Review

Match the following

• Polynomial Function

• 2x+3

• Quadratic Function

• Linear Function

• Exponential Function

The function is has a leading coefficient of ​ (a)   and a degree of ​ (b)  

• 5

• 3

• -5

• -3

• -8

• 4

Answer explanation

The question asks for the leading coefficient and degree of a function. The leading coefficient is the number in front of the highest-degree term, and the degree is the highest power of the variable in the function. In this case, the leading coefficient is -5, and the degree is 3.

What is the leading coefficient?

Answer explanation

The leading coefficient is the numerical coefficient of the term with the highest degree in a polynomial. In this case, the leading coefficient is -7, which is the correct choice provided in the options.

Samuel is trying to write the polynomial 3x^2 + 2x - 5 in standard form for his math homework. Can you help him?

• 3x^2 + 2x - 5

• 3x^2 + 5x - 2

• 2x^2 + 3x - 5

• 3x^2 - 2x + 5

Answer explanation

The question asks for the standard form of the polynomial 3x^2 + 2x - 5. The standard form of a polynomial is written with the terms in descending order of their degrees. In this case, the given polynomial is already in standard form, which is 3x^2 + 2x - 5.

Convert the polynomial -4x^3 + 7x^2 - 2x + 1 to standard form.

• -4x^3 + 7x^2 + 2x + 1

• -4x^3 + 7x^2 - 2x - 1

• 4x^3 + 7x^2 - 2x + 1

• -4x^3 + 7x^2 - 2x + 1

Answer explanation

The question asks to convert the polynomial to standard form. The polynomial is already in standard form, which is written in descending order of exponents. The correct choice is -4x^3 + 7x^2 - 2x + 1, which matches the given polynomial exactly.

Rearrange the polynomial 2x^4 - 3x^2 + 6x - 1 in standard form.

• 2x^4 - 3x^2 + 6x - 1

• -3x^2 + 2x^4 + 6x - 1

• 2x^4 + 6x - 3x^2 - 1

• 6x - 3x^2 + 2x^4 - 1

Answer explanation

The given polynomial is already in standard form, which is arranging the terms in descending order of their degrees. The correct choice is 2x^4 - 3x^2 + 6x - 1, as it follows the standard form with the highest degree term first, followed by the lower degree terms.

What is the standard form of the polynomial 3 + 4x^2 - 2x + -x^3?

• -x^3 + 4x^2 + 2x + 3

• x^3 + 4x^2 - 2x + 3

• -x^3 + 4x^2 - 2x + 3

Answer explanation

The standard form of a polynomial arranges the terms by degree in descending order. In the given question, the polynomial 3 + 4x^2 - 2x - x^3 is rearranged as -x^3 + 4x^2 - 2x + 3, which matches the correct answer.

• 5x^3 + 7x - 4 - 2x^2

• -5x^3 - 2x^2 + 7x 4

• 5x^3 + 2x^2 + 7x +4

• 5x^3 - 2x^2 + 7x - 4

Answer explanation

The standard form of a polynomial is written with the terms in descending order by degree. So, the given polynomial 5x^3+7x-4-2x^2 should be rearranged as 5x^3 - 2x^2 + 7x - 4. This matches the correct option provided.