(6x^2+x-7)/(2x+3)
I'm not sure how to do this can someone explain how the steps for this?
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calc101.com
click on the "long division" button
Thank you
To simplify the expression (6x^2 + x - 7) / (2x + 3), you can use polynomial long division. Here's an explanation of the steps involved:
Step 1: Start by dividing the first term of the numerator by the first term of the denominator. In this case, divide 6x^2 by 2x. The quotient will be 3x.
Step 2: Multiply the entire denominator (2x + 3) by the quotient obtained in the previous step (3x). You get 6x^2 + 9x.
Step 3: Subtract the result obtained in step 2 from the numerator (6x^2 + x - 7) by removing all the terms. So, (6x^2 + x - 7) - (6x^2 + 9x) gives you -8x - 7.
Step 4: Bring down the next term from the numerator, which is -8x. Simply write it next to the result obtained in the previous step.
Step 5: Divide the new expression (-8x - 7) by the first term of the denominator (2x). The quotient will be -4.
Step 6: Multiply the entire denominator (2x + 3) by the quotient obtained in the previous step (-4). You get -8x - 12.
Step 7: Subtract the result obtained in step 6 from the new expression (-8x - 7) by removing all the terms. So, (-8x - 7) - (-8x - 12) gives you 5.
Step 8: Since there are no more terms left in the numerator, the division process stops. The final remainder is 5.
Therefore, the simplified form of (6x^2 + x - 7) / (2x + 3) is 3x - 4 with a remainder of 5.
It's important to note that you can also rewrite the remainder as a fractional form by dividing it by the original denominator. In this case, 5 divided by (2x + 3) is 5 / (2x + 3). So, an alternate simplified form would be 3x - 4 + 5 / (2x + 3).