Aim: How Do We Solve Quadratic Equations by

Factoring

Do Now:Factor: x2+3x-18

Example: Solve.x2+3x-18=0

x2+3x-18=0 Factor the left side(x+6)(x-3)=0 set each factor =0

x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your

solutions!

Example: Solve.2t2-17t+45=3t-5

2t2-17t+45=3t-5 Set eqn. =02t2-20t+50=0 factor out GCF of 22(t2-10t+25)=0 divide by 2t2-10t+25=0 factor left side(t-5)2=0 set factors =0t-5=0 solve for t+5 +5t=5 check your solution!

Example: Solve.3x-6=x2-10

3x-6=x2-10 Set = 00=x2-3x-4 Factor the right side0=(x-4)(x+1) Set each factor =0x-4=0 OR x+1=0 Solve each eqn. +4 +4 -1 -1x=4 OR x=-1 Check your solutions!

Solve for x: 5)1(3 xx

3 + x2 – x = 5

x2 – x – 2 = 0

(x – 2)(x + 1) = 0

x = 2, x = –1

Solve for x: 2x2 + 4x = 30

2(x2 + 2x – 15) = 0

x2 + 2x – 15 = 0

(x + 5)(x - 3) = 0

x = -5, x = 3

Solve x2 – 5x = 0.

x(x – 5) = 0 x = 0, x = 5

Solve (x – 5)2 – 100 = 0.

The left side of the equation is the difference of two squares, then factor it into two binomials

[(x – 5) + 10][(x – 5) – 10] = 0

(x +5)(x – 15) = 0

x = -5, x = 15

Solve for x: 2x2 – 4x = 12 + x

2x2 – 5x – 12 = 0

(2x + 3)(x – 4) = 0

2x + 3 = 0, x – 4 = 0

2

3x x = 4

You Try It!You Try It!

• Solve the following equations:1. x2 – 25 = 0

2. x2 + 7x – 8 = 0

3. x2 – 12x + 36 = 0

4. c2 – 8c = 0

5. 5b3 + 34b2 = 7b

Finding the Zeros of an Finding the Zeros of an EquationEquation

• The Zeros of an equation are the x-intercepts !

• First, change y to a zero.• Now, solve for x.• The solutions will be the zeros of

the equation.

Example: Find the Zeros ofy=x2-x-6

y=x2-x-6 Change y to 00=x2-x-6 Factor the right side0=(x-3)(x+2) Set factors =0x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions!

If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).