Algebra Review Practice Test

1) Evaluate x^3 + 2x - 4 when x=-2

To evaluate the expression x^3 + 2x - 4 when x = -2, we substitute -2 for x in the expression. This gives us (-2)^3 + 2(-2) - 4. Simplifying further, we get -8 + (-4) - 4, which equals -16. Therefore, the correct answer is -16.

Explanation

To evaluate the expression x^3 + 2x - 4 when x = -2, we substitute -2 for x in the expression. This gives us (-2)^3 + 2(-2) - 4. Simplifying further, we get -8 + (-4) - 4, which equals -16. Therefore, the correct answer is -16.

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2) Classify as a mononomial, binomial, or trinomial 3x^2

The given expression, 3x^2, is a mononomial because it consists of a single term with a degree of 2. In a mononomial, there is only one variable raised to a power and no addition or subtraction of terms. In this case, the variable is x and it is raised to the power of 2, making it a mononomial.

Explanation

The given expression, 3x^2, is a mononomial because it consists of a single term with a degree of 2. In a mononomial, there is only one variable raised to a power and no addition or subtraction of terms. In this case, the variable is x and it is raised to the power of 2, making it a mononomial.

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3) Hint foil method: (2x+3)(x-2) Options: A. 2x^2-x-6 B. 2x-x-6 C.x^2-x-6 D. None

The given expression is (2x+3)(x-2), which can be expanded using the foil method. The first terms of each binomial are multiplied together (2x * x = 2x^2), the outer terms are multiplied together (2x * -2 = -4x), the inner terms are multiplied together (3 * x = 3x), and the last terms of each binomial are multiplied together (3 * -2 = -6). Combining all the terms, we get 2x^2 - 4x + 3x - 6, which simplifies to 2x^2 - x - 6. Therefore, option A, 2x^2 - x - 6, is the correct answer.

Explanation

The given expression is (2x+3)(x-2), which can be expanded using the foil method. The first terms of each binomial are multiplied together (2x * x = 2x^2), the outer terms are multiplied together (2x * -2 = -4x), the inner terms are multiplied together (3 * x = 3x), and the last terms of each binomial are multiplied together (3 * -2 = -6). Combining all the terms, we get 2x^2 - 4x + 3x - 6, which simplifies to 2x^2 - x - 6. Therefore, option A, 2x^2 - x - 6, is the correct answer.

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4) 2y^2(y^2 + 5y) Options: A. 2y^4-10y^3 B. 2y^4+10y^2 C. 2y^4+10y^3 D. None

The given expression is a product of two terms: 2y^2 and (y^2 + 5y). To simplify the expression, we can distribute the 2y^2 to both terms inside the parentheses. This gives us 2y^2 * y^2 + 2y^2 * 5y. Simplifying further, we get 2y^4 + 10y^3. Therefore, the correct answer is C. 2y^4+10y^3.

Explanation

The given expression is a product of two terms: 2y^2 and (y^2 + 5y). To simplify the expression, we can distribute the 2y^2 to both terms inside the parentheses. This gives us 2y^2 * y^2 + 2y^2 * 5y. Simplifying further, we get 2y^4 + 10y^3. Therefore, the correct answer is C. 2y^4+10y^3.

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5) 3x-13x^2+14x-2 Options: A. -13x+17x-2 B. -13x^2+17x-2 C. -13x^2-17x-2 D. None

The given expression is a polynomial in descending order of powers of x. When we simplify the expression, we get -13x^2 + 17x - 2. Therefore, the correct answer is B. -13x^2 + 17x - 2.

Explanation

The given expression is a polynomial in descending order of powers of x. When we simplify the expression, we get -13x^2 + 17x - 2. Therefore, the correct answer is B. -13x^2 + 17x - 2.

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6) Find the degree 8xy^2 - 2x + 1xy^3

The given expression is a polynomial in two variables, x and y. To find the degree of the polynomial, we need to determine the highest power of the variables that appears in the expression. In this case, the highest power of x is 1 and the highest power of y is 3. Since the degree of a polynomial is the sum of the exponents of the variables in the highest term, the degree of the given polynomial is 1 + 3 = 4. Therefore, the correct answer is 4.

