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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 70 Page 84

Be sure that all of the terms of are on the same side and in the correct order for the standard form of a quadratic function.

- 5/3, 5/3

Practice makes perfect

To solve the given equation by factoring, we will start by identifying the values of a, b, and c. 9x^2-25=0 ⇔ 9x^2+ 0x+( - 25)=0 Notice that this equation follows a special pattern. It can be factored as a difference of squares. Let's factor the equation!

9x^2-25=0

Write as a power

3^2x^2-5^2=0

a^m b^m = (a b)^m

(3x)^2-5^2=0

a^2-b^2=(a+b)(a-b)

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

Now we are ready to use the Zero Product Property.

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

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Solve using the Zero Product Property

Use the Zero Product Property

lc3x+5=0 & (I) 3x-5=0 & (II)

(I): LHS-5=RHS-5

lc3x=- 5 & (I) 3x-5=0 & (II)

(I): .LHS /3.=.RHS /3.

lcx=- 53 & (I) 3x-5=0 & (II)

(II): LHS+5=RHS+5

lcx=- 53 & (I) 3x=5 & (II)

(II): .LHS /3.=.RHS /3.

lcx=- 53 & (I) x= 53 & (II)

We found that the solutions to the given equation are x=- 53 and x= 53. To check our answer, we will graph the related function f(x)=9x^2-25 using a calculator.

We can see that the x-intercepts are - 53 and 53. Therefore, our solutions are correct.

Subchapter links

1 Adding and Subtracting Polynomials p.81

2 Multiplying a Polynomial by a Monomial p.81

3 Multiplying Polynomials p.81

4 Special Products p.82

5 Using the Distributive Property p.82

6 Solving x^2+bx+c=0 p.83

7 Solving ax^2+bx+c=0 p.83

8 Differences of Squares p.84

9 Perfect Squares p.84

10 Roots and Zeros p.85