7 4 Solving Polynomial Equations in Factored Form

Example 1 Solve each equation. a. ) 2 x(x-4) = 0 b. ) (x-3)(x-9)

Example 2 Solve each equation. a. ) (2 x+7)(2 x-7) = 0 b. )

Monitoring Progress Solve each equation. 1. x(x-1)=0 2. 3 t(t+2)=0 3. (z-4)(z-6)=0 4. (3

Example 3 Factor out the Greatest Common Monomial from 4 x 4+24 x 3.

First, we need to move 15 n to set the equation =0 Subtract 15

Monitoring Progress Factor the Greatest Common Monomial. 7. 8 y 2 – 24 y

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7. 4 Solving Polynomial Equations in Factored Form

Example 1 Solve each equation. a. ) 2 x(x-4) = 0 b. ) (x-3)(x-9) = 0 Notice that the equations are = 0 This is very important. We are solving for x, which means we are finding the x-intercept(s). Remember x-intercepts have a y-value of 0 (___, 0) 2 x=0 x-4=0 Set both expressions = 0 Solve for x x=0 and x= 4 x-3=0 x-9=0 Set both expressions = 0 Solve for x Easy! x= 3 and x=9

Example 2 Solve each equation. a. ) (2 x+7)(2 x-7) = 0 b. ) (x-1)2 = 0 c. )(x+1)(x-3)(x-2)=0 Notice that the equations are = 0 This is very important. We are solving for x, which means we are finding the x-intercept(s). Remember x-intercepts have a y-value of 0 (___, 0) 2 x+7=0 2 x-7=0 Set both expressions = 0 Solve for x x-1=0 Set both expressions = 0 Solve for x x= 1 Repeated root Easy! x+1=0 x-3=0 x-2=0 Set the expressions = 0 Solve for x x= -1 x= 3 and x=2

Monitoring Progress Solve each equation. 1. x(x-1)=0 2. 3 t(t+2)=0 3. (z-4)(z-6)=0 4. (3 x+5)(5 x+8)=0 5. (b+7)2=0 6. (d-2)(d+6)(d+8)=0 Set each expression = 0 and solve for x.

Example 3 Factor out the Greatest Common Monomial from 4 x 4+24 x 3. This question is different because we have to rewrite it in factored form. List the factors of 4 and 24 4: 1, 2, 4 24: 1, 2, 3, 4, 6, 8, 12, 24 4 is the Greatest Common Factor Use 4 and x 3 4 x 3(x+6) That is it! Leave it like this. We only had to factor, not solve.

First, we need to move 15 n to set the equation =0 Subtract 15 n from both sides to get 6 n 2 – 15 n = 0 Example 4 Solve a. ) 2 x 2+8 x=0 b. ) 6 n 2=15 n This question is different because we have to rewrite it in factored form & then solve for x. List the factors of 6 and 15 List the factors of 2 and 8 6: 1, 2, 3, 6 3 is the Greatest 2: 1, 2 2 is the Greatest Common Factor 15: 1, 3, 5, 15 8: 1, 2, 4, 8 Common Factor x is the GCF of x 2 and x Use 2 and x x= 0 and x= - 4 Use 3 and n 2 x(x+4) = 0 n is the GCF of n 2 and n Solve for x. 3 n(2 n-5) = 0 Solve for x.

Monitoring Progress Factor the Greatest Common Monomial. 7. 8 y 2 – 24 y Only factor for 7 8 -10, Factor then Solve. 8. a 2+5 a =0 1 st Factor 2 nd Set each expression = 0 3 rd Solve for x. 9. 3 s 2 – 9 s = 0 10. 4 x 2=2 x Look at Example 4 b when you solve 10