CPM Homework Help : INT3 Problem 8-50

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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.

$P\left(x\right) = 6x^{4} - 3x^{3} + 5x^{2} + x + 8$
Answer (a):
Degree $4$ ,
$a_{4} = 6, a_{3} = −3, a_{2} = 5,$
$a_{1} = 1, a_{0} = 8$

$P\left(x\right) = -5x^{3} + 10x^{2} + 8$
Answer (b):
Degree $3$ ,
$a_{3} = −5, a_{2} = 10,$
$a_{1} = 0, a_{0} = 8$

$P\left(x\right) = -x^{2} + x$
Hint (c):
See the Math Notes box and parts (a) and (b).

$P\left(x\right) = x\left(x - 3\right)\left(x - 5\right)$
Hint (d):
Write the polynomial in standard form first.
Answer (d):
Degree $3$ ,
$a_{3} = 1, a_{2} = −8,$
$a_{1} = 15, a_{0} = 0$

$P\left(x\right) = x$
Hint (e):
See the Math Notes box and parts (a) and (b).

$P\left(x\right) = 10$
Hint (f):
See the Math Notes box and parts (a) and (b).

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