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Algebra 1 : How to add polynomials

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Example Questions

Example Question #1 : How To Add Polynomials

Subtract $\left ( -3x^{3}+2x^{2}-xy -13 \right )$ from $\left ( x^{5}-4x^{4}-2x^{3}-9xy \right )$ .

Possible Answers:

$x^{5}-4x^{4}+x^{3}-2x^{2}-8xy +13$

$x^{5}+4x^{4}+x^{3}+2x^{2}-8xy-13$

$x^{5}-4x^{4}-5x^{3}-2x^{2}-10xy-13$

$x^{5}-4x^{4}+x^{3}-2x^{2}+13$

$x^{5}-4x^{4}+x^{3}-8xy-13$

Correct answer:

$x^{5}-4x^{4}+x^{3}-2x^{2}-8xy +13$

Explanation:

Subtract the first expression from the second to get the following:

$x^{5}-4x^{4}-2x^{3}-9xy - \left ( -3x^{3}+2x^{2}-xy -13 \right )$

This is equal to:

$x^{5}-4x^{4}-2x^{3}-9xy+3x^{3}-2x^{2}+xy+13$

Combine like terrms:

$x^{5}-4x^{4}+x^{3}-2x^{2}-8xy+13$

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Example Question #1 : How To Add Polynomials

Simplify the following: (x^2+3.5x+10)-(5x^2-1.5x+2)

Possible Answers:

-4x^2+2x+8

-4x^2+5x+8

6x^2+5x+8

6x^2+2x+8

Correct answer:

-4x^2+5x+8

Explanation:

(x^2+3.5x+10)-(5x^2-1.5x+2)=x^2+3.5x+10-5x^2+1.5x-2

=x^2-5x^2+3.5x+1.5x+10-2=-4x^2+5x+8

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Example Question #1 : Simplifying Expressions

Simplify x(4 – x) – x(3 – x).

Possible Answers:

x²

Correct answer:

Explanation:

You must multiply out the first set of parenthesis (distribute) and you get 4x – x². Then multiply out the second set and you get –3x + x². Combine like terms and you get x.

x(4 – x) – x(3 – x)

4x – x² – x(3 – x)

4x – x² – (3x – x²)

4x – x² – 3x + x² = x

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Example Question #1 : Simplifying Polynomials

Simplify the following expression.

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

Possible Answers:

$2p^{2}+13$

$2p^{2}+3$

$-3p^{2}-3$

$-3p^{2}+13$

$-3p^{2}+40$

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 #2 : How To Add Polynomials

Simplify the expression.

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

Possible Answers:

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

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

None of the other answers are correct.

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

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

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 #3 : How To Add Polynomials

Simplify the following expression.

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

Possible Answers:

$5c^{2}-5c$

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

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

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 #74 : 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:

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

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

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

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

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

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 #6 : How To Add Polynomials

Add:

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

Possible Answers:

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

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

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

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

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 #4 : How To Add Polynomials

Simplify

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

Possible Answers:

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

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

$5x^{2}-6$

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

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 #21 : Intermediate Single Variable Algebra

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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Algebra 1 : How to add polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Add Polynomials

Example Question #1 : How To Add Polynomials

Example Question #1 : Simplifying Expressions

Example Question #1 : Simplifying Polynomials

Example Question #2 : How To Add Polynomials

Example Question #3 : How To Add Polynomials

Example Question #74 : Polynomials

Example Question #6 : How To Add Polynomials

Example Question #4 : How To Add Polynomials

Example Question #21 : Intermediate Single Variable Algebra

All Algebra 1 Resources

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