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Algebra 1 : Polynomial Operations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #33 : How To Subtract Polynomials

Subtract the polynomials 3x^2-3x-6 and -2x^2-x-3

Possible Answers:

5x^2-2x-3

x^2-2x-9

5x^2-4x-9

5x^2-4x-3

x^2-4x-9

Correct answer:

5x^2-2x-3

Explanation:

Set up an expression and enclose both polynomials with parentheses.

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

Remove the parentheses and distribute the negative sign through each term in the second polynomial.

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

Combine like-terms.

The answer is: 5x^2-2x-3

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Example Question #33 : How To Subtract Polynomials

Translate and simplify:

The sum of

$\left (x^{3}-2x^{2}+3x -5 \right )$

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

subtracted from

$\left ( -3x^{3}+5x^{2} -7x+15\right )$ .

Possible Answers:

$-2x^{3}+12x^{2}-10x+11$

$2x^{3}-2x^{2}+10x-11$

$-2x^{3}+2x^{2}-10x+11$

$-6x^{3}+2x^{2}-10x+29$

$2x^{3}-12x^{2}+10x-11$

Correct answer:

$-2x^{3}+12x^{2}-10x+11$

Explanation:

Sum the first two expressions:

$\left ( x^{3}-2x^{2}+3x -5 \right )$

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

$=-x^{3}-7x^{2}+3x+4$

Subtract the sum from $-3x^{3}+5x^{2}-7x +15$ to get:

$-3x^{3}+5x^{2}-7x+15 -( -x^{3}-7x^{2}+3x+4)$

By combining like terms we get:

$-2x^{3}+12x^{2}-10x +11$

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Example Question #2161 : Sat Mathematics

Simplify the following expression:

$(2q^{2}+4q+7)-(3q^{2}-5)$

Possible Answers:

$-3q^{2}+12$

-q^2+4q+2

$-q^{2}+4q+12$

$-5q^{2}+4q+2$

Correct answer:

$-q^{2}+4q+12$

Explanation:

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

Add like terms together:

$2q^{2}-3q^{2}=-1q^{2}=-q^2$

has no like terms.

7-(-5)=12

Combine these terms into one expression to find the answer:

$-q^{2}+4q+12$

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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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Algebra 1 : Polynomial Operations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #33 : How To Subtract Polynomials

Example Question #33 : How To Subtract Polynomials

Example Question #2161 : Sat Mathematics

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

All Algebra 1 Resources

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