Try to find the middle through trial and error

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Presentation transcript:

Try to find the middle through trial and error Factoring Greatest Common Factor 2 5x- 15x = 5x(1-3x) 2 4 3 Grouping 5x – 10x – 2x + 4 5x (x – 2) – 2(x - 2) (5x – 2) (x – 2) Difference of Squares a - b = (a – b) (a+b) 4x – 49 = (2x – 7)(2x + 7) Difference of Cubes a + b = (a + b) (a + ab + b ) 8x – 1 = (2x – 1)(4x + 2x + 1) Reverse Foil Try to find the middle through trial and error Ax + Bx + c or Ax + Bx + c ( + + ) = ( + ) ( + ) ( - + ) = ( - ) ( - ) ( + - ) = ( - )( + ) or (+)(-) ( - - ) = ( - )( + ) or (+)(-) 3 2 2 2 2 2 2 4 2 2 2 - 2 3 3 3 2

Factoring Polynomials Different Ways to Factor GCF (Greatest Common Factor) Grouping Reverse Foil Calculator with Grouping Cube Pattern

GCF Factor 4x²y + 8x³y. What is the largest thing that both terms have in common? What should we do when we find the GCF? Write it in its factored form.

Factor the following 20a²b³ + 30a5b² 33p4r³ - 9pr³ 45xyz³ - 36x³yz + 18xy³z

Grouping A lot like GCF, just group terms first. 4xy + 2x + 6y + 3 21 – 7t + 3r – rt 4x² - 4xy + 8x – 8y

Reverse Foil Works with TRInomials Always look for a GCF first!!! x² + 5x + 6 Using what you already know about FOIL, try to come up with a basic idea of what the factored form would look like.

Factor Each Expression x² + 7x + 6 x² - 6x + 8 x² + 11x + 24 x² - 7x – 18 x² + 3x – 10 x² - 4x – 12 2x² + 3x + 1

Special case in factoring… Factor x² - 9 How could we re-write x² - 9? Now factor. x² - 100 4x² - 49

Now for some fun ones… 3x² - 27y² p4 – 1 y4 – 81 3x² - 3y²

What about polynomials with leading coefficients? Factor 2x² + 5x + 3. Here’s a shortcut… a●c (2 ●3=6) Rewrite as x² + 5x + 6, then factor. (x + )(x + )

Then divide out the 2 we originally multiplied (it was the coefficient of the x²). (x + 3/2)(x + 2/2) “Reduce” the fractions and if there is still a denominator, put it in the front.

Factor the following polynomials. 5x² + 34x + 24 6x² + x – 15 15x² + 26x + 8 4x² - 22x + 30 (hint: find a GCF first)

Factor 8x³ - 1 Take the cube root of each term Cube root of 8x³ = 2x Cube root of -1 = -1 (2x – 1) Square each of those and put them in a trinomial at the beginning and end (4x + 1)

(2x – 1)(4x + 1) Multiply the terms from the binomial and change the sign 2x●-1 = -2x 2x Put that in the middle of the trinomial (2x – 1)(4x + 2x + 1)

Factor the following 8x³ + 27 x³ - 64 x³ + 8y³ -27x³ + 8