CONCEPT PREVIEW Fill in the blank to correctly complete each sent...

Question

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence.

The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the degree of the following polynomial expression. Our expression is nine X raise to the seventh plus three X minus 97. Our answer choices are answer choice, A seven answer choice B three, answer choice C nine and answer choice D eight. All right. To find the degree of our expression, we first want to find the degree of each of our terms. We have three terms in this expression. The first one is nine X rays to the seventh power. The second one is a positive three X and the third term is a negative 97. Now, to find the degree, we want to look at the exponent of each variable. The first terms variable is X raised to the seventh power. The exponent there is seventh. The second term variable is just an X. That one doesn't have an exponent written. And when there isn't one written, it's just an understood one. Now, for negative 97 that doesn't have a variable listed. When there's no variable listed, it does have a variable. It's just going to be X raised to the zeroth power to say there are zero XS here. So now we're going to compare the exponents for each of these three terms. The first term has an exponent of seven. The second term has an exponent of one. And the third term has an exponent of zero to find the degree of the whole expression. We choose the highest degree of all the terms. The highest degree of all three of these terms is seven. So seven is the degree of our expression. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.

Key Concepts

Polynomial Degree

Trinomial Definition

Polynomial Classification

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