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Algebra II : Intermediate Single-Variable Algebra

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Example Questions

Example Question #13 : Understanding Quadratic Equations

Simplify the function, if possible: $\frac{8x-10+2x^2}{-16+16x}$

Possible Answers:

$\frac{3}{16}x-\frac{3}{16}$

$\textup{The expression cannot be factored.}$

$\frac{1}{16}x+\frac{5}{16}$

$\frac{1}{8}x+\frac{5}{8}$

$\frac{1}{16}x-\frac{5}{16}$

Correct answer:

$\frac{1}{8}x+\frac{5}{8}$

Explanation:

The expression will need to be rearranged from highest to lowest powers in order to be simplified.

$\frac{8x-10+2x^2}{-16+16x} =\frac{2x^2+8x-10}{16x-16}$

Factor a 2 in the numerator.

2x^2+8x-10 = 2(x^2+4x-5)

Factor the term in parentheses.

2(x^2+4x-5) = 2(x-1)(x+5)

Factor the denominator.

16x-16 = 16(x-1)

Divide the numerator with the denominator.

$\frac{2(x-1)(x+5)}{16(x-1)}$

The expression becomes:

$\frac{x+5}{8}$

The answer is: $\frac{1}{8}x+\frac{5}{8}$

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Example Question #17 : Quadratic Equations And Inequalities

Solve for x:

$\frac{6}{x}=\frac{x+2}{4}$

Possible Answers:

-12,2

12,-2

-6,4

-4,6

None of the other answers

Correct answer:

-6,4

Explanation:

The correct answer is x=-6 or x=4 . The first step of the problem is to cross multiply. This will give the following equation:

24=x^2+2x

After subtracting from each side the equation looks like:

0=x^2+2x-24

The expression on the right hand side can be factored into:

0=(x-4)(x+6 )

Both and satisfy the above equation and are therefore the correct answers.

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Example Question #1 : Simplifying Polynomials

Expand this expression:

(x-4) (2x+4)

Possible Answers:

2x^2 - 4x - 16

2x^2 - 4x + 16

2x - 4x - 16

2x^2 + 4x + 16

2x^2 + 4x - 16

Correct answer:

2x^2 - 4x - 16

Explanation:

Use the FOIL method (First, Outer, Inner, Last):

x * 2x = 2x^2

x * 4 = 4x

-4 * 2x = -8x

-4 * 4 = -16

Put all of these terms together:

2x^2 + 4x - 8x - 16

Combine like terms:

2x^2 - 4x - 16

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Example Question #2 : Foil

Evaluate $(2x+3)^{2}$

Possible Answers:

$\dpi{100} 4x^{2}+9x+9$

$\dpi{100} 4x^{3}+12x^{2}+9x$

$\dpi{100} 4x+12$

$\dpi{100} \dpi{100} 4x^{2}+9$

$4x^{2}+12x+9$

Correct answer:

$4x^{2}+12x+9$

Explanation:

In order to evaluate $(2x+3)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} (2x+3)^{2}=(2x+3)(2x+3)$

Multiply terms by way of FOIL method.

=(2x*2x)+(2x*3)+(3*2x)+(3*3)

Now multiply and simplify.

$=4x^{2}+6x+6x+9$

$\rightarrow 4x^{2}+12x+9$

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Example Question #2 : How To Simplify Binomials

Simplify:

(x-3)^2

Possible Answers:

x^2+9x+9

x^2-9x+9x

x^2-6x+9

x^2+6x+9

Correct answer:

x^2-6x+9

Explanation:

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

a=x

b=-3

x^2+2(-3)(x)+(-3)^2=x^2-6x+9

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Example Question #1 : Foil

Foil:

(x+7)(x-2)

Possible Answers:

$\small x^2+9x+14$

$\small x^2-5x-14$

$\small x^{2}+5x-14$

$\small x^2-9x+14$

Correct answer:

$\small x^{2}+5x-14$

Explanation:

First: $\small x\ times\ x\ =\ x^2$

Outside: $\small x\ times\ -2\ =\ -2x$

Inside: $\small x\ times\ 7\ =\ 7x$

Last: $\small -2\ times\ 7\ =\ -14$

$\small x^2-2x+7x-14\ =\ x^2+5x-14$

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Example Question #1 : Foil

FOIL (2x + 3)(x + 5) .

Possible Answers:

2x^2 + 7x + 8

x^2 + 13x + 8

2x^2 + 13x + 8

2x^2 + 7x + 15

2x^2 + 13x + 15

Correct answer:

2x^2 + 13x + 15

Explanation:

(2x + 3)(x + 5)

First: 2x multiplied by x = 2x²

Outer: 2x multiplied by 5 = 10x

Inner: 3 multiplied by x = 3x

Lasts: 3 multiplied by 5 = 15

Put it all together: 2x² + 10x + 3x + 15

Simplify: 2x² + 13x + 15

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Example Question #22 : Understanding Quadratic Equations

Use FOIL method to expand the product.

(2x+6)(x-4)

Possible Answers:

$2x^{2}-2x-2$

$2x^{2}-14x-24$

$x^{2}-2x-24$

$2x^{2}-2x-24$

$2x^{2}-3x-12$

Correct answer:

$2x^{2}-2x-24$

Explanation:

Remember that FOIL stands for First, Outside, Inside, Last.

Multiply using FOIL and group like terms.

$(2x+6)(x-4)=2x^{2}-8x+6x-24=2x^{2}-2x-24$

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Example Question #4 : Foil

Expand the following expression:

(x-6)(7x+4)

Possible Answers:

$7x^{2}+28x-24$

$7x^{2}-38x-24$

$14x^{2}-24x+40$

$8x^{2}-24x+36$

$6x^{2}-32x+64$

Correct answer:

$7x^{2}-38x-24$

Explanation:

Expand the expression (x-6)(7x+4) using the FOIL Method:

FIRST: $x\times7x = 7x^{2}$

OUTER: $x\times 4 = 4x$

INNER: $(-6) \times7x=-42x$

LAST: $(-6)\times4=-24$

Therefore:

(x-6)(7x+4)

$= 7x^{2} +4x-42x-24$

$= 7x^{2}-38x-24$

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Example Question #5 : Foil

Simplfy and combine like terms:

(2x+3)(x-5)

Possible Answers:

2x^2-13x-15

2x^2+10x-15

2x^2+7x+15

2x^2-7x-15

Correct answer:

2x^2-7x-15

Explanation:

For this problem we need to use FOIL which stands for Firsts, Outters, Inners, Last. This describes the order of distributing and multiplying the binomials.

(2x+3)(x-5)

Firsts gets us 2x*x=2x^2

Outters gets us 2x*-5=-10x

Inners gets us 3*x=3x

Lasts gets us 3*-5=-15

Rewriting these in an equation form we get:

2x^2-10x+3x-15

Now we combine the like terms of -10x and 3x which results in:

2x^2-7x-15

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Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #13 : Understanding Quadratic Equations

Example Question #17 : Quadratic Equations And Inequalities

Example Question #1 : Simplifying Polynomials

Example Question #2 : Foil

Example Question #2 : How To Simplify Binomials

Example Question #1 : Foil

Example Question #1 : Foil

Example Question #22 : Understanding Quadratic Equations

Example Question #4 : Foil

Example Question #5 : Foil

All Algebra II Resources

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