### Home > INT3 > Chapter 8 > Lesson 8.1.3 > Problem8-50

8-50.

For each of the following polynomial functions, state the degree, list the coefficients, and then label them $a_{0}$ through $a_{n}$. Refer to the example in the Math Notes box in Lesson 8.1.1 about polynomial notation.

1. $P\left(x\right) = 6x^{4} – 3x^{3} + 5x^{2} + x + 8$

Degree $4$,
$a_{4} = 6, a_{3} = −3, a_{2} = 5,$
$a_{1} = 1, a_{0} = 8$

1. $P\left(x\right) = –5x^{3} + 10x^{2} + 8$

Degree $3$,
$a_{3} = −5, a_{2} = 10,$
$a_{1} = 0, a_{0} = 8$

1. $P\left(x\right) = –x^{2} + x$

See the Math Notes box and parts (a) and (b).

1. $P\left(x\right) = x\left(x – 3\right)\left(x – 5\right)$

Write the polynomial in standard form first.

Degree $3$,
$a_{3} = 1, a_{2} = −8,$
$a_{1} = 15, a_{0} = 0$

1. $P\left(x\right) = x$

See the Math Notes box and parts (a) and (b).

1. $P\left(x\right) = 10$

See the Math Notes box and parts (a) and (b).