Question

Which expression is equal to the polynomial

below?
2x ⁴+ 5x³-8x – 20?
a) 2(x⁴+2x³−4x−10)
b) 2(x²+2x+1)(x²−4)
c) (x²−2)(2x2 +4x+10)
d) (2x²−2)(x 2+4x+10)

Answer 1

The correct expression equal to the given polynomial 2x⁴ + 5x³ - 8x - 20 is option (a) 2(x⁴ + 2x³ - 4x - 10), which simplifies to the original polynomial when distributed.

Step-by-step explanation:

The student has asked which expression