(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
AAAaannndd the bot gets it wrong yet again!
(10x^2 – 13x + 12) ÷ (5x + 1) = 2x-3 + 15/(5x+1)
check:
(2x-3)(5x+1) = 10x^2 - 13x - 3
To divide the expression (10x^2 – 13x + 12) by (5x + 1), we can use polynomial long division. Here are the steps:
Step 1: Divide the first term of the dividend (10x^2) by the first term of the divisor (5x).
(10x^2 ÷ 5x = 2x)
Step 2: Multiply the result (2x) by the entire divisor (5x + 1).
(2x * (5x + 1) = 10x^2 + 2x)
Step 3: Subtract the previous result from the dividend.
(10x^2 – 13x + 12) - (10x^2 + 2x) = -15x + 12.
Step 4: Bring down the next term from the dividend (-15x).
(-15x)
Step 5: Divide the first term of the new dividend (-15x) by the first term of the divisor (5x).
(-15x ÷ 5x = -3)
Step 6: Multiply the result (-3) by the entire divisor (5x + 1).
(-3 * (5x + 1) = -15x - 3)
Step 7: Subtract the previous result from the new dividend.
(-15x + 12) - (-15x - 3) = 15x + 15.
Step 8: Bring down the last term from the dividend (+15).
(15)
The final result of the division is:
2x - 3 + (15x + 15) / (5x + 1).
Therefore, the answer is option A: 2x minus 3 plus 15 over 5x plus 1.
To divide the polynomial (10x^2 - 13x + 12) by (5x + 1), you can use long division or synthetic division. Let's use long division to find the quotient.
First, write the dividend (10x^2 - 13x + 12) and divisor (5x + 1) in the division format:
___________________
5x + 1 | 10x^2 - 13x + 12
To begin the long division, divide the first term of the dividend (10x^2) by the first term of the divisor (5x). The result is 2x:
2x
___________________
5x + 1 | 10x^2 - 13x + 12
Next, multiply the divisor (5x + 1) by the quotient (2x). The result is 10x^2 + 2x:
2x
___________________
5x + 1 | 10x^2 - 13x + 12
- (10x^2 + 2x)
Subtract the result from the dividend (10x^2 - 13x + 12 - (10x^2 + 2x)):
2x
___________________
5x + 1 | 10x^2 - 13x + 12
- (10x^2 + 2x)
___________________
- 11x + 12
Bring down the next term (-11x) from the dividend:
2x - 3
___________________
5x + 1 | 10x^2 - 13x + 12
- (10x^2 + 2x)
___________________
- 11x + 12
- (-11x - 3)
Subtract the result from the dividend (-11x + 12 - (-11x - 3)):
2x - 3
___________________
5x + 1 | 10x^2 - 13x + 12
- (10x^2 + 2x)
___________________
- 11x + 12
- (-11x - 3)
___________________
15
There is no remainder, so the quotient is 2x - 3.
Therefore, the correct answer is A. 2x minus 3 plus 15 over 5x plus 1.