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Algebra 1 : Algebra 1

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Example Questions

Example Question #1 : Simplifying Polynomials

Simplify the following expression.

$(3p^{2}+8)+(-p^{2}+5)$

Possible Answers:

$2p^{2}+13$

$2p^{2}+3$

$-3p^{2}+40$

$-3p^{2}-3$

$-3p^{2}+13$

Correct answer:

$2p^{2}+13$

Explanation:

$(3p^{2}+8)+(-p^{2}+5)$

This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.

Add like terms to solve.

$3p^{2}-p^{2}=2p^{2}$

8+5=13

Combining these terms into an expression gives us our answer.

$2p^{2}+13$

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Example Question #1 : How To Add Polynomials

Simplify the expression.

$15x^{3}y^{2}+8x^{2}+3x^{3}y^{2}-4x^{2}$

Possible Answers:

$22x^3y^{2}x^{2}$

$18x^{3}y^{2}-4x^{2}$

$18x^{3}y^{2}+4x^{2}$

None of the other answers are correct.

$22x^{6}y^{4}$

Correct answer:

$18x^{3}y^{2}+4x^{2}$

Explanation:

When simplifying polynomials, only combine the variables with like terms.

$15x^{3}y^{2}$ can be added to $3x^{3}y^{2}$ , giving $18x^{3}y^{2}$ .

$4x^{2}$ can be subtracted from $8x^{2}$ to give $4x^{2}$ .

Combine both of the terms into one expression to find the answer: $18x^{3}y^{2}+4x^{2}$

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Example Question #2 : How To Add Polynomials

Simplify the following expression.

$(5c^{2}+5)+(-5c-5)$

Possible Answers:

$5c^{2}-5c-25$

$5c^{2}-5c+10$

$5c^{2}-5c$

Correct answer:

$5c^{2}-5c$

Explanation:

$(5c^{2}+5)+(-5c-5)$

This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.

Add like terms to solve.

$5c^{2}$ and -5c have no like terms and cannot be combined with anything.

5 and -5 can be combined however:

5-5=0

This leaves us with $5c^{2}-5c$ .

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Example Question #5 : How To Add Polynomials

Find the LCM of the following polynomials:

$2x\left ( x+1 \right )$ , $4x^{2}\left ( x^{2} -1\right )$ , $6\left ( x-1 \right )$

Possible Answers:

$6x\left ( x+1 \right )\left ( x-1 \right )$

$12\left ( x+1 \right )\left ( x-1 \right )$

$12x^{2}\left ( x+1 \right )$

$12x\left ( x-1 \right )$

$12x^{2}\left ( x+1 \right )\left ( x-1 \right )$

Correct answer:

$12x^{2}\left ( x+1 \right )\left ( x-1 \right )$

Explanation:

LCM of 2,4,6=12

LCM of $x, x^{2}=x^{2}$

and since $\left ( x^{2} -1 \right )= \left ( x+1 \right )\left ( x-1 \right )$

The LCM $=12x^{2}\left ( x+1 \right )(x-1)$

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Example Question #4 : How To Add Polynomials

Add:

$\frac{x}{x^{2}-2x-3} + \frac{1}{x^{2}-2x -3}$

Possible Answers:

$\frac{x+1}{x^{2}-2x-3}$

$\frac{1}{x-3}$

$\frac{x-3}{x+1}$

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

Correct answer:

$\frac{1}{x-3}$

Explanation:

First factor the denominators which gives us the following:

$\frac{x}{\left ( x+1 \right )\left ( x-3 \right )} + \frac{1}{\left ( x+1 \right )\left ( x-3 \right )}$

The two rational fractions have a common denominator hence they are like "like fractions". Hence we get:

$\frac{x+1}{\left ( x+1 \right )\left ( x-3 \right )}$

Simplifying gives us

$\frac{1}{x-3}$

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Example Question #11 : Intermediate Single Variable Algebra

Simplify

$(2x^{2}-5) + (4x^{3}-3x^{2}+2x-1)$

Possible Answers:

$4x^{3}-6x^{2}+1x-6$

$4x^{3}-x^{2}+2x-6$

$5x^{2}+2x-6$

$5x^{2}-6$

Correct answer:

$4x^{3}-x^{2}+2x-6$

Explanation:

$(2x^{2}-5) + (4x^{3}-3x^{2}+2x-1)$

To simplify you combind like terms:

$(4x^{3}\boldsymbol{-3x^{2}+2x^{2}} +2x\boldsymbol{-1-5)}$

Answer:

$4x^{3}-x^{2}+2x-6$

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Example Question #1 : How To Add Polynomials

Combine:

3x^2y^3z+8m^4n^5-12x^2y^3z-2m^4n^5

Possible Answers:

11x^2y^3z

36x^2y^3z-16m^4n^5

21m^4n^5x^2y^3z

-9x^2y^3z+6m^4n^5

Correct answer:

-9x^2y^3z+6m^4n^5

Explanation:

When combining polynomials, only combine like terms. With the like terms, combine the coefficients. Your answer is -9x^2y^3z+6m^4n^5 .

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Example Question #22 : Polynomials

Simplify this expression: (2y)(4x^2z^2 + 2a^2b^2) + (5x^2z^2y + 7a^2b^2y)

Possible Answers:

11y + a^2 b^2 y+13 x^2 y z^2

a^2 b^2 y+13 x^2 y z^2

11 a^2 b^2 y+13 x^2 y z^2

11 a^2 b^2 y + 15 x^2 y z^2

Not able to simplify further

Correct answer:

11 a^2 b^2 y+13 x^2 y z^2

Explanation:

Don't be scared by complex terms! First, we follow our order of operations and multiply the into the first binomial. Then, we check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was 3x + 3x .

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match after we follow our order of operations! So we just add the coefficients of the matching terms and we get our answer: 11 a^2 b^2 y+13 x^2 y z^2

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Example Question #91 : Polynomial Operations

Simplify the following: (x^3+2x-1)+(-2x^3-1)

Possible Answers:

-x^3+2x

-x^3+2x-2

x^3+2x-2

x^3+2x

-x^3-2x-2

Correct answer:

-x^3+2x-2

Explanation:

To solve (x^3+2x-1)+(-2x^3-1) , identify all the like-terms and regroup to combine the values.

x^3-2x^3+2x-1-1= -x^3+2x-2

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Example Question #93 : Polynomial Operations

Evaluate the following expression:

(x^3 +3x^2 -2x-7)+(2x^3+3x+6)

Possible Answers:

2x^3 +3x^2 -x -1

3x^3 +3x^2 +x -1

4x^3 +3x^2 -x +1

3x^3 +6x^2 -2x -1

3x^3 +3x -1

Correct answer:

3x^3 +3x^2 +x -1

Explanation:

To add two polynomials together, you combine all like terms.

Combining the x^3 terms gives us 3x^3

Combining the x^2 terms gives us 3x^2 , since there is only 1 of those terms in the expression it remains the same.

Combining the terms gives us

and finally combining theconstants gives us

summing all these together gives us

3x^3 +3x^2 +x -1

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Simplifying Polynomials

Example Question #1 : How To Add Polynomials

Example Question #2 : How To Add Polynomials

Example Question #5 : How To Add Polynomials

Example Question #4 : How To Add Polynomials

Example Question #11 : Intermediate Single Variable Algebra

Example Question #1 : How To Add Polynomials

Example Question #22 : Polynomials

Example Question #91 : Polynomial Operations

Example Question #93 : Polynomial Operations

All Algebra 1 Resources

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