What is the simplified form of (6x+10) divide (3x-2)
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To simplify the expression (6x+10) divided by (3x-2), you can perform polynomial long division or use the synthetic division method. Here, I'll guide you through the polynomial long division method:
Step 1: Write the expression in division form:
________
(3x-2) | (6x+10)
Step 2: Divide the first term of the numerator by the first term of the denominator:
2x
Step 3: Multiply the entire denominator (3x-2) by the quotient found in the previous step, in this case 2x:
2x * (3x-2) = 6x^2 - 4x
Step 4: Subtract the result obtained in step 3 from the numerator:
(6x+10) - (6x^2 - 4x) = 10x + 10
Step 5: Repeat steps 2 to 4 with the new expression (10x+10) obtained in step 4:
Multiply: 2x * (3x-2) = 6x^2 - 4x
Subtract: (10x + 10) - (6x^2 - 4x) = 14x + 10
Step 6: Continue repeating steps 2 to 4 until there are no more terms left in the numerator. In this case, we stop here since there are no more terms left after step 5.
Step 7: Write the final answer by combining all the quotients obtained in each step.
Therefore, the simplified form of (6x+10) divided by (3x-2) is:
2x + (14x + 10) / (3x-2)