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Algebra 1 : Polynomials

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Example Questions

Example Question #1 : How To Subtract Polynomials

Simplify the expression: (5x^2z^4 + 4z^3y^3) - (2x^2z^4 - 3z^3y^3)

Possible Answers:

x^2 z^4+ y^3 z^3

Cannot be simplified further

3 x^2 z^4+7 y^3 z^3

3 x^4 z^8+7 y^6 z^6

Correct answer:

3 x^2 z^4+7 y^3 z^3

Explanation:

Don't be scared by complex terms! First, 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! So we just subtract the coefficients of the matching terms and we get our answer:

3 x^2 z^4+7 y^3 z^3

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Example Question #1 : Simplifying Polynomials

Rewrite the expression in simplest terms.

$5x^{^{3}} - 14x^{2} - 10x + 3 - (4x+3) * x^{2} - (8-10x)$

Possible Answers:

5x^3 -17x^2 - 4x - 5

5x^3 -11x^2 - 24x - 5

x^3 - 11x^2 - 5

$x^{3}-17x^{2}-5$

x^3 - 11x^2 - 20x - 5

Correct answer:

$x^{3}-17x^{2}-5$

Explanation:

In simplifying this expression, be mindful of the order of operations (parenthical, division/multiplication, addition/subtraction).

$5x^{^{3}} - 14x^{2} - 10x + 3 - (4x+3) * x^{2} - (8-10x)$

Since operations invlovling parentheses occur first, distribute the factors into the parenthetical binomials. Note that the x^2 outside the first parenthetical binomial is treated as -x^2 since the parenthetical has a negative (minus) sign in front of it. Similarly, multiply the members of the expression in the second parenthetical by because of the negative (minus) sign in front of it. Distributing these factors results in the following polynomial.

5x^3 - 14x^2 - 10x + 3 - 4x^3 - 3x^2 - 8 + 10x

Now like terms can be added and subtracted. Arranging the members of the polynomial into groups of like terms can help with this. Be sure to retain any negative signs when rearranging the terms.

5x^3 - 4x^3 -14x^2 - 3x^2 - 10x + 10x + 3 - 8

Adding and subtracting these terms results in the simplified expression below.

x^3 - 17x^2 -5

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Example Question #3 : Solving Rational Expressions

Solve:

$\frac{5}{x+1}-\frac{3x}{\left ( x+1 \right )\left ( x-2 \right )}= \frac{3}{x-2}$

Possible Answers:

$\frac{13}{2}$

Correct answer:

Explanation:

First we convert each of the denominators into an LCD which gives us the following:

$\frac{5\left ( x-2 \right )}{\left ( x+1 \right )\left ( x-2 \right )}- \frac{3x}{\left ( x+1 \right )\left ( x-2 \right )}= \frac{3\left ( x+1 \right )}{\left ( x+1 \right )\left ( x-2 \right )}$

Now we add or subtract the numerators which gives us:

$5\left ( x-2 \right )-3x= 3\left ( x+1 \right )$

Simplifying the above equation gives us the answer which is:

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Example Question #111 : Polynomials

Simplify the following:

4x^3-2x(x-2)(x+3)

Possible Answers:

8x^3-2x+16

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

4x^3-2x^3-2x^2+12x

4x^3-2x(x^2+x-6)

None of the other answers are correct.

Correct answer:

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

Explanation:

4x^3-2x(x-2)(x+3)

First, FOIL the two binomials:

4x^3-2x(x^2+x-6)

Then distribute the through the terms in parentheses:

4x^3-2x^3-2x^2+12x

Combine like terms:

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

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Example Question #11 : Intermediate Single Variable Algebra

Simplify.

$(4a^{2}b+2ab) - (3a^{2}b+4ab+2)$

Possible Answers:

$a^{2}b+6ab+2$

$a^{2}b-2ab-2$

$a^{2}b+2ab-2$

$a^{2}b-6ab-2$

Correct answer:

$a^{2}b-2ab-2$

Explanation:

Simplify

$(4a^{2}b+2ab) - (3a^{2}b+4ab+2)$

Distribute the negative: $\boldsymbol{-}3a^{2}b\boldsymbol{-}4ab\boldsymbol{-}2$

Then combinde like terms

$\mathbf{\boldsymbol{-}3a^{2}b+4a^{2}b}(\mathbf{\boldsymbol{-}4ab+2ab})\boldsymbol{-}2$

Answer:

$a^{2}b-2ab-2$

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Example Question #4 : How To Subtract Polynomials

Subtract:

$(7.5x^{2} + 1.4x - 4.6) - (x^{2} + 6.2x - 3.5)$

Possible Answers:

