For the following exercises, find the degree and leading coefficient

namenerk

namenerk

Answered question

2021-12-28

For the following exercises, find the degree and leading coefficient for the given polynomial.
x(4x2)(2x+1)

Answer & Explanation

Terry Ray

Terry Ray

Beginner2021-12-29Added 50 answers

Step 1
Given expression:
x(4x2)(2x+1)
Step 2
Solution:
(4xx3)(2x+1)
2x(4xx3)+1(4xx3)
8x22x4+4xx3
2x4x3+8x2+4x
Thus degree of polynomials is = 4
Leading coefficient = -2
Virginia Palmer

Virginia Palmer

Beginner2021-12-30Added 27 answers

Step 1
Expression:
x(4x2)(2x+1)
Step 2
Apply distributive property to expand the parentheses:
=x(8x+42x3x2)
And again:
=8x2+4x2x4x3
Rearrange to write in descending order of power:
=2x4x3+8x2+4x
The highest power of x is 4 so its degree is 4 and its coefficient is -2.
Result:
The function has a coefficient of -2 and its degree is 4.
Vasquez

Vasquez

Expert2022-01-09Added 669 answers

Step 1
x(4x2)(2x+1)
We do not need to expand. Just look for the term with the highest possible degree:
x(x2)(2x)=2x4
Degree=4, Leading coefficient = -2
Result:
Degree=4, Leading coefficient = -2

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