Give a polynomial division that has a quotient of x+5 and a remainder of -2.

Give a polynomial division that has a quotient of x+5 and a remainder of -2.

Question
Polynomial factorization
asked 2021-01-10
Give a polynomial division that has a quotient of x+5 and a remainder of -2.

Answers (1)

2021-01-11
Step 1
The quotient is x+5 and the remainder is -2
By using the formula,
Polynomial = Divisor \(\displaystyle\times\) Quotient + Remainder
Take divisor = x + 1
Thus, the polynomial is
Polynomial \(\displaystyle={\left({x}+{1}\right)}\times{\left({x}+{5}\right)}+{\left(-{2}\right)}\)
Polynomial \(\displaystyle={x}^{{2}}+{6}{x}+{5}-{2}\)
Polynomial \(\displaystyle={x}^{{2}}+{6}{x}+{3}\)
Step 2
By using the polynomial division,
\(\displaystyle\frac{{{x}^{{2}}+{6}{x}+{3}}}{{{x}+{1}}}\)
The first term is x2 so the first term in the quotient is x
\(\displaystyle{x}{\left({x}+{1}\right)}={x}^{{2}}+{x}\)
So, \(\displaystyle{x}^{{2}}+{6}{x}+{3}-{\left({x}^{{2}}+{x}\right)}={5}{x}+{3}\)
Now if 5x + 3 divide by x +1 then the quotient is x
5(x+1) = 5x + 5
So, 5x + 3 - (5x + 5) = -2 (This is the remainder)
The quotient is x+5 and remainder is -2
Hence, the solution
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