Solving Quadratics by Factoring By Anthony, Salma, Emily, & Henry

Definitions Binomials - an expression with 2 terms: x+3 Trinomials - an expression with 3 terms: x²+8x+19 Quadratic - x²+9 or x²+3x+19

(x+4)(x+3) Factoring allows you to find a solution for a trinomial. We’re trying to find factors (a factor is something that can be multiplied by) For example: x²+7x+12=0 (x+4)(x+3) So the solutions will be x=-4 and x=-3

How to Factor -7+5=-2 -7×5=-35 So the factors will be (x-7)(x+5)=0 a+b=-2 a×b=-35 Factors of: 35: 1,5,7,35 -7+5=-2 -7×5=-35 So the factors will be (x-7)(x+5)=0

Quadratic Solution So now we have the factor (x-7)(x+5)=0 The Zero Factor Property tells us if a × b = 0 then a = 0 or b = 0 (or both a=0 and b=0) So you set them both equal to zero x-7=0 x+5=0 Solve Solutions for the quadratic equation is x=7,-5

Checking Work The solutions to quadratic equations may be verified by plugging them back into the original equation. This makes sure that they work and that they result in a true statement. Checking 7 in x²-2x-35=0 (7)²-2(7)-35=0 49-14-35 Checking -5 in x²-2x-35=0 (-5)²-2(-5)-35=0 25+10-35 Equals zero Equals zero

Now try this: x²-16x+64=0 (x-8)² x-8=0 x=8 x-8=0 x=8

Here’s another example: x² +2x-3=0 (x+3)(x-1) x+3=0 x=-3 x-1=0 x=1