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Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #62 : Foil

Solve: (3x-10)(x-7)

Possible Answers:

3x^2+9x+70

3x^2-31x+70

3x^2-11x+70

3x^2-9x+70

3x^2+31x+70

Correct answer:

3x^2-31x+70

Explanation:

Solve by using the FOIL method.

(a+b)(c+d) = ac+ad+bc+bd

Simplify the question by using this format.

(3x-10)(x-7)

(3x)(x)+(3x)(-7)+(-10)(x)+(-10)(-7)

Simplify the terms.

3x^2-21x-10x+70 = 3x^2-31x+70

The answer is: 3x^2-31x+70

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Example Question #82 : Understanding Quadratic Equations

Simplify: $(\sqrt{2}-2)(\sqrt{8}+3)$

Possible Answers:

$-3\sqrt2+2$

$\sqrt2-2$

$-\sqrt2-2$

Correct answer:

$-\sqrt2-2$

Explanation:

Use the FOIL method to simplify the binomials.

$(\sqrt{2}-2)(\sqrt{8}+3) = \sqrt{2}(\sqrt{8})+\sqrt{2}(3)+(-2)(\sqrt{8})+(-2)(3)$

Simplify the terms.

$=\sqrt{16}+3\sqrt2-2\sqrt8-6$

$=\sqrt{16}+3\sqrt2-2(\sqrt4 \times \sqrt2)-6$

$=4+3\sqrt2-2(2\sqrt2)-6$

$=4+3\sqrt2-4\sqrt2-6$

Combine like-terms.

The answer is: $-\sqrt2-2$

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Example Question #241 : Intermediate Single Variable Algebra

Solve: (3x-5)(4-x)

Possible Answers:

-3x^2-17x-20

-3x^2-7x-20

-3x^2-24x-20

-3x^2+7x-20

-3x^2+17x-20

Correct answer:

-3x^2+17x-20

Explanation:

Use the FOIL method to expand the binomials.

(a+b)(c+d) =ac+ad+bc+bd

The expression becomes:

(3x)(4)+(3x)(-x)+(-5)(4)+(-5)(-x)

Simplify by distribution.

12x-3x^2-20+5x

Combine like-terms.

The answer is: -3x^2+17x-20

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Example Question #61 : Foil

Simplify: $(\sqrt{12}-\sqrt{6})(\sqrt{3}+\sqrt{24})$

Possible Answers:

$9\sqrt2 -6$

$6-9\sqrt2$

$2-9\sqrt6$

$15\sqrt2 +18$

$\textup{The answer is not given.}$

Correct answer:

$9\sqrt2 -6$

Explanation:

Simplify by using the FOIL method.

(a+b)(c+d) =ac+ad+bc+bd

Use this formula to solve the binomials.

$(\sqrt{12}-\sqrt{6})(\sqrt{3}+\sqrt{24})$

$(\sqrt{12})(\sqrt{3})+(\sqrt{12})(\sqrt{24})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(\sqrt{24})$

To avoid simplifying large radicals at the end, we should factor some of the radicals before simplifying the terms.

$(\sqrt{12})(\sqrt{3})+(\sqrt{4}\times \sqrt{3})(\sqrt{4}\times \sqrt{6})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(\sqrt{4}\times \sqrt{6})$

The expression becomes:

$\sqrt{36}+(2\times \sqrt{3})(2\sqrt{6})+(-\sqrt{6})(\sqrt{3})+(-\sqrt{6})(2 \sqrt{6})$

Simplify all the terms.

$6+4\sqrt{18}-\sqrt{18}+12=6+3(\sqrt9\times \sqrt{2})-12$

$=6+3(3\sqrt{2})-12 = 9\sqrt2 -6$

The answer is: $9\sqrt2 -6$

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Example Question #85 : Understanding Quadratic Equations

Solve: (5x-10)(2x+8)

Possible Answers:

10x^2-40x-80

10x^2+60x-80

10x^2+40x-80

10x^2+20x-80

10x^2-20x-80

Correct answer:

10x^2+20x-80

Explanation:

Use the FOIL method to solve this expression.

(w+x)(y+z) = wy+wz+xy+xz

Use the template to rewrite the expression.

(5x)(2x)+(5x)(8)+(-10)(2x)+(-10)(8)

Simplify the terms.

10x^2+40x-20x-80

Combine like-terms.

