divide 15x^2 + 10x -5 by 5x
To divide the polynomial 15x^2 + 10x - 5 by 5x, we can use long division. Here's how you can do it step by step:
Step 1: Write the polynomial in descending order of exponents. In this case, it's already in descending order.
15x^2 + 10x - 5
Step 2: Divide the first term of the polynomial (15x^2) by the divisor (5x). The result is 3x. Write this above the horizontal line.
3x
______________
5x | 15x^2 + 10x - 5
Step 3: Multiply the divisor (5x) by the quotient (3x), and write the product beneath the 10x term of the polynomial.
3x
______________
5x | 15x^2 + 10x - 5
- (15x^2 + 0x)
Step 4: Subtract the product from the polynomial to get the new polynomial.
3x
______________
5x | 15x^2 + 10x - 5
- (15x^2 + 0x)
__________
10x - 5
Step 5: Divide the first term of the new polynomial (10x) by the divisor (5x). The result is 2. Write this above the horizontal line.
3x + 2
______________
5x | 15x^2 + 10x - 5
- (15x^2 + 0x)
__________
10x - 5
Step 6: Multiply the divisor (5x) by the new quotient (2), and write the product beneath the -5 term of the new polynomial.
3x + 2
______________
5x | 15x^2 + 10x - 5
- (15x^2 + 0x)
__________
10x - 5
- (10x + 0)
_______
-5
Step 7: Subtract the product from the new polynomial to get the remainder.
3x + 2
______________
5x | 15x^2 + 10x - 5
- (15x^2 + 0x)
__________
10x - 5
- (10x + 0)
_______
-5
Step 8: Since the degree of the remainder, -5, is less than the degree of the divisor, 5x, we stop here.
So, the quotient is 3x + 2 and the remainder is -5.
Therefore, the division of 15x^2 + 10x - 5 by 5x is equal to 3x + 2 with a remainder of -5.
( 15 x ^ 2 + 10 x - 5 ) / 5 x =
5 ( 3 x ^ 2 + 2 x - 1 ) / 5 x =
( 3 x ^ 2 + 2 x - 1 ) / x =
3 x + 2 - 1 / x