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High School Math : Intermediate Single-Variable Algebra

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Solving Quadratic Equations

Find the zeros.

$f(x)=27x^{2}-45x-18$

Possible Answers:

$x=-\frac{1}{3},2$

$x=\frac{1}{3}$

$x=9,-\frac{1}{3},2$

x=-2,-9

$x=\frac{1}{3},2$

Correct answer:

$x=-\frac{1}{3},2$

Explanation:

Factor out a from the entire equation. After that, you get 9(3x^2-5x-2) . Factor the expression to (3x+1)(x-2) . Set both of those equal to zero and your answers are $-\frac{1}{3}$ and .

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Example Question #4 : Solving Quadratic Equations

Find the zeros.

$f(x)=25x^{2}-81$

Possible Answers:

$x=-\frac{9}{5}$

x=9,-9

$x=\frac{9}{5},-\frac{9}{5}$

x=5

$x=\frac{9}{5}$

Correct answer:

$x=\frac{9}{5},-\frac{9}{5}$

Explanation:

This expression is the difference of perfect squares. Therefore, it factors to (5x-9)(5x+9) . Set both of those equal to zero and your answers are $\frac{9}{5}$ and $-\frac{9}{5}$ .

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Example Question #1 : Solving Quadratic Equations

Find the zeros.

f(x)= 36x^2-9x

Possible Answers:

x=8

x=0,4

$x=0,\frac{1}{4}$

x=0

$x=\frac{1}{4}$

Correct answer:

$x=0,\frac{1}{4}$

Explanation:

Factor the equation to 9x(4x-1) . Set both equal to and you get and $\frac{1}{4}$ .

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Example Question #6 : Solving Quadratic Equations

Find the zeros.

$f(x)=\frac{1}{4}x^2 +\frac{5}{4}x+\frac{3}{2}$

Possible Answers:

x=4,2

x=3,2

x=-3,3

x=2

x=-3,-2

Correct answer:

x=-3,-2

Explanation:

Factor a $\frac{1}{4}$ out of the quation to get

$\frac{1}{4}\left ( x^{2}+5x+6 \right )$

which can be further factored to

$\frac{1}{4}(x+3)(x+2)$ .

Set the last two expressions equal to zero and you get and .

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Example Question #31 : Quadratic Equations And Inequalities

Find the zeros.

f(x)=x(x-6)^2

Possible Answers:

x=-6,6

x=1,-1

x=0

x=0,6

x=6

Correct answer:

x=0,6

Explanation:

Set each expression equal to zero and you get 0 and 6.

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Example Question #8 : Solving Quadratic Equations

Find the zeros.

f(x)=(x-2)(x+4)^3

Possible Answers:

x=4

x=2,-4

x=0,2,-2

x=2

x=-2,4

Correct answer:

x=2,-4

Explanation:

Set both expressions equal to . The first factor yields . The second factor gives you .

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Example Question #3 : Solving Quadratic Equations

Find the zeros.

f(x)=(x+5)(x-8)^2

Possible Answers:

x=-5,8

x=5,8

x=-8

x=-5

x=0

Correct answer:

x=-5,8

Explanation:

Set both expressions to and you get and .

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Example Question #11 : Solving Quadratic Equations

Solve the following equation by factoring.

x^2+7x-8=0

Possible Answers:

$x=8\ or\ 1$

$x=8\ or\ -1$

$x=-8\ or\ 1$

$x=-8\ or\ -1$

Correct answer:

$x=-8\ or\ 1$

Explanation:

We can factor by determining the terms that will multiply to –8 and add to +7.

$8*-1=-8\ and\ 8+(-1)=7$

Our factors are +8 and –1.

0=x^2+7x-8=(x+8)(x-1)

Now we can set each factor equal to zero and solve for the root.

$x+8=0\ or\ x-1=0$

$x=-8\ or\ x=1$

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Example Question #12 : Solving Quadratic Equations

Solve the following equation by factoring.

2x^2-8x-10=0

Possible Answers:

$x=-5\ or\ 1$

$x=5\ or\ 1$

$x=5\ or\ -1$

$x=-5\ or\ -1$

Correct answer:

$x=5\ or\ -1$

Explanation:

We know that one term has a coefficient of 2 and that our factors must multiply to –10.

$2*-5=-10\ and\ 2+2(-5)=-8$

Our factors are +2 and –5.

0=2x^2-8x-10=(2x+2)(x-5)

Now we can set each factor equal to zero and solve for the root.

$2x+2=0\ or\ x-5=0$

$x=-1\ or\ 5$

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Example Question #13 : Solving Quadratic Equations

Solve the following equation by factoring.

0=x^3+4x^2+4x

Possible Answers:

$x=0,-4\ or\ 1$

$x= 0,2\ or\ -2$

$x=0\ or\ -2$

$x=0\ or\ 2$

Correct answer:

$x=0\ or\ -2$

Explanation:

First, we can factor an term out of all of the values.

0=x^3+4x^2+4x=x(x^2+4x+4)

We can factor remaining polynomial by determining the terms that will multiply to +4 and add to +4.

$2*2=4\ and\ 2+2=4$

Our factors are +2 and +2.

0=x(x+2)(x+2)=x(x+2)^2

Now we can set each factor equal to zero and solve for the root.

$x=0\ or\ (x+2)^2=0$

$x=0\ or\ -2$

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All High School Math Resources

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High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Solving Quadratic Equations

Example Question #4 : Solving Quadratic Equations

Example Question #1 : Solving Quadratic Equations

Example Question #6 : Solving Quadratic Equations

Example Question #31 : Quadratic Equations And Inequalities

Example Question #8 : Solving Quadratic Equations

Example Question #3 : Solving Quadratic Equations

Example Question #11 : Solving Quadratic Equations

Example Question #12 : Solving Quadratic Equations

Example Question #13 : Solving Quadratic Equations

All High School Math Resources

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