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ACT Math : Algebra

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14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1121 : Algebra

Distribute:

$\displaystyle (3x+5)(x+2)$

Possible Answers:

3x+10 $\displaystyle 3x+10$

3x^2+10 $\displaystyle 3x^2+10$

$\displaystyle 3x^2+11x+10$

$\displaystyle 3x^2+11x-10$

Correct answer:

$\displaystyle 3x^2+11x+10$

Explanation:

FOIL using the distributive property:

$\displaystyle (3x+5)(x+2)=3x^2+6x+5x+10=3x^2+11x+10$

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Example Question #1122 : Algebra

Distribute:

$(2x+4)^{2}$ $\displaystyle (2x+4)^{2}$

Possible Answers:

4x^2+16 $\displaystyle 4x^2+16$

4x^2+8 $\displaystyle 4x^2+8$

$4x^{2}+8x+16$ $\displaystyle 4x^{2}+8x+16$

$\displaystyle 4x^2+16x+16$

Correct answer:

$\displaystyle 4x^2+16x+16$

Explanation:

FOIL using the distributive property.

$\displaystyle (2x+4)^2=4x^2+8x+8x+16=4x^2+16x+16$

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Example Question #1123 : Algebra

Distribute:

$(x^{2}-3)^{2}$ $\displaystyle (x^{2}-3)^{2}$

Possible Answers:

x^4+9 $\displaystyle x^4+9$

$\displaystyle x^4+6x^2+9$

$\displaystyle x^4+6x^2-9$

$\displaystyle x^4-6x^2+9$

Correct answer:

$\displaystyle x^4-6x^2+9$

Explanation:

FOIL using the distributive property.

$\displaystyle x^4-3x^2-3x^2+9=x^4-6x^2+9$

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Example Question #1124 : Algebra

Distribute:

$\displaystyle (2x+3)(x^2-4)$

Possible Answers:

$\displaystyle 2x^3-3x^2-8x-12$

$\displaystyle 2x^3+3x^2-8x+12$

$\displaystyle 2x^3+3x^2-8x-12$

$\displaystyle 2x^3+3x^2+8x-12$

Correct answer:

$\displaystyle 2x^3+3x^2-8x-12$

Explanation:

FOIL using the distributive property.

$\displaystyle 2x^3-8x+3x^2-12=2x^3+3x^2-8x-12$

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Example Question #1125 : Algebra

Distribute:

$\displaystyle (x-1)(2x+7)$

Possible Answers:

$\displaystyle 2x^2+5x+7$

$\displaystyle 2x^2-5x-7$

$\displaystyle 2x^2+5x-7$

$\displaystyle -2x^2+5x-7$

Correct answer:

$\displaystyle 2x^2+5x-7$

Explanation:

Use the distributive property to FOIL

$\displaystyle 2x^2+7x-2x-7$

Simplify.

$\displaystyle 2x^2+5x-7$

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Example Question #1126 : Algebra

Distribute:

(x-5)^2 $\displaystyle (x-5)^2$

Possible Answers:

$\displaystyle 2x^2-10x+25$

$\displaystyle x^2-10x+25$

$\displaystyle x^2+10x+25$

$\displaystyle x^2+10x-25$

Correct answer:

$\displaystyle x^2-10x+25$

Explanation:

FOIL using the distributive property.

$\displaystyle (x-5)(x-5)=x^2-5x-5x+25$

Simplify.

$\displaystyle x^2-10x+25$

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Example Question #1127 : Algebra

Distribute:

$\displaystyle (4x+6)(15-x)$

Possible Answers:

$\displaystyle 4x^2+54x+90$

$\displaystyle 4x^2+54x+45$

$\displaystyle 2x^2+54x+90$

$\displaystyle 16x^2+54x+90$

Correct answer:

$\displaystyle 4x^2+54x+90$

Explanation:

Use the distributive property to FOIL.

$\displaystyle 60x-4x^2+90-6x$

Simplify.

$\displaystyle 4x^2+54x+90$

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Example Question #1128 : Algebra

$\displaystyle (x-5)(x+5)=$

Possible Answers:

x^2-25 $\displaystyle x^2-25$

$\displaystyle x^2+10x-25$

$\displaystyle x^2+5x-25$

$\displaystyle x^2-5x-25$

Correct answer:

x^2-25 $\displaystyle x^2-25$

Explanation:

Foil using the distributive property.

$\displaystyle x^2+5x-5x-25$

=x^2-25 $\displaystyle =x^2-25$

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Example Question #1129 : Algebra

$\displaystyle (2x+3)^2$

Possible Answers:

$\displaystyle 4x^2+6x+9$

$\displaystyle 2x^2+12x+9$

$\displaystyle 4x^2+12x+3$

$\displaystyle 4x^2+12x+9$

Correct answer:

$\displaystyle 4x^2+12x+9$

Explanation:

FOIL using the distributive property.

$\displaystyle (2x+3)(2x+3)=4x^2+6x+6x+9$

$\displaystyle =4x^2+12x+9$

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Example Question #1130 : Algebra

$\displaystyle (x-3)(2+x)=$

Possible Answers:

x^2-x-6 $\displaystyle x^2-x-6$

$\displaystyle 2x^2-x-6$

$\displaystyle x^2-3x-6$

$\displaystyle x^2-2x-6$

Correct answer:

x^2-x-6 $\displaystyle x^2-x-6$

Explanation:

FOIL using the distributive property.

$\displaystyle (x-3)(2+x)=2x+x^2-6-3x$

$\displaystyle =x^2-x-6$

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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1121 : Algebra

Example Question #1122 : Algebra

Example Question #1123 : Algebra

Example Question #1124 : Algebra

Example Question #1125 : Algebra

Example Question #1126 : Algebra

Example Question #1127 : Algebra

Example Question #1128 : Algebra

Example Question #1129 : Algebra

Example Question #1130 : Algebra

All ACT Math Resources

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