Divide.
(20x^2-12x+8) (2x-8)
First, let's factor out the greatest common factor of the expression inside the parentheses, which is 4:
4(5x^2 - 3x + 2) (2x - 8)
Next, we notice that we can further simplify the expression inside the parentheses by factoring it using the quadratic formula or by guessing and checking. Either way, we end up with:
4(5x + 2)(x - 1) (2x - 8)
Now, we can cancel out the factor of 2 from both the second and third terms in the expression inside the parentheses:
4(5x + 2)(x - 1) 2(x - 4)
Finally, we can simplify further by canceling out the factor of 2 between the 4 and the 2, leaving us with the final answer:
8(5x + 2)(x - 1)(x - 4)
To divide the polynomial (20x^2 - 12x + 8) by (2x - 8), you can use long division. Here are the steps:
Step 1: Write the dividend (20x^2 - 12x + 8) and the divisor (2x - 8) as shown:
____________________________
2x - 8 | 20x^2 - 12x + 8
Step 2: Divide the first term of the dividend (20x^2) by the first term of the divisor (2x). The quotient is 10x. Write this above the line, aligned with the first term of the dividend:
10x
____________________________
2x - 8 | 20x^2 - 12x + 8
Step 3: Multiply the divisor (2x - 8) by the quotient (10x). The result is 20x^2 - 80x. Write this below the dividend:
10x
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
Step 4: Subtract the result from Step 3 from the original dividend:
10x
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
_____________________
68x + 8
Step 5: Bring down the next term, which is +8, and rewrite it below the line:
10x
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
_____________________
68x + 8
+ 8
Step 6: Divide the first term of the new dividend (68x) by the first term of the divisor (2x). The quotient is 34. Write this above the line, aligned with the first term of the new dividend:
10x + 34
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
_____________________
68x + 8
+ 8
Step 7: Multiply the divisor (2x - 8) by the new quotient (34). The result is 68x - 272. Write this below the new dividend:
10x + 34
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
_____________________
68x + 8
+ 8
- (68x - 272)
Step 8: Subtract the result from Step 7 from the new dividend:
10x + 34
____________________________
2x - 8 | 20x^2 - 12x + 8
- (20x^2 - 80x)
_____________________
68x + 8
+ 8
- (68x - 272)
_____________________
280
Step 9: Since there are no more terms to bring down, the division process is complete. The remainder is 280. Therefore, the division result is:
Quotient: 10x + 34
Remainder: 280
Hence, the result of dividing (20x^2 - 12x + 8) by (2x - 8) is (10x + 34) with a remainder of 280.