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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #43 : Polynomials

Simplify: (2x^2+3x+2)(x^2-4x-5)

Possible Answers:

2x^4+5x^3-24x^2-23x-10

2x^4+5x^3-24x^2-7x-10

2x^4-5x^3-20x^2-7x-10

2x^4-5x^3-20x^2-23x-10

3x^2-12x-10

Correct answer:

2x^4-5x^3-20x^2-23x-10

Explanation:

In order to multiply both terms, first distribute the first term of the first polynomial with the the second polynomial.

2x^2(x^2-4x-5) = 2x^4-8x^3-10x^2

Repeat the process for the second and third terms.

3x(x^2-4x-5)=3x^3-12x^2-15x

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

Add all the trinomials together and combine like-terms.

(2x^4-8x^3-10x^2)+(3x^3-12x^2-15x)+(2x^2-8x-10)

The answer is: 2x^4-5x^3-20x^2-23x-10

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Example Question #41 : Polynomials

Simplify: 4x^2-x+9x^2+5x^3-11x

Possible Answers:

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

x^3+13x^2-12x

5x^3+13x^2

5x^3+13x^2-x

5x^3+13x^2-12x

Correct answer:

5x^3+13x^2-12x

Explanation:

To simplify this expression, combine all like terms:

4x^2+9x^2=13x^2

-x-11x=-12x

Put your simplified terms together:

5x^3+13x^2-12x

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Example Question #1181 : Algebra Ii

Simplify: 9(x^2-4)+5(2x+3)

Possible Answers:

9x^2+10x-21

3x^2+10x-21

9x^2+10x-20

9x^2+2x-21

9x^2+10x+21

Correct answer:

9x^2+10x-21

Explanation:

The first step here is to use the distributive property:

9x^2-36+10x+15

Now combine your like terms to get your final answer:

9x^2+10x-21

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Example Question #46 : Polynomials

Simplify the polynomial.

4x^2 + 7x -3 -2x^2 + 6x + 9

Possible Answers:

2x^2+13x-6

2x^2-13x+6

2x^2-13x-6

2x^2+13x+6

-2x^2+13x+6

Correct answer:

2x^2+13x+6

Explanation:

Simplify the polynomial.

4x^2+7x-3-2x^2+6x+9

Step 1: Rearrange the expression so that like terms are next to each other.

Remember: Like terms are terms with the same type of variable.

4x^2-2x^2+7x+6x-3+9

Step 2: Simplify by adding or subtracting like terms.

2x^2+13x+6

Solution:

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Example Question #47 : Polynomials

Simplify this polynomial: 5x^4+x^4+3x^2-8+3x-x(3+8x)-10

Possible Answers:

6x^4+3x^2-8x-18

6x^4+11x^2-18

6x^4-5x^2-18

6x^4+11x^2+6x-18

None of the other answers.

Correct answer:

6x^4-5x^2-18

Explanation:

In order to correctly simplify this problem you must pay attention to which terms are actually considered "like terms" and pay attention to signs. For instance 6x and 6x^2 are not like terms. Neither are 3 and 3x.

5x^4+x^4+3x^2-8+3x-x(3+8x)-10

Start by distributing within the parenthesis:

5x^4+x^4+3x^2-8+3x-3x-8x^2-10

Next simplify the like terms based on your preference. We will start with the highest powers (largest exponents):

6x^4+3x^2-8+3x-3x-8x^2-10

Now the squared exponents:

5x^4+x^4-5x^2-8+3x-3x-10

Now the x terms cancel and simplify the constants:

6x^4-5x^2-18

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Example Question #4 : Factoring Polynomials

Find the zeros.

$f(x)=x^{3}-1$

Possible Answers:

x=1

x=0

x=-1

x=1,-1

x=10

Correct answer:

x=1

Explanation:

This is a difference of perfect cubes so it factors to (x-1)(x^2+x+1) . Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the -axis. Therefore, your answer is only 1.

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Example Question #1182 : Algebra Ii

Find the zeros.

f(x)=2x^5-8x^3+8x

Possible Answers:

$x=\sqrt{2}$

$x= \sqrt{-2}}$

x=0

x=2,0

$x=0, \sqrt{2}, -\sqrt{2 }$

Correct answer:

$x=0, \sqrt{2}, -\sqrt{2 }$

Explanation:

Factor the equation to 2x(x^4-4x^2+4) . Set 2x=0 and get one of your 's to be . Then factor the second expression to (x^2-2) (x^2-2) . Set them equal to zero and you get $\pm \sqrt{2}$ .

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Example Question #361 : College Algebra

Factor the polynomial:

$16x^{3} -48x^{2} + 32x$

Possible Answers:

8x(x-2)(x+1)

16x(x+2)(x+1)

16x(x+2)(x-1)

16x(x-2)(x-1)

8x(x-2)(x-1)

Correct answer:

16x(x-2)(x-1)

Explanation:

First, begin by factoring out a common term, in this case 16x :

$16x^{3} -48x^{2} + 32x = 16x(x^{2}-3x+2)$

Then, factor the terms in parentheses by finding two integers that sum to and multiply to :

16x(x-2)(x-1)

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Example Question #2 : How To Factor A Variable

Factor the following expression:

a^3b^2 + a^4b + a^2bc^3 - a^3b^3c^2

Possible Answers:

a^2b(ab + a^2 + c^3 - ab^2c^2)

a^3b(b + a + c^3 - b^2c^2)

abc(a^2b + a^2 + ac^2 - a^2b^2c)

a^2bc(ab + a^2 + c^2 - ab^2c)

Correct answer:

a^2b(ab + a^2 + c^3 - ab^2c^2)

Explanation:

Here you have an expression with three variables. To factor, you will need to pull out the greatest common factor that each term has in common.

Only the last two terms have so it will not be factored out. Each term has at least a^2 and so both of those can be factored out, outside of the parentheses. You'll fill in each term inside the parentheses with what the greatest common factor needs to be multiplied by to get the original term from the original polynomial:

a^3b^2 + a^4b + a^2bc^3 - a^3b^3c^2 = a^2b(ab + a^2 + c^3 - ab^2c^2)

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Example Question #4232 : Algebra 1

Which of the following values of would make the trinomial $\small \small \small x^{2}+Bx+36$ prime?

Possible Answers:

Correct answer:

Explanation:

For the trinomial $\small \small \small x^{2}+Bx+36$ to be factorable, we would have to be able to find two integers with product 36 and sum ; that is, would have to be the sum of two integers whose product is 36.

Below are the five factor pairs of 36, with their sum listed next to them. must be one of those five sums to make the trinomial factorable.

1, 36: 37

2, 18: 20

3, 12: 15

4, 9: 13

6, 6: 12

Of the five choices, only 16 is not listed, so if B = 16 , then the polynomial is prime.

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #43 : Polynomials

Example Question #41 : Polynomials

Example Question #1181 : Algebra Ii

Example Question #46 : Polynomials

Example Question #47 : Polynomials

Example Question #4 : Factoring Polynomials

Example Question #1182 : Algebra Ii

Example Question #361 : College Algebra

Example Question #2 : How To Factor A Variable

Example Question #4232 : Algebra 1

All Algebra II Resources

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