Divide. x^2+7x-37/x+9. Please help me.
To divide a polynomial expression by another expression, we can use the long division method. Here's how you can divide (x^2 + 7x - 37) by (x + 9):
Step 1: Write the expression in long division format:
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x + 9 | x^2 + 7x - 37
Step 2: Divide the first term of the dividend (x^2) by the first term of the divisor (x). Write the result above the line as the quotient, and then multiply the divisor (x + 9) by the quotient (x).
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x + 9 | x^2 + 7x - 37
- (x^2 + 9x)
Step 3: Subtract the obtained product (x^2 + 9x) from the dividend (x^2 + 7x - 37). Write the result below the line and bring down the next term.
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x + 9 | x^2 + 7x - 37
- (x^2 + 9x)
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-2x - 37
Step 4: Repeat steps 2 and 3 with the new expression (-2x - 37). Divide (-2x) by (x) and write the result above the line. Multiply the divisor (x + 9) by the quotient (-2).
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x + 9 | x^2 + 7x - 37
- (x^2 + 9x)
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-2x - 37
- (-2x - 18)
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-19
Step 5: Since the degree of the remainder term (-19) is less than the degree of the divisor (x + 9), there are no more terms to bring down. Hence, the division is complete.
The quotient is x - 2 and the remainder is -19. Therefore, the division result is:
x^2 + 7x - 37 / (x + 9) = (x - 2) - 19/(x + 9)