Q. Divide the polynomials.Your answer should be a polynomial.x+3x2−x−12=
Set up division format: Set up the division of the polynomials in long division format.We want to divide x2−x−12 by x+3.
Divide first terms: Divide the first term of the dividend, x2, by the first term of the divisor, x, to get the first term of the quotient.x2 divided by x is x.Write x above the division bar.
Multiply and subtract: Multiply the divisor, x+3, by the first term of the quotient, x, to get x(x+3)=x2+3x. Subtract this from the dividend under the division bar.
Perform subtraction: Perform the subtraction step by subtracting (x2+3x) from (x2−x).x2−x−(x2+3x)=−x−3x=−4x. Bring down the next term of the dividend, which is −12, to get −4x−12.
Bring down next term: Divide the new first term of the remaining dividend, −4x, by the first term of the divisor, x, to get the next term of the quotient.−4x divided by x is −4.Write −4 next to x above the division bar, making the quotient x−4.
Divide new first term: Multiply the divisor, x+3, by the new term of the quotient, −4, to get −4(x+3)=−4x−12. Subtract this from the remaining dividend under the division bar.
Multiply and subtract: Perform the subtraction step by subtracting (−4x−12) from (−4x−12).−4x−12−(−4x−12)=0.There is no remainder, so the division is complete.
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