Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Divide the polynomials.
Your answer should be a polynomial.

(x^(2)-12 x+20)/(x-10)=

Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex212x+20x10= \frac{x^{2}-12 x+20}{x-10}=

Full solution

Q. Divide the polynomials.\newlineYour answer should be a polynomial.\newlinex212x+20x10= \frac{x^{2}-12 x+20}{x-10}=
  1. Set up division: Set up the division of the polynomials in long division format.\newlineWe want to divide (x212x+20)(x^2 - 12x + 20) by (x10)(x - 10).
  2. Divide first term: Divide the first term of the numerator by the first term of the denominator.\newlineDivide x2x^2 by xx to get xx.
  3. Multiply and write: Multiply the divisor (x10)(x - 10) by the result from Step 22 (x)(x) and write it under the dividend.\newlinex×(x10)=x210x.x \times (x - 10) = x^2 - 10x.
  4. Subtract and simplify: Subtract the result from Step 33 from the dividend.\newline(x212x+20)(x210x)=12x+20(10x)=12x+20+10x=2x+20(x^2 - 12x + 20) - (x^2 - 10x) = -12x + 20 - (-10x) = -12x + 20 + 10x = -2x + 20.
  5. Bring down next term: Bring down the next term of the dividend if there is one.\newlineSince we have already brought down all terms, we proceed to the next step.
  6. Divide new first term: Divide the new first term of the remaining dividend by the first term of the divisor.\newlineDivide 2x-2x by xx to get 2-2.
  7. Multiply and write: Multiply the divisor (x10)(x - 10) by the result from Step 66 (2)(-2) and write it under the remaining dividend.\newline2×(x10)=2x+20-2 \times (x - 10) = -2x + 20.
  8. Subtract and simplify: Subtract the result from Step 77 from the remaining dividend.\newline(2x+20)(2x+20)=0(-2x + 20) - (-2x + 20) = 0.
  9. Check for remainder: Since the remainder is 00, the division is complete, and the quotient is the final answer.\newlineThe quotient is x2x - 2.