$6.5x^{2} - 4.8x - 1.1$

$7.5x^{2} - 4.8x - 1.1$

$7.5x^{2} +7.2x - 1.1$

$6.5x^{2} +7.2x - 1.1$

$6.5x^{2} - 4.8x - 8.1$

Correct answer:

$6.5x^{2} - 4.8x - 1.1$

Explanation:

$(7.5x^{2} + 1.4x - 4.6) - (x^{2} + 6.2x - 3.5)$

$= 7.5x^{2} + 1.4x - 4.6 - x^{2} - 6.2x + 3.5$

$= 7.5x^{2} - 1x^{2} + 1.4x- 6.2x - 4.6 + 3.5$

$= 6.5x^{2} - 4.8x - 1.1$

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Example Question #82 : Expressions

Subtract:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

Possible Answers:

$\frac{1}{4}x + \frac{5}{6}$

$-\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{1}{9}$

$\frac{1}{4}x + \frac{1}{2}$

$-\frac{1}{4}x + \frac{1}{2}$

Correct answer:

$\frac{1}{4}x + \frac{5}{6}$

Explanation:

$\left (\frac{1}{2}x + \frac{2}{3} \right ) - \left (\frac{1}{4}x - \frac{1}{6} \right )$

$=\frac{1}{2}x + \frac{2}{3} - \frac{1}{4}x + \frac{1}{6}$

$=\frac{1}{2}x - \frac{1}{4}x + \frac{2}{3} + \frac{1}{6}$

$=\frac{2}{4}x - \frac{1}{4}x + \frac{4}{6} + \frac{1}{6}$

$=\frac{1}{4}x + \frac{5}{6}$

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Example Question #112 : Polynomials

Subtract:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

Possible Answers:

$6.5x^{2} + 5.6x - 3.1$

$6.5x^{2} + 5.6x - 6.1$

$6.5x^{2} -0.8x - 3.1$

$6.5x^{2} -0.8x - 6.1$

$7.5x^{2} + 5.6x - 3.1$

Correct answer:

$6.5x^{2} + 5.6x - 3.1$

Explanation:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

$= 7.5x^{2} + 2.4x - 4.6 - x^{2} + 3.2x +1.5$

$= 7.5x^{2} - 1x^{2} + 2.4x + 3.2x - 4.6 +1.5$

$= 6.5x^{2} + 5.6x - 3.1$

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Example Question #1 : Elementary Operations

Subtract:

$\left (\frac{3}{4}x + \frac{2}{5} \right ) - \left (\frac{1}{8}x - \frac{1}{10} \right )$

Possible Answers:

$\frac{5}{8}x - \frac{1}{2}$

$\frac{5}{8}x + \frac{3}{10}$

$\frac{5}{8}x + \frac{1}{15}$

$\frac{5}{8}x - \frac{3}{10}$

$\frac{5}{8}x + \frac{1}{2}$

Correct answer:

$\frac{5}{8}x + \frac{1}{2}$

Explanation:

$\left (\frac{3}{4}x + \frac{2}{5} \right ) - \left (\frac{1}{8}x - \frac{1}{10} \right )$

$=\frac{3}{4}x + \frac{2}{5} - \frac{1}{8}x + \frac{1}{10}$

$=\frac{3}{4}x- \frac{1}{8}x + \frac{2}{5} + \frac{1}{10}$

$=\frac{6}{8}x- \frac{1}{8}x + \frac{4}{10} + \frac{1}{10}$

$=\frac{5}{8}x + \frac{5}{10}$

$=\frac{5}{8}x + \frac{1}{2}$

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Example Question #21 : Polynomials

Simplify the following expression.

(6x^2-9x+1)-(4x^2+2x-4)

Possible Answers:

2x^2-11x+5

10x^2-7x-3

-2x^2+11x-5

x^2+8x-12

8x^2-7x+3

Correct answer:

2x^2-11x+5

Explanation:

(6x^2-9x+1)-(4x^2+2x-4)

First, we will need to distribute the minus sign.

6x^2-9x+1-4x^2-2x+4)

Then, combine like terms.

(6x^2-4x^2)+(-9x-2x)+(1+4)

2x^2-11x+5

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Algebra 1 : Polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Subtract Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #3 : Solving Rational Expressions

Example Question #111 : Polynomials

Example Question #11 : Intermediate Single Variable Algebra

Example Question #4 : How To Subtract Polynomials

Example Question #82 : Expressions

Example Question #112 : Polynomials

Example Question #1 : Elementary Operations

Example Question #21 : Polynomials

All Algebra 1 Resources

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