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GED Math : GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #33 : Simplifying, Distributing, And Factoring

Factor completely:

$6t ^{2} + t - 15$

Possible Answers:

$\left ( 3t + 5 \right )\left ( 2t - 3 \right )$

$\left ( 3t - 5 \right )\left ( 2t + 3 \right )$

$\left ( 6t - 5 \right )\left ( t + 3 \right )$

$\left ( 6t + 5 \right )\left ( t - 3 \right )$

Correct answer:

$\left ( 3t + 5 \right )\left ( 2t - 3 \right )$

Explanation:

For a quadratic trinomial with a quadratic coefficient other than 1, use the factoring by grouping method.

First, find two integers whose product is $6 \times (-15) = -90$ (the product of the quadratic and constant coefficients) and whose sum is 1 (the implied coefficient of ). By trial and error, we find that these are -9, 10 .

Split the linear term accordingly, then factor by grouping, as follows.

$6t ^{2} + t - 15$

$= 6t ^{2} - 9t +10 t - 15$

$=\left ( 6t ^{2} - 9t \right )+\left (10 t - 15 \right )$

$= \left ( 3t \cdot 2t - 3t \cdot 3 \right )+\left (5 \cdot 2t - 5 \cdot 3 \right )$

$= 3t \left ( 2t - 3 \right )+ 5 \left ( 2t - 3 \right )$

$=\left ( 3t + 5 \right )\left ( 2t - 3 \right )$

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Example Question #591 : Ged Math

Factor:

$4y^{3} - 12y ^{2}- 72y$

Possible Answers:

y (y+2)(4y-9)

y (y-6)(4y+3)

4y (y-6)(y+3)

4y (y+2)(y-9)

Correct answer:

4y (y-6)(y+3)

Explanation:

The greatest common factor of the terms is , so factor it out:

$4y^{3} - 12y ^{2}- 72y$

$=4y \cdot y^{2} - 4y \cdot 3y - 4y \cdot 18$

$=4y \left ( y^{2} - 3y - 18 \right )$

The trinomial might be able to be factored as

(y+A)(y + B) ,

where AB = -18 and A + B = -3 .

By trial and error, we find that

A = -6 , B = 3 ,

so the factorization becomes

4y (y-6)(y+3) .

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Example Question #33 : Simplifying, Distributing, And Factoring

Decrease 8t + 72 by 40%. Which of the following will this be equal to?

Possible Answers:

4.8t + 43.2

4.8t + 72

3.2t + 28.8

3.2t + 72

Correct answer:

4.8t + 43.2

Explanation:

A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6.

Therefore, 8t + 72 decreased by 40% is 0.6 times this, or

$0.6 \left (8t + 72 \right ) =4.8t + 43.2$ .

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Example Question #34 : Simplifying, Distributing, And Factoring

Increase 8x + 9y by 20%. Which of the following will this be equal to?

Possible Answers:

8.2x+9.2y

9.6x + 10.8 y

9x + 10y

9.2x+10 y

Correct answer:

9.6x + 10.8 y

Explanation:

A number increased by 20% is equivalent to 100% of the number plus 20% of the number. This is taking 120% of the number, or, equivalently, multiplying it by 1.2.

Therefore, 8x + 9y increased by 20% is 1.2 times this, or

$1.2 \left (8x + 9y \right ) = 1.2 \cdot 8x + 1.2 \cdot 9y = 9.6x + 10.8 y$ .

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Example Question #35 : Simplifying, Distributing, And Factoring

Which of the following is a prime factor of $n^{4} - 16n^{2} - 225$ ?

Possible Answers:

$n^{2}+9$

$n^{2}+3$

$n^{2}+25$

$n^{2}+75$

Correct answer:

$n^{2}+9$

Explanation:

This can be most easily solved by first substituting for $n^{2}$ , and, subsequently, $t^{2}$ for $n^{4}$ :

$n^{4} - 16n^{2} - 225$

$= t^{2} - 16t - 225$

This becomes quadratic in the new variable, and can be factored as

$\left (t +\; \; \right )\left (t +\; \; \right )$ ,

filling out the blanks with two numbers whose sum is and whose product is . Through some trial and error, the numbers can be seen to be 9, -25 .

