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Factortopia

Factortopia. By Alex Bellenie. What is Factoring?. Factoring is a process where we find what we multiply in order to get a quantity. Factoring is effectively “undoing” multiplying. You also using the distributive property backwards. Why is it important.

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Factortopia

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  1. Factortopia By Alex Bellenie

  2. What is Factoring? • Factoring is a process where we find what we multiply in order to get a quantity. • Factoring is effectively “undoing” multiplying. You also using the distributive property backwards.

  3. Why is it important • Factoring is one of the most important parts of algebra, it is used in a large part of algebra and is a building block of math. • Factoring has many applications it is used to solve quadratic equations, such as 9x2+6x+0, and is used to simplify rational expressions.

  4. Examples • For example when you multiply • 5(x+3)(monomial)(binomial) you would distribute the 5 into both terms ins the parenthesis • Pq(2p2q+p+1)(monomial)(trinomial) you distribute pq in to the terms and you would get 2p3q2+p2q+pq • (A+B)2 (binomial)(binomial) you plug the numbers into a base like this A2 + 2AB + B2 • (5x+6)(4x+3) you would use FOIL where you would multiply the First, outside, inside, and last terms to get 20x+15x+24x+18 then you would put like terms together and get 20x+39x+18

  5. Examples • For a binomial multiplied by a trinomial like this (2x+3)(4x+4x-2) you would use the box method because Foil will not work • The box method requires one set of terms to be written vertically and the other set to be horizontal you would then make a chart and multiply and combine like terms • and for trinomial multiplied by a trinomial like (4x2+3x-5)(7y2-5y-2) you would use the box method for this type of multiplication problem

  6. The Factoring Cross • The factoring cross is used to factor problems like these • Ax2+bx+c A x C goes in the top • B goes in the bottom

  7. The Factoring Cross • To use the cross you find two numbers that when multiplied equal AxC and when added equal B • Ex. X2+5x+6 6 2 3 5 (x+2)(x+3)

  8. Common Factors • Common factors are easily found in polynomials • They simplify the factoring of Polynomials • First find a number that you can take out of both terms and remove it • 5x+15 can be simplified to 5(x+3) • It is the distributive property used backwards • Try these: 2A2+6A+4 4y2+8y+16

  9. Difference of squares • When you multiply: (A+B)(A-B)= A2-B2 • The answer will always have: • two terms and both will be squares • There will be a minus sign between the terms • This is called The Difference of Squares

  10. Difference of squares • Are these a difference of squares? • X2-25 -36-X2 4x2-25 • To Factor a difference of squares use backwards multiplication • A2-B2= (A+B)(A-B) • As always with some problems you will be able to factor out a common term • 5-20Y9 = 5(1-4y6)= 5(1+2y3)

  11. Trinomial Squares • You will get a trinomial square when you multiply (a+b)2=a2+2ab+b2 • (a-b)2=a2-2ab+b2 • You can determine whether the answer you got is a trinomial square by looking for the following: two of the terms must be squares a2 and b2, there is no minus before a2 and b2, and the middle term must be +2ab or -2ab • Are these Trinomial Squares? • X2+6x+9 X2+6X+11

  12. Factoring X2+bx+c • Foil is used for multiplying terms like (x+3)(x+6) • But to Factor their product you simply use Foil in reverse and use the factoring cross • Ax2+bx+c • X2+7x+10 10 2 5 7 (x+5)(x+2) Try These: X2+7x+12 X2+13x+36

  13. Factoring ax2+bx+c Part 2 • This process involves both the cross method and the factoring box • If the leading coefficient is not 1, the product of a will go in the first spot in both (_x+_)(_x+_) and the product of C will go in the second spot in both

  14. Factoring ax2+bx+c Part 2 • 3x2+5x+2 6 2 3 5 3x2+2x+3x+2 now you can factor by grouping or use the factoring box X(3x+2)+1(3x+2) (x+1)(3x+2) Try these:6x2+7x+2 8x2+10x-3

  15. Factoring by grouping • X3+X2+2x+2 next you will add parenthesis but you can add them when you write the problem • (X3+x2)+(2x+) next you take out a number to make both sets of terms the same • X2(X+1)+2(X+1) • Now you put the terms that you took out into a set and put the same terms into one • (X2+2)(x+1) • Try these: (8x3+2x2)+(12x+3) (x3+x2)+(x+1)

  16. Factoring completely • To find out whether you have factored completely you check many things to find out or “Look” • Look: for a common factor • Look: at the number of terms • Two terms: Difference of squares? • Three terms: Square or Binomial? If not. Test the factor of the terms • Look: to see if you are done…factor completely

  17. Conclusion • Factoring is a highly important process in Algebra and must never ever be overlooked. It is used to solve many tricky problems and is a simple process used to simplify polynomials and many other Algebra terms.

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