Divide.
(10x2 – 13x + 12) ÷ (5x + 1)
A. 2x minus 3 plus 15 over 5x plus 1
B. 2x minus 5 plus 6 over 5x plus 1
C. 2x minus 3 minus 15 over 5x plus 1
D. 2x + 12
B. 2x minus 5 plus 6 over 5x plus 1
To divide the expression (10x^2 - 13x + 12) by (5x + 1), we can use polynomial long division. Here are the steps:
1. Arrange the terms in descending order of degree: (10x^2 - 13x + 12) ÷ (5x + 1)
2. Divide the first term of the numerator (10x^2) by the first term of the denominator (5x), which gives 2x.
3. Multiply the entire denominator (5x + 1) by the result from step 2 (2x), which gives 10x^2 + 2x.
4. Subtract the result from step 3 (10x^2 + 2x) from the numerator (10x^2 - 13x + 12). The result is -15x + 12.
5. Bring down the next term from the numerator (-15x) and divide it by the first term of the denominator (5x). This gives -3.
6. Multiply the entire denominator (5x + 1) by the result from step 5 (-3), which gives -15x - 3.
7. Subtract the result from step 6 (-15x - 3) from the numerator (-15x + 12). The result is 15.
8. Since there are no more terms in the numerator, the division is complete.
The quotient is 2x - 3, and the remainder is 15. Therefore, the correct option is A. 2x minus 3 plus 15 over 5x plus 1.