Question

Which of the following polynomials can approximate the expression (4x³+5)(3x⁶−8x²)/(2x²−8x−4)−4x³−2x+13?

a) 2x³−7x²+5x+2
b) 6x⁵+4x²−8x+10
c) 12x7−2x⁴−6x³+26x²−48
d) 3x²−4x+7

Answer 1

To approximate the given expression, we need to factor the numerator and simplify the expression by dividing it by the denominator. The correct answer is option c) 12x7−2x⁴−6x³+26x²−48.

Step-by-step explanation:

To approximate the expression (4x³+5)(3x⁶−8x²)/(2x²−8x−4)−4x³−2x+13, we can factor the numerator and simplify the expression. The factored form of (4x³+5)(3x⁶−8x²) is 4x³(3x⁶−8x²) + 5(3x⁶−8x²). We can then divide this by the denominator (2x²−8x−4) and simplify further. Computing the expression will give us the final polynomial.

The correct answer is option c) 12x7−2x⁴−6x³+26x²−48.