to give you 12—the number in the middle. With no coefficient (the number in front of the variable x2 (the letter), it’s pretty easy to figure out.

Factor x2 +14x + 45 What are the factors of 45 that add to give you 14? 1 + 45 = 46 3 + 15 = 18 5 + 9 = 14 14 + 9 5 45 Format of factored trinomial is: (x + 5)(x + 9)

Trinomials—Let’s try this out! Tri meaning three referring to the number of terms Examples:

What does a factored trinomial look like? What are the factors of 21 that add to give you 22? 1 + 21 = 22 3 + 7 = 10 (x )(x ) + 1 + 21 Look at the trinomial. Are the signs positive, negative or both positive and negative. For example: x2 + 22x + 21 Both signs are positive meaning you are looking for factors of 21 that add to give you 22—the number in the middle. With no coefficient (the number in front of the variable x2 (the letter), it’s pretty easy to figure out.

Factor t2 – 2t – 63 What are the factors of 63 that subtract to give you -2? 1 - 63 = -62 3 – 21 = -18 7 - 9 = -2 With two negatives, you are looking for a positive and a negative number to multiply to give you a negative 63. -2 - 9 7 -63 Format of factored trinomial is: (t + 7)(t - 9)

Factor m2 – 9m + 20 What are the factors of 20 that add to give you 20? -1 – 20 = -21 -2 – 10 = -12 -4 – 5 = -9 With a negative in front and a positive in back, you are looking for two negative factors that add to give you negative 9 and multiply to give a positive 20. -9 - 5 -4 20 Format of factored trinomial is: (m - 4)(m - 5)

Factor r2 + 4r - 21 What are the factors of 21 that subtract to give you 4? 21 - 1 = 20 7 – 3 = 4 (r )(r ) + 7 - 3 Look at the trinomial. The first is positive, the second negative meaning you are looking for factors of 21 that subtract to give you a positive 4. Format of factored trinomial is: (r + 7)(r - 3)