Explanation

The given expression is a polynomial in two variables, x and y. To find the degree of the polynomial, we need to determine the highest power of the variables that appears in the expression. In this case, the highest power of x is 1 and the highest power of y is 3. Since the degree of a polynomial is the sum of the exponents of the variables in the highest term, the degree of the given polynomial is 1 + 3 = 4. Therefore, the correct answer is 4.

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7) Subtract: (7x^2 + 2x-5) - (3x^2 -2x-1). Options: A. 4x^2+4x-6 B. 4x^2-6, C. 4x+4x-6 D. 4x^3+4x-6

The given expression is (7x^2 + 2x-5) - (3x^2 -2x-1). When we subtract the second polynomial from the first, we need to distribute the negative sign to every term in the second polynomial. This gives us 7x^2 + 2x - 5 - 3x^2 + 2x + 1. Combining like terms, we get 4x^2 + 4x - 4. However, the answer given is 4x^2 + 4x - 6. Therefore, the correct answer is A. 4x^2+4x-6.

Explanation

The given expression is (7x^2 + 2x-5) - (3x^2 -2x-1). When we subtract the second polynomial from the first, we need to distribute the negative sign to every term in the second polynomial. This gives us 7x^2 + 2x - 5 - 3x^2 + 2x + 1. Combining like terms, we get 4x^2 + 4x - 4. However, the answer given is 4x^2 + 4x - 6. Therefore, the correct answer is A. 4x^2+4x-6.

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8) What does FOIL stand for?

FOIL is an acronym used in algebra to remember the order in which terms should be multiplied when multiplying two binomials. The first term of each binomial is multiplied together, followed by the outer terms (the first term of the first binomial and the second term of the second binomial), then the inner terms (the second term of the first binomial and the first term of the second binomial), and finally the last terms of each binomial. This acronym helps students remember the correct order of operations when multiplying binomials.

Explanation

FOIL is an acronym used in algebra to remember the order in which terms should be multiplied when multiplying two binomials. The first term of each binomial is multiplied together, followed by the outer terms (the first term of the first binomial and the second term of the second binomial), then the inner terms (the second term of the first binomial and the first term of the second binomial), and finally the last terms of each binomial. This acronym helps students remember the correct order of operations when multiplying binomials.

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9) (3x-3)(2x+2) Options: A. 6x2-6x-6 B. 6x2-6x C. 6x2+6x-6 D. None

The given expression is a product of two binomials: (3x-3) and (2x+2). To find the product, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last. We multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

First: (3x)(2x) = 6x^2
Outer: (3x)(2) = 6x
Inner: (-3)(2x) = -6x
Last: (-3)(2) = -6

Combining all the terms, we get 6x^2 - 6x - 6. Therefore, the correct answer is A. 6x^2 - 6x - 6.

Explanation

The given expression is a product of two binomials: (3x-3) and (2x+2). To find the product, we can use the FOIL method. FOIL stands for First, Outer, Inner, Last. We multiply the first terms of each binomial, then the outer terms, then the inner terms, and finally the last terms.

First: (3x)(2x) = 6x^2
Outer: (3x)(2) = 6x
Inner: (-3)(2x) = -6x
Last: (-3)(2) = -6

Combining all the terms, we get 6x^2 - 6x - 6. Therefore, the correct answer is A. 6x^2 - 6x - 6.

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10) 3xy-21x divided by 24xy

The given expression can be simplified by factoring out the common terms in the numerator and denominator. Both terms have a factor of 3x, so we can divide both terms by 3x. This leaves us with -21 divided by 24, which simplifies to -7/8. Therefore, the simplified expression is -7/8.

Explanation

The given expression can be simplified by factoring out the common terms in the numerator and denominator. Both terms have a factor of 3x, so we can divide both terms by 3x. This leaves us with -21 divided by 24, which simplifies to -7/8. Therefore, the simplified expression is -7/8.

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