Factoring By Natalie Northcutt What is Factoring is
Factoring By: Natalie Northcutt
What is Factoring is a process where the factors of a composite number or expression are found and the number or expression is shown as a product of these two factors. Ex. 15=3*5 or 4 x+2=2(2 x+1). Factoring is an important process in math used to simplify fractions, expressions, and solve equations.
Factoring Trinomials Here you will factor a trinomial into two binomials. You can do this using the table method. Ex. x²+5 x+6, you place the x² term in the center box, and the 6 term in the bottom-right corner box. And then you solve to get the values that add up to 5 x. Your answer is (x+3)(x+2). x +2 x x² 2 x +3 3 x 6
More Examples x²+x-12 -3) x -3 x x² -3 x 4 4 x -12 2 x 2 x²-12+16 -4) x -4 (x+4)(x -4 (2 x-4)(x 2 x² 16
Factoring Trinomials to solve an Equation First, you set the equation equal to zero. Then, you try and find a common factor of all your values. ex. 3 x²+6 x+6=-3, set the equation equal to zero by adding three to both sides, you get 3 x²+6 x+9=0, you can factor out 3 to make it 3(x²+2 x+3)=0. Then you change your trinomial into two binomials. You can use the table method here. You will end up with 3(x+2)(x+1)=0. You then will set each value equal to x. x=3; x+2=0(x=-2); x+1=0(x=-1). And that is how you factor trinomials to solve an equation.
More Examples x²-6 x=-8; x²-6 x+8; (x-4)(x-2); x-4=0 x-2=0; x=4 x=2 4 x²+10 x+6=0; (2 x+2)(2 x+3); 2 x=-3 2 x=-2; x=-1. 5 x=-1
Perfect Squares If an expression contains numbers that are squares or variables with even exponents, they can be expressed as perfect squares. Ex. x²+4=(x+2)² or 4 x²+25=(2 x+5)². Sometimes getting your expression to be a perfect square will require some factoring. Ex. 3 x²+27= 3(x²+9)=3(x+3)² or x³+16 x=x(x²+16)= x(x+4)²
More Examples x� =(x²)² 4 x²+81=(2 x+9)² 12 x²+27=3(4 x²+9)=3(2 x+3)² 12 x� +48 x³=12 x³(x²+4)=12 x³(x+2)²
History of Factoring In Renaissance times, polynomial factoring was a royal sport. Kings sponsored contests and the best mathematicians in Europe traveled from court to demonstrate their skills. Polynomial factoring techniques were closely guarded secrets, and the topics of intrigues and betrayals. Quadratic equations were solved by completing the square & quadratic formula before they solved by factoring by the Babylonians
Real Life Instances in which you would use Factoring You can use factoring to calculate the temperature increase or decrease over time. You can use factoring to find the height reached and distance traveled of a thrown item over time. You can use factoring to find the slope or steepness of a cliff, mountain, or hill.
More Help For more help understanding factoring, or more sample problems, try these websites www. algebrahelp. com www. onlinemathlearning. com/quadraticequations. html www. mathwarehouse. com/quadratic/solve-quadraticequation-by-factoring. php www. coolmath. com/algebra/04 -factoring/index. html
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