Use the polynomial division algorithm to write the rational function in the form Q(x) + R(x)/D(x), where the degree of R is less than the degree of D. x^2 +x+1/x^2 +x-2

Tiffany Page

Tiffany Page

Answered question

2022-11-18

Use the polynomial division algorithm to write the rational function in the form Q(x) + R(x)/D(x), where the degree of R is less than the degree of D. x 2 + x + 1 / x 2 + x 2

Answer & Explanation

Cseszteq5j

Cseszteq5j

Beginner2022-11-19Added 17 answers

We use the division algorithm to find the quotient and remainder:
1 _ ( x 2 + x 2 ) x 2 + x + 1 x 2 x + 2 _ 3
Thus
Q ( x ) + R ( x ) D ( x ) = 1 + 3 x 2 + x 2 Substitute Q(x)=1, R(x)=3, and D ( x ) = x 2 + x 2
Result:
1 + 3 x 2 + x 2

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