Divide. (35x2 – 11x – 8) ÷ (5x + 2)
A. 7x minus 5 plus StartFraction 2 over 5 x plus 2 EndFraction
B. 7x plus 5 plus StartFraction 2 over 5 x plus 2 EndFraction
C. 7x minus 5 minus StartFraction 2 over 5 x plus 2 EndFraction
D. 7x plus 5 minus StartFraction 2 over 5 x plus 2 EndFraction
To divide the expression (35x^2 - 11x - 8) by (5x + 2), we can use long division. Here are the steps:
7x - 5
-----------------
5x + 2 | 35x^2 - 11x - 8
- (35x^2 + 14x)
-----------------
-25x - 8
- (-25x - 10)
-----------------
2
The result of the division is a quotient of 7x - 5 and a remainder of 2.
So, the correct answer choice is A. 7x minus 5 plus StartFraction 2 over 5 x plus 2 EndFraction.
To divide the expression (35x^2 – 11x – 8) by (5x + 2), you can use the long division method. Here is a step-by-step explanation of how to do it:
1. Divide the first term of the numerator (35x^2) by the first term of the denominator (5x). The result is 7x.
- Write 7x above a horizontal line.
7x
2. Multiply the denominator (5x + 2) by the value above the line (7x). The result is 35x^2 + 14x.
- Write 35x^2 + 14x below the numerator.
7x
___________________
5x + 2 | 35x^2 - 11x - 8
35x^2 + 14x
_____________
- 25x - 8
3. Subtract the result (35x^2 + 14x) from the numerator (35x^2 – 11x – 8). The result is -25x - 8.
- Write -25x - 8 below the line.
7x
___________________
5x + 2 | 35x^2 - 11x - 8
35x^2 + 14x
_____________
- 25x - 8
4. Repeat steps 1-3 with the new numerator (-25x - 8) until no more terms can be divided.
5. Divide the new first term of the numerator (-25x) by the first term of the denominator (5x). The result is -5.
- Write -5 above the line.
7x - 5
6. Multiply the denominator (5x + 2) by the value above the line (-5). The result is -25x - 10.
- Write -25x - 10 below the numerator.
7x - 5
___________________
5x + 2 | 35x^2 - 11x - 8
35x^2 + 14x
_____________
- 25x - 8
- 25x - 10
_____________
+2
7. Subtract the result (-25x - 10) from the numerator (-25x - 8). The result is 2.
7x - 5
___________________
5x + 2 | 35x^2 - 11x - 8
35x^2 + 14x
_____________
- 25x - 8
- 25x - 10
_____________
+2
8. There are no more terms left to divide. The remainder is 2.
So, the division (35x^2 – 11x – 8) ÷ (5x + 2) is equal to 7x - 5 plus (2 / (5x + 2)), which can be written as:
A. 7x minus 5 plus StartFraction 2 over 5 x plus 2 EndFraction