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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Simplifying Polynomials

Simplify the following expressions by combining like terms:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Distribute the negative sign through all terms in the parentheses:

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

Add the second half of the expression, $x^{5}-4x^{4}-2x^{3}-9xy$ to get:

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

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Example Question #42 : How To Add Polynomials

Simplify the following expression.

$(2x^{2}+7x-11)+(8x^{2}-5x+19)$

Possible Answers:

$16x^{2}-35x-209$

None of the other answers.

$10x^{2}+12x+30$

$10x^{2}-2x-8$

Correct answer:

Explanation:

Place like terms (with the same variable and exponent) together.

$(2x^{2}+8x^{2})+(7x-5x)+(-11+19)$

Add the like terms.

$10x^{2}+2x+8$

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Example Question #42 : How To Add Polynomials

Add (2x+8) , $(4x^{2}-5x+18)$ , and $(9y-x^{2})$ .

Possible Answers:

$-4x^{2}-3x+26+9y$

None of the other answers.

$3x^{2}+10x+26+9y$

$-3x^{2}-3x-10+9y$

Correct answer:

Explanation:

Add (2x+8) , $(4x^{2}-5x+18)$ , and $(9y-x^{2})$ .

Group like terms (with the same variable and exponent). Line up the polynomials in columns to make grouping the terms from several polynomials easier. Then add down.

2x+8

$4x^{2}-5x+18$

$-x^{2}$ +9y

$3x^{2}-3x+26+9y$

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Example Question #1 : How To Find The Degree Of A Polynomial

Give the degree of the polynomial.

$6x^{5}+5x^{4}-3x^{2}+x^{7}$

Possible Answers:

Correct answer:

Explanation:

$6x^{5}+5x^{4}-3x^{2}+x^{7}$

The degree of an individual term of a polynomial is the exponent of its variable; the exponents of the terms of this polynomial are, in order, 5, 4, 2, and 7.

The degree of the polynomial is the highest degree of any of the terms; in this case, it is 7.

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

$ab^{2}+a^{2}b^{3}-a^{3}b^{1}$

Possible Answers:

Correct answer:

Explanation:

$ab^{2}+a^{2}b^{3}-a^{3}b^{1}$

To find the degree of the polynomial, you first have to identify each term [term is for example $ab^{2}$ ], so to find the degree of each term you add the exponents.

EX: $ab^{2}$ $= a^{1}b^{2} = 1+2= 3$ - Degree of 3

Highest degree is $5\rightarrow$ $a^{2}b^{3}= 2+3= 5$

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the polynomial?

12x^2y^3+6xy^4z-2xz+1

Possible Answers:

Correct answer:

Explanation:

To find the degree of the polynomial, add up the exponents of each term and select the highest sum.

12x²y³: 2 + 3 = 5

6xy⁴z: 1 + 4 + 1 = 6

2xz: 1 + 1 = 2

The degree is therefore 6.

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Example Question #1 : How To Find The Degree Of A Polynomial

x^5+x^3+x^2+x+1

What is the degree of the polynomial?

Possible Answers:

Correct answer:

Explanation:

The degree is the highest exponent value of the variables in the polynomial.

Here, the highest exponent is x⁵, so the degree is 5.

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Example Question #1 : How To Find The Degree Of A Polynomial

Simplify:

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

Possible Answers:

None of the above

-1

Correct answer:

-1

Explanation:

The given expression can be re-written as:

$\frac{2x-5}{\left -(2x-5 \right )}$

Cancel (2x - 5):

$\frac{1}{-1} = -1$

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Example Question #1 : How To Find The Degree Of A Polynomial

Find the degree of the polynomial: $y=\frac{1}{x}-\frac{1}{x^2}$

Possible Answers:

$\textup{These are not polynomial terms.}$

Correct answer:

$\textup{These are not polynomial terms.}$

Explanation:

The polynomial terms may only have variables raised to positive integer exponents. No square roots, fraction powers, and variables in the denominator are allowed.

The correct answer is:

$\textup{These are not polynomial terms.}$

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Example Question #1 : How To Find The Degree Of A Polynomial

What is the degree of the following polynomial? y=6x^5-2x^2+3x^6+x-3x^4

Possible Answers:

Correct answer:

Explanation:

The degree of the polynomial is the highest power in the polynomial.

The highest power given is the term: 3x^6

Therefore, the degree of the polynomial is .

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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #21 : Simplifying Polynomials

Example Question #42 : How To Add Polynomials

Example Question #42 : How To Add Polynomials

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

Example Question #1 : How To Find The Degree Of A Polynomial

All Algebra 1 Resources

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