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Divide the polynomials. Your answer should be a polynomial.

(x^(2)-3x-10)/(x-5)=

Divide the polynomials. Your answer should be a polynomial.\newlinex23x10x5= \frac{x^{2}-3 x-10}{x-5}=

Full solution

Q. Divide the polynomials. Your answer should be a polynomial.\newlinex23x10x5= \frac{x^{2}-3 x-10}{x-5}=
  1. Set up division format: Set up the division of the polynomials in long division format.\newlineWe want to divide x23x10x^2 - 3x - 10 by x5x - 5. This is similar to long division with numbers.
  2. Divide first terms: Divide the first term of the dividend, x2x^2, by the first term of the divisor, xx, to get the first term of the quotient.\newlinex2÷x=xx^2 \div x = x.\newlineWrite xx above the division bar.
  3. Multiply and subtract: Multiply the divisor x5x - 5 by the first term of the quotient xx and write the result under the dividend.\newlinex×(x5)=x25xx \times (x - 5) = x^2 - 5x.
  4. Simplify and divide again: Subtract the result of the multiplication from the dividend.\newline(x23x10)(x25x)=x23x10x2+5x(x^2 - 3x - 10) - (x^2 - 5x) = x^2 - 3x - 10 - x^2 + 5x.
  5. Multiply and subtract again: Simplify the subtraction to find the new dividend.\newlinex23x10x2+5x=2x10x^2 - 3x - 10 - x^2 + 5x = 2x - 10.
  6. Simplify and find remainder: Divide the new dividend 2x102x - 10 by the first term of the divisor xx to find the next term of the quotient.\newline2x÷x=22x \div x = 2.\newlineWrite 22 above the division bar next to the first term of the quotient.
  7. Simplify and find remainder: Divide the new dividend 2x102x - 10 by the first term of the divisor xx to find the next term of the quotient.\newline2x÷x=22x \div x = 2.\newlineWrite 22 above the division bar next to the first term of the quotient.Multiply the divisor x5x - 5 by the new term of the quotient 22 and write the result under the new dividend.\newline2×(x5)=2x102 \times (x - 5) = 2x - 10.
  8. Simplify and find remainder: Divide the new dividend 2x102x - 10 by the first term of the divisor xx to find the next term of the quotient.\newline2x÷x=22x \div x = 2.\newlineWrite 22 above the division bar next to the first term of the quotient.Multiply the divisor x5x - 5 by the new term of the quotient 22 and write the result under the new dividend.\newline2×(x5)=2x102 \times (x - 5) = 2x - 10.Subtract the result of the multiplication from the new dividend.\newline(2x10)(2x10)=2x102x+10(2x - 10) - (2x - 10) = 2x - 10 - 2x + 10.
  9. Simplify and find remainder: Divide the new dividend 2x102x - 10 by the first term of the divisor xx to find the next term of the quotient.\newline2x÷x=22x \div x = 2.\newlineWrite 22 above the division bar next to the first term of the quotient.Multiply the divisor x5x - 5 by the new term of the quotient 22 and write the result under the new dividend.\newline2×(x5)=2x102 \times (x - 5) = 2x - 10.Subtract the result of the multiplication from the new dividend.\newline(2x10)(2x10)=2x102x+10(2x - 10) - (2x - 10) = 2x - 10 - 2x + 10.Simplify the subtraction to find the remainder.\newline2x102x+10=02x - 10 - 2x + 10 = 0.\newlineThe remainder is 00, so the division is exact.