Final answer:
By expanding the polynomial and identifying the coefficients A, B, C, D, and E, we find that A=8, B=-46, C=81, D=-17, and E=-35. Substituting these into the expression 80A + 28B + 8C + 4D gives us a result of -68.
Step-by-step explanation:
To find the values of A, B, C, D, and E in the expanded form of the given expression, we need to perform polynomial multiplication.
The given expression is: (x² - 5x + 7)(4x - 5)(2x + 1).
First, let's expand the first two polynomials: (x² - 5x + 7)(4x - 5).
4x³ - 5x² - 20x² + 25x + 28x - 35
4x³ - 25x² + 53x - 35
Next, we'll multiply this result by the third polynomial: (4x³ - 25x² + 53x - 35)(2x + 1).
8x´ - 50x³ + 106x² - 70x + 4x³ - 25x² + 53x - 35
8x´ - 46x³ + 81x² - 17x - 35
This gives us the final polynomial, which can be compared with Ax´ + Bx³ + Cx² + Dx + E:
A=8, B=-46, C=81, D=-17, and E=-35.
Finally, to find the value of 80A + 28B + 8C + 4D, we just substitute the values we found:
80(8) + 28(-46) + 8(81) + 4(-17) = 640 - 1288 + 648 - 68
80A + 28B + 8C + 4D = -68