x squared-13x+36/x-9 equals what dividing polynomials
To divide polynomials, we typically use long division or synthetic division. Let's use long division to find the quotient of the given expression, (x^2 - 13x + 36)/(x - 9).
Step 1: Write the dividend (x^2 - 13x + 36) as the numerator inside the division symbol (÷), and the divisor (x - 9) as the denominator outside the division symbol.
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(x - 9) | (x^2 - 13x + 36)
Step 2: Divide the first term of the dividend (x^2) by the first term of the divisor (x).
x
Step 3: Multiply the divisor (x - 9) by the quotient (x).
x(x - 9) = x^2 - 9x
Step 4: Subtract the product obtained in Step 3 from the dividend.
(x^2 - 13x + 36) - (x^2 - 9x) = -4x + 36
Step 5: Bring down the next term from the dividend (-4x).
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(x - 9) | (x^2 - 13x + 36)
- 4x
Step 6: Divide the new first term of the dividend (-4x) by the first term of the divisor (x).
- 4
Step 7: Multiply the divisor (x - 9) by the new quotient (-4).
- 4(x - 9) = -4x + 36
Step 8: Subtract the product obtained in Step 7 from the dividend.
(-4x + 36) - (-4x + 36) = 0
Step 9: Since the result of the subtraction is zero, we have obtained the last term of the quotient.
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(x - 9) | (x^2 - 13x + 36)
- 4x + 36
Therefore, the quotient is x - 4.