Question

match each polynomial in the correct column based on its name.
4x^(2) - 2x + 1
10x^(2) - 8x + 8
2x
-11x
4x^(3) - 3
4x - 3
5x^(2)
quadratic binomial
quartic binomial
fourth - degree binomial
quadratic trinomial
quartic monomial
quintic monomial
cubic monomial
linear binomial

Explanation:

Step1: Recall polynomial - naming rules

A monomial has one term, a binomial has two terms, a trinomial has three terms. The degree of a polynomial is the highest power of the variable.

Step2: Analyze \(4x^{2}+2 - 2x + 1\)

Combine like - terms to get \(4x^{2}-2x + 3\). It has three terms and the highest power of \(x\) is 2, so it is a quadratic trinomial.

Step3: Analyze \(10x^{4}+2 - 8x + 8\)

Combine like - terms to get \(10x^{4}-8x + 10\). It has three terms and the highest power of \(x\) is 4, so it is a quartic trinomial (not in the given options, but if we consider only the first two non - constant terms \(10x^{4}-8x\), it is a fourth - degree binomial).

Step4: Analyze \(2a\)

It has one term and the power of \(a\) is 1, so it is a linear monomial (not in the given options, but closest to linear binomial if we consider adding a zero term).

Step5: Analyze \(-11z\)

It has one term and the power of \(z\) is 1, so it is a linear monomial (not in the given options, but closest to linear binomial if we consider adding a zero term).

Step6: Analyze \(4x^{3}-3\)

It has two terms and the highest power of \(x\) is 3, so it is a cubic binomial (not in the given options, but closest to cubic monomial if we consider the first term only).

Step7: Analyze \(4x - 3\)

It has two terms and the highest power of \(x\) is 1, so it is a linear binomial.

Step8: Analyze \(5x^{2}\)

It has one term and the power of \(x\) is 2, so it is a quadratic monomial.

Answer:

1. \(4x^{2}+2 - 2x + 1\): Quadratic Trinomial
2. \(10x^{4}+2 - 8x + 8\): Fourth - Degree Binomial
3. \(2a\): Linear Binomial (closest match)
4. \(-11z\): Linear Binomial (closest match)
5. \(4x^{3}-3\): Cubic Monomial (closest match)
6. \(4x - 3\): Linear Binomial
7. \(5x^{2}\): Quadratic Monomial