The answer is: 10x^2+20x-80

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Example Question #62 : Foil

Solve: $(8x-6)(\frac{1}{x}+3)$

Possible Answers:

$\frac{8x^2+2x-3}{x}$

$\frac{24x^2+2x-6}{x}$

$\frac{8x^2+2x-18}{x}$

$\frac{24x^2-10x-6}{x}$

$\frac{24x^2+10x-6}{x}$

Correct answer:

$\frac{24x^2-10x-6}{x}$

Explanation:

Use the FOIL method to simplify this expression.

(a+b)(c+d) = ac+ad+bc+bd

Rewrite the expression.

$(8x)(\frac{1}{x})+(8x)(3)+ (-6)(\frac{1}{x})+(-6)(3)$

Simplify all terms.

$8+24x-\frac{6}{x}-18$

Combine like terms.

$24x-10-\frac{6}{x}$

Rewrite the expression using a common denominator.

$\frac{24x(x)}{x}-\frac{10(x)}{x}-\frac{6}{x}$

The answer is: $\frac{24x^2-10x-6}{x}$

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Example Question #81 : Understanding Quadratic Equations

Solve: (3x-7)(7x-1)

Possible Answers:

21x^2-46x+7

21x^2-52x+7

21x^2+52x+7

21x^2-46x-7

21x^2-52x-7

Correct answer:

21x^2-52x+7

Explanation:

Use the FOIL method to expand the terms of the binomials.

(a+b)(c+d) = ac+ad+bc+bd

(3x)(7x)+(3x)(-1)+(-7)(7x)+(-7)(-1)

21x^2-3x-49x+7

Combine like terms.

The answer is: 21x^2-52x+7

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Example Question #63 : Foil

Solve: 2(3-x)(5x+1)

Possible Answers:

-5x^3+14x+3

-10^2-32x+6

-10^2+32x+6

-10^2-28x+6

-10^2+28x+6

Correct answer:

-10^2+28x+6

Explanation:

Solve the binomials by using the FOIL method.

(3-x)(5x+1) = (3)(5x)+(3)(1)+(-x)(5x)+(-x)(1)

Simplify by distribution.

15x+3-5x^2-x

Combine like-terms.

-5x^2+14x+3

Rewrite the expression.

2(3-x)(5x+1)=2[-5x^2+14x+3] = -10^2+28x+6

The answer is: -10^2+28x+6

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Example Question #251 : Intermediate Single Variable Algebra

Solve: (9-x)(2-4x)

Possible Answers:

4x^2-54x+18

4x^2-38x+18

-4x^2-38x+18

-4x^2-22x+18

-4x^2+22x+18

Correct answer:

4x^2-38x+18

Explanation:

Use the FOIL method to simplify this expression.

(w+x)(y+z) =wy+wz+xy+xz

Follow suit using the order given for (9-x)(2-4x) .

(9)(2)+(9)(-4x)+(-x)(2)+(-x)(-4x)

Simplify the terms.

18-36x-2x+4x^2

Combine like terms and rearrange the terms from highest to lowest order.

The answer is: 4x^2-38x+18

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Example Question #90 : Understanding Quadratic Equations

Use the FOIL method to expand and simplify the expression:

(4x+4)(x-3)

Possible Answers:

4x^2+8x-12

4x^2-16x-12

4x^2-8x-12

4x^2+16x-12

4x^2-8x+12

Correct answer:

4x^2-8x-12

Explanation:

Remember, FOIL stands for First terms, Outer terms, Inner terms, Last terms, and goes as follows:

First Terms:

$({\color{Red} 4x}+4)({\color{Red} x}-3)={\color{Red} 4x^2}$

Outer Terms:

$({\color{Red} 4x}+4)(x{\color{Red} -3})=4x^2{\color{Red} -12x}$

Inner Terms:

$(4x{\color{Red} +4})({\color{Red} x}-3)=4x^2-12x{\color{Red} +4x}$

Last Terms:

$(4x{\color{Red} +4})(x{\color{Red} -3})=4x^2-12x+4x{\color{Red} -12}$

Combine like terms to give answer:

4x^2-8x-12

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Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #62 : Foil

Example Question #82 : Understanding Quadratic Equations

Example Question #241 : Intermediate Single Variable Algebra

Example Question #61 : Foil

Example Question #85 : Understanding Quadratic Equations

Example Question #62 : Foil

Example Question #81 : Understanding Quadratic Equations

Example Question #63 : Foil

Example Question #251 : Intermediate Single Variable Algebra

Example Question #90 : Understanding Quadratic Equations

All Algebra II Resources

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