Divide this rational expression and polynomial
(12x^2 + 9x-7)/(3x)
(12x^2 + 9x-7)/(3x)
= 4x + 3 -7/3x
Thank you but can you put it in "factor form" or show how you got the answer?
12x^2/3x + 9x/3x -73x
(4x *3x)/3x + (3* 3x)/3x -7/3x
4x + 3 -7/3x
Thanks much -- this help me learn.
To divide a rational expression by a polynomial, you need to perform polynomial long division. Here's how you can divide the rational expression (12x^2 + 9x - 7) by the polynomial (3x):
Step 1: Write the polynomial long division setup:
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3x | 12x^2 + 9x - 7
Step 2: Divide the first term of the numerator by the first term of the divisor:
12x^2 ÷ 3x = 4x
Step 3: Multiply the divisor by the quotient obtained in the previous step and write the result below the numerator:
4x * 3x = 12x^2
Step 4: Subtract the result obtained above from the numerator:
(12x^2 + 9x - 7) - (12x^2) = 9x - 7
Step 5: Bring down the next term:
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3x | 12x^2 + 9x - 7
9x - 7
Step 6: Repeat steps 2-5 using the new numerator (9x - 7):
Divide (9x ÷ 3x) = 3
Multiply the divisor and quotient: 3 * 3x = 9x
Subtract: (9x - 7) - (9x) = -7
Step 7: Bring down the next term (which is 0 in this case, since there are no more terms):
_________________________
3x | 12x^2 + 9x - 7
9x - 7
0
Step 8: The quotient obtained from the division is the sum of the quotients obtained in each step: 4x + 3.
Therefore, the division of the rational expression (12x^2 + 9x - 7) by the polynomial (3x) is equal to 4x + 3.