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# Polynomials

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If f(x) is a polynomial of degree 3, and g(x) is a polynomial of degree 6, then what is the degree of polynomial 2f(x) + 4g(x)?

Dec 10, 2021

#1
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The coefficients don't change the degree. The degree is just 6.

Dec 10, 2021
#2
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Step-by-step explanation

Given

Degree of f(x) = 3

Degree of g(x) = 5

Required

Degree of 2f(x) + 4g(x)

Analyzing both polynomials

f(x)

2f(x) means 2 * f(x)

Since 2 is a constant

Multiplying f(x) by 2 will result in a polynomial with a degree of 3

Hence 2f(x) has a degree of 3

g(x)

4g(x) means 4 * g(x)

Since 4 is also a constant

Multiplying g(x) by 4 will result in a polynomial with a degree of 5

Hence 4g(x) has a degree of 5

Having said that;

When 2 polynomials of different degrees are added together, the degree of the result will be the higher degree of both polynomials;

This means that;

Adding a polynomial of degree 3 and another of degree 5 will result in a polynomial of degree 5.

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Dec 10, 2021
edited by AlgebraGuru  Dec 10, 2021
edited by AlgebraGuru  Dec 10, 2021