8th,+Team+4

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Ex1. Find the Degree of a Monomial

6x^3*3 The degree of the monomial is 3 because it is the exponent of x.

Ex.2 (5x^3-2x+x^2+7)+(3x^2+7-4x) 5x^3+4x^2-6x+14 you combine like terms and you get your answer

Ex3. (2x^2=x-5)+(x+x62+6) x^62+2x^2+2x+1 Combine like terms and you get your answers   10.4! Example 1 Using the zero-product property

Solve the equation (x-2)(x+5)

Solution (x-2)(x+5)=0 write original equation x-2=0 or x+3=0 set each factor equal to zero x=2 | x=-3 solve for

answer: the solutions are 2 and -3. Check these in the original equation

Example 2 solve a repeated-factor equation

solve (x+5)^2

 This Equation is a square of a binomial,so the factor (x+5) is a repeated factor. Repeated factors are used twice or more in an equation. To solve this equation you set (x+5) equal to zero.

(x+5)^2=0 write original equation  x+5=0 set factor equal to zero x=-5 solve for x

Answer: the solution is -5

Check substitute the solution into the original equation to check

(x+5)^2=0 write original equation

(-5+5)^2=0 substitute -5 for x.

0=0 simplify. solution is correct

example 3 solve a factored cubic equation

solve (2x+1)(3x-2)(x-1)=0

Solution

(2x+1)(3x-2)(x-2)=0  write original equation 

2x+1=0 or 3x-2=0 or x-1=0 set factors equal to zero

2x=-1 | 3x=2 | x=1 solve for x

x=-1/2 | x=2/3 |

Answer: the solutions are -1/2,2/3,and 1. check these in the original equation.

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