Question

Pick the expression that matches this description: A polynomial of the 5 th 5 th 5, start superscript, start text, to, end text, end superscript degree with a leading coefficient of 7 77 and a constant term of 6 66 Choose 1 answer: Choose 1 answer: (Choice A) A 7 x 6 − 6 x 4 + 5 7x 6 −6x 4 +57, x, start superscript, 6, end superscript, minus, 6, x, start superscript, 4, end superscript, plus, 5 (Choice B) B 6 x 7 − x 5 + 5 6x 7 −x 5 +56, x, start superscript, 7, end superscript, minus, x, start superscript, 5, end superscript, plus, 5 (Choice C) C 6 x 5 + x 4 + 7 6x 5 +x 4 +76, x, start superscript, 5, end superscript, plus, x, start superscript, 4, end superscript, plus, 7 (Choice D) D 7 x 5 + 2 x 2 + 6 7x 5 +2x 2 +6

Answer 1

For any polynomial of degree n, we can write the general form as:

`a_1x^n+a_2x^(n-1)+a_3x^(n-2)\text{ + }\ldots+a_n\text{ = 0}`

Where:

`\begin{gathered} a_1\text{ is the leading coefficient} \\ \text{and } \\ a_{n\text{ }}\text{ is the constant term} \end{gathered}`

We are given that the degree of the polynomial is 5 and it has a leading coefficient of 7 and a constant term of 6.

Checking through the options:

Option A

`7x^6-6x^4\text{ }+\text{ 5}`

It has a degree of 6, hence it is wrong.

Option B

`6x^7-x^5\text{ + 5}`

It has a leading coefficient of 6, hence it is wrong.

Option C

`6x^5+x^{4\text{ }}-7`

It has a leading coefficient of 6, hence it is wrong.

Option D

`7x^5+2x^2+\text{ 6}`

It has a degree of 5, a leading coefficient of 7, and a constant term of 6, hence it is correct

Answer: Option D