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Rules of Factoring Polynomials

Rules of Factoring Polynomials. A presentation for RHHS Grade 10 Wonderful Students By Ms. Wang. Main Menu. Rules. Step by Step. Easy Problems. Medium Problems. Hard Problems. Word Problems. Division of polynomial by monomial. Find dimensions when area is given. Rules of Factoring.

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Rules of Factoring Polynomials

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  1. Rules of Factoring Polynomials A presentation for RHHS Grade 10 Wonderful Students By Ms. Wang

  2. Main Menu Rules Step by Step Easy Problems Medium Problems Hard Problems Word Problems Division of polynomial by monomial Find dimensions when area is given

  3. Rules of Factoring

  4. Flowchart of Factoring polynomials GCF and Leading “-” Factor out GCF and rewrite the left polynomial inside a parenthesis Binomial Trinomial XBOX Difference of two squares

  5. Stepby Step Is there a GCF? Yes Factor as the product of the GCF and one other factor—i.e. GCF•(the other factor). Look at the other factor and go to the next step below with it. No Go the the next step. Is it a binomial? Yes Is it a difference of two squares? (a2-b2) Yes—Factor as (a+b)(a-b). No—It can’t be factored any more. No Go to the next step.

  6. Is it a trinomial? Yes Use the X BOX pattern to look for factors. No Go to the next step.

  7. NOTE: At EVERY step along the way, you must look at the factors that you get to see if they can be factored any more. Factoring completely means that no factors can be broken down any further using any of the rules you’ve learned.

  8. Practice Factor completely. Is there a GCF? No. Is it a binomial or trinomial? It’s a trinomial. XBOX

  9. 24 x x x2 Use your handy-dandy calculator or your super math skills to find 12 and 2 as the factors to use. 12 2 12x + 2x = 14x Rewrite the equation with those two factors in the middle. Write the two factors. Neither one of these factors can be broken down any more, so you’re done.

  10. Factor completely Is there a GCF? Yes. Write the GCF first and the remaining factor after it. Look at the remaining factor. (x-3) Is it a binomial or trinomial? It’s a binomial. Is it a difference of two squares? (a2-b2) No. You can’t do anything else. is the completely factored form.

  11. Factor completely Is there a GCF? Yes. Write the GCF first and the remaining factor after it. Look at the remaining factor. (s2-4) Is it a binomial, trinomial? It’s a binomial. Is it a difference of two squares? (a2-b2) Yes. s2 is a square (s • s) and 4 is a square (2 • 2). Factor as (s+2)(s-2). Then write the complete factorization.

  12. Factor completely Is there a GCF? No. Is it a binomial or trinomial? It’s a trinomial.

  13. 6y2 b Check the sum of the cross product is -5y 2y -3 2 3y 2*2y + 3y *(-3) = -5y Rewrite the equation with those two factors in the middle. Write the two factors.

  14. Factor completely Is there a GCF? Yes. Write the GCF first and the remaining factor after it. Look at the remaining factor. Is it a binomial or trinomial? It’s a trinomial.

  15. 2x2 -3 Check the sum of the cross product is 5x. 2x -1 3 x 2x*3 + x*(-1) =5x Rewrite the equation with those two factors in the middle. Write all three factors.

  16. Factor completely Is there a GCF? Yes. Write the GCF first and the remaining factor after it. Look at the remaining factor. Is it a binomial, trinomial, or four-term polynomial? It’s a binomial. Is it a difference of two squares? (a2-b2) Yes. x8 is a square (x4• x4) and 16 is a square (4 • 4). Factor as (x4+ 4)(x4- 4). So far we have 2(x4+ 4)(x4- 4).(Please continue—not done yet!!)

  17. 2(x4+4)(x4-4) Look at what you have. Can either of the binomials be broken down? (x4+4) Is this binomial a difference of two squares? (a2-b2) No. It can’t be broken down. So, we have to keep this factor. What about the other binomial? (x4-4) Is this binomial a difference of two squares? (a2-b2) Yes. x4 is a square (x2• x2) and 4 is a square (2 • 2). Factor as (x2+ 2)(x2- 2).

  18. Put it all together. =2(x4+4)(x4-4) Not a difference of squares. Can’t go any farther!! =2(x4+4)(x2+2)(x2-2)

  19. Word Problem #1 What is the quotient when is divided by 4x? This question is asking you to find the OTHER FACTOR after you take out the greatest common factor of 4x. Simplify each term.

  20. Word Problem #2 A rectangular garden plot has an area represented by the expression Find the dimensions of the garden plot. This is a factoring problem. You need to find the two factors that multiply together to give you

  21. Is there a GCF? No. Is it a binomial, trinomial, or four-term polynomial? It’s a trinomial.

  22. 18x2 -28 Check the sum of the cross product of the XBOX is -3x. -4 3x 6x 7 Rewrite the equation with those two factors in the middle. Write the two factors. Length is 3x - 4 and width is 6x + 7

  23. The End Practice Makes Master!

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