Polynomial Operations Quiz

Answer explanation

To add the polynomials, combine like terms: (3x^2 + 2x + 1) + (2x^2 - 3x + 4) = 5x^2 - x + 5. Therefore, the correct answer is 5x^2 - x + 5.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To subtract the polynomials, combine like terms: (5x^2 + x - 2) - (2x^2 - 4x + 3) = 3x^2 + 5x - 5. Therefore, the correct answer is 3x^2 + 5x - 5.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To multiply the polynomials (x + 3) and (x - 2), use the distributive property. The result is x^2 + x - 6, which is the correct choice.

Tags

CCSS.HSA.APR.A.1

• quadratic

• cubic

• quartic

• linear

Answer explanation

The degree of a polynomial is determined by the highest power of the variable present. In this case, the highest power is 3, so the degree of the polynomial is 3, cubic.

Answer explanation

To factor the quadratic x^2 - 5x + 6, we look for two numbers that multiply to 6 and add up to -5. These numbers are -2 and -3, so the factored form is (x - 2)(x - 3).

Answer explanation

The correct choice is 3x(2x^2 - 3x + 5) because the greatest common factor of the polynomial 6x^3 - 9x^2 + 15x is 3x, which can be factored out to get 3x(2x^2 - 3x + 5).

• Monomial

• Binomial

• Trinomial

• Polynomial

Answer explanation

The given polynomial has more than three terms, so it is classified as a Polynomial.

Answer explanation

The result of multiplying the polynomials (3x - 4) and (x + 5) is found by multiplying each term in the first polynomial by each term in the second polynomial. This results in 3x^2 + 11x - 20, which matches the correct answer choice.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To subtract the polynomials, start with the "from value" and distribute the minus to everything being subtracted. Then combine like terms. Subtract corresponding coefficients of each term. Result: 2x^3 + 3x^2 - 11.

Tags

CCSS.HSA.APR.A.1

• constant

• linear

• quadratic

• cubic

Answer explanation

The degree of a polynomial is determined by the highest power of the variable present. In this case, the polynomial is of degree 1 because the highest power of x is 1, linear.