 Step 1: Multiply the F IRST terms in the brackets.

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Presentation transcript:

 Step 1: Multiply the F IRST terms in the brackets.

 Step 2: Multiply the O UTSIDE terms.

 Step 3: Multiply the I NSIDE terms.

 Step 4: Multiply the L AST terms.

 Step 5: Collect like terms.

x x + 16 = (x + 2)(x + 8) x 2 + 9x + 20 = (x + 5)(x + 4) x x + 24 = (x + 8)(x + 3) x 2 + 5x + 4 = (x + 4)(x + 1) = x 2 + 8x + 2x + 16 = x x + 16 Factoring Simple Trinomials Check by FOILing What relationship is there between product form and factored form?

Many trinomials can be written as the product of 2 binomials. Recall: (x + 4)(x + 3)= x 2 + 3x + 4x + 12 = x 2 + 7x + 12 The middle term of a simple trinomial is the SUM of the last two terms of the binomials. The last term of a simple trinomial is the PRODUCT of the last two terms of the binomials. Factoring Simple Trinomials Therefore this type of factoring is referred to as SUM-PRODUCT!

1, ,6 8 3,4 7 x12 +7 (x + 3)(x + 4) To factor trinomials, you ask yourself… x 2 + 7x + 12

x 2 – 8x +12 – 8 x , , , , -6 ( x – 2)( x – 6) Factor:

m 2 – 5m x (-14) 13 -1, , , 7 2, -7 (m + 2) (m – 7) Factor:

x x + 24 x x + 36 x x + 33 Factor:

x x + 32 x x + 75 x 2 + 4x – 45 x x + 72 x 2 - 7x – 8 Factor:

- 5t – 3t t 2 – 3 - 3t Factor: t 2 – 8t +12 STEP 1: Combine Like terms - 8 x , , , , -6 ( x – 2 )( x – 6)

Factor: STEP 1: Pull out the GCF 7q 2 – 14q ( q 2 –2q –3) , 3 -3, 1 7 ( q – 3)( q + 1)

To Summarize: 1.Always check to see if you can simplify first! 2.Then check to see if you can pull out a common factor. 3.Write 2 sets of brackets with x in the first position. 4.Find 2 numbers whose sum is the middle coefficient, and whose product is the last term. 5.Check by foiling the factors. ex. + = 7 x = 10 5, 2 ex. + = 1 x = , 5 common factor?

How could we factor this using algebra tiles? x + 2 x Create a rectangle using the exact number of tiles in the given expression. 2.Remember that a trinomial represents area – two binomials multiplied together. 3.What is the width and length of the rectangle? 4.These are the FACTORS of the original rectangle. Does that make sense? (x+3)(x+2)

1.Create a rectangle using the exact number of tiles in the given expression. 2.Remember that a trinomial represents area – two binomials multiplied together. 3.What is the width and length of the rectangle? 4.These are the FACTORS of the original rectangle.