Therefore, after factoring and substituting back,

$n^{4} - 16n^{2} - 225$

$= t^{2} - 16t - 225$

= (t+9)(t-25)

$= (n^{2}+9)(n^{2}-25)$

The first factor, the sum of squares, is prime. The second factors as the difference of squares, so the final factorization is

$(n^{2}+9)(n+5)(n-5)$ .

Of the choices given, $n^{2}+9$ is correct.

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Example Question #41 : Simplifying, Distributing, And Factoring

A triangle has a base of x-2 ft and height of 2x+2 ft. What is the area (in square feet) of the triangle?

Possible Answers:

$2x^{2}+2x-4$

x^2-x-2

$2x^{2}-2x-4$

Correct answer:

x^2-x-2

Explanation:

The area of a triangle is: $A= \frac{1}{2}bh$

Use the FOIL Method to simplify.

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

$= \frac{1}{2}((x)(2x)) + (x)(2)+ (-2)(2x)-4)$

$= \frac{1}{2}(2x^2+2x-4x-4)$

$= \frac{1}{2}(2x^2-2x-4)$

A = x^2 - x -2

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Example Question #41 : Simplifying, Distributing, And Factoring

Simplify

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

Possible Answers:

x - 32

9x - 8

9x - 32

x - 8

Correct answer:

x - 32

Explanation:

The first step is to distribute the number outside of the parenthesis to the values inside the parenthesis.

(5x - 20) - (4x + 12)

Then in order to simplify you would combine like terms.

5x - 4x = x .

-20 - 12 = -32

x - 32

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Example Question #43 : Algebra

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

Possible Answers:

$-\frac{21}{13}$

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

$-\frac{9}{13}$

$\frac{9}{13}$

$\frac{7}{9}$

Correct answer:

$-\frac{21}{13}$

Explanation:

Distribute the terms on both sides.

3(x)+3(5) = -2(5x)+(-2)(3)

3x+15 = -10x-6

Add 10x on both sides.

3x+15 +10x= -10x-6+10x

13x+15 = -6

Subtract 15 on both sides.

13x+15 -15= -6-15

13x =-21

Divide by 13 on both sides.

$\frac{13x}{13} =\frac{-21}{13}$

The answer is: $-\frac{21}{13}$

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Example Question #41 : Algebra

Solve: 3x+7 = -19(-2x)

Possible Answers:

$-\frac{26}{5}$

$-\frac{1}{5}$

$\frac{7}{18}$

$\frac{1}{5}$

Correct answer:

$\frac{1}{5}$

Explanation:

Simplify the right side.

3x+7 =38x

Subtract on both sides.

3x+7-3x =38x-3x

7= 35x

Divide both sides by 35.

$\frac{7}{35}=\frac{ 35x}{35}$

The answer is: $\frac{1}{5}$

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Example Question #41 : Algebra

Simplify by distributing:

-7 (3x + 8y - 7z )

Possible Answers:

-21 x -56y+49z

-21 x +56y+49z

-21 x +56y-49z

-21 x -56y-49z

Correct answer:

-21 x -56y+49z

Explanation:

Using the Distributive Property of Multiplication over Addition, multiply by each of the terms between the parentheses:

-7 (3x + 8y - 7z )

$=(-7 ) \cdot 3x +(-7 ) \cdot 8y - (-7 ) \cdot 7z$

Multiply out each coefficient:

= -21 x +(-56)y - (-49)z

Simplify the addition and subtraction of the resulting negatives in the second and third terms:

= -21 x -56y+49z

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All GED Math Resources

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #33 : Simplifying, Distributing, And Factoring

Example Question #591 : Ged Math

Example Question #33 : Simplifying, Distributing, And Factoring

Example Question #34 : Simplifying, Distributing, And Factoring

Example Question #35 : Simplifying, Distributing, And Factoring

Example Question #41 : Simplifying, Distributing, And Factoring

Example Question #41 : Simplifying, Distributing, And Factoring

Example Question #43 : Algebra

Example Question #41 : Algebra

Example Question #41 : Algebra

All GED Math Resources

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