Algebra 7.1-7.4 Review (Prior to Quiz)

Classify by number of terms:

3x² – 8x + 1

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Answer explanation

The given expression has three terms, making it a trinomial. A trinomial consists of three terms.

Classify by number of terms:
9x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Answer explanation

The given expression '9x' has only one term, making it a monomial.

Simplify (-4m³-m+9) - (4m²+m-12)

• -4m³-4m²-2m-21

• -4m³-4m²-2m+21

• -8m³-2m+21

• -4m³+4m²+2m+21

Answer explanation

To simplify the expression, distribute the negative sign in the second parenthesis. Then combine like terms to get -4m^3 - 4m^2 - 2m + 21.

Simplify (8xy²+6xy) + (-12x²y+13xy²)

• 21xy² +12x²y+6xy

• 21xy² -12x²y-6xy

• 21xy² +12x²y-6xy

• 21xy² -12x²y+6xy

Answer explanation

The correct answer is 21xy^2 - 12x^2y + 6xy. Combine like terms by adding the coefficients of the same variables. The final expression is obtained by simplifying the given expression.

Find the sum.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

• 4x³ + 1x² – 3x + 1

• 2x³ + 1x² - 5x + 9

• 6x³ + 1x - 1x² - 3

• 3x⁵ +1x - 1x⁵ - 3x

Answer explanation

To find the sum, combine like terms: (3x^3 + x^3) + (3x^2 - 2x^2) + (-4x + x) + (5 - 4) = 4x^3 + x^2 - 3x + 1

(3x + 4y - 3z) - (2x - 6y + 7z)

• x + 10y - 10z

• -x +10y - 10z

• x -10y - 10z

• -x -10y - 10z

Answer explanation

To simplify the expression, distribute the negative sign in the second parenthesis: 3x + 4y - 3z - 2x + 6y - 7z = 3x + 4y - 3z - 2x + 6y - 7z = x + 10y - 10z

Which of the following are examples of like terms?

• 2 and 2x

• y³ and x³

• y and x

• -3x and 3x

Answer explanation

-3x and 3x are like terms because they have the same variable (x) raised to the same power and differ only in their coefficients.

Determine the simplified form of the expression 5(3x + 2)

• 3x + 10

• 15x + 10

• 15x - 10

• 3x - 10

Answer explanation

To simplify the expression 5(3x + 2), distribute the 5 to both terms inside the parentheses: 5*3x + 5*2 = 15x + 10. Therefore, the simplified form is 15x + 10.

Expand 3a(5a² + 8a + 2) using the distributive property.

• 15a³ + 24a² + 6a

• 10a³ + 24a + 6

• 8a³ + 11a² + 6a

• 15a² + 24a + 6

Answer explanation

Choose the correct answer choice that expands the expression correctly using the distributive property.

Simplify the following expression using FOIL.
(x + 5)(x + 4)

• x² + x + 20

• x² + 20x + 9

• x² + 9x + 20

• x² - 9x + 54

Answer explanation

Choose the correct answer by multiplying (x + 5)(x + 4) using FOIL method to get x^2 + 9x + 20. First = x(x), Outside = x(4), Inside = 5(x), Last = 5(4). Then add your outside and inside together.