Question 458886: Classify the polynomial as either constant, liner, quadratic, cubic, or quartic and determine the leading term, the leading coefficient, and the degree of the polynomial.
g(x)=-5x^4-6
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
If a function f(x), g(x), h(x), etc., has no x's on the
right side, it is a CONSTANT FUNCTION.
Examples: f(x) = 5, g(x) = -3, h(x) = 0 are all CONSTANT functions:
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If a function f(x), g(x), h(x), etc., has 1 understood
as its largest power of x on the right side, it is a
LINEAR FUNCTION.
Examples: f(x) = x, g(x) = -4x+7, h(x) = 7-5x are all LINEAR functions:
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If a function f(x), g(x), h(x), etc., has 2 as its largest
power of x on the right side, it is a QUADRATIC FUNCTION.
Examples: f(x) = 4x² - 3x + 7, g(x) = -x², h(x) = 9-6x² are
all QUADRATIC functions:
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If a function f(x), g(x), h(x), etc., has 3 as its largest
power of x on the right side, it is a CUBIC FUNCTION.
Examples: f(x) = -3x³ - 8x² + 7x + 6,
g(x) = x³, h(x) = 9x² - 7x³ are all CUBIC functions:
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If a function f(x), g(x), h(x), etc., has 4 as its largest
power of x on the right side, it is a QUARTIC FUNCTION.
Examples: f(x) = -7x4 - 9x³ + 7x² + 6x - 4,
g(x) = -x4, h(x) = 6x² - 7x4 are all
QUARTIC functions:
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So your function g(x) = -5x4 - 6
is a QUARTIC function.
The degree is 4, the largest exponent of x.
The leading coefficient is the coefficient of the term
with the largest power of x, which in this case is -5
Edwin
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