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

Ava-May Nelson 2021-01-10 Answered
Give a polynomial division that has a quotient of x+5 and a remainder of -2.
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joshyoung05M
Step 1
The quotient is x+5 and the remainder is -2
By using the formula,
Polynomial = Divisor $×$ Quotient + Remainder
Take divisor = x + 1
Thus, the polynomial is
Polynomial $=\left(x+1\right)×\left(x+5\right)+\left(-2\right)$
Polynomial $={x}^{2}+6x+5-2$
Polynomial $={x}^{2}+6x+3$
Step 2
By using the polynomial division,
$\frac{{x}^{2}+6x+3}{x+1}$
The first term is x2 so the first term in the quotient is x
$x\left(x+1\right)={x}^{2}+x$
So, ${x}^{2}+6x+3-\left({x}^{2}+x\right)=5x+3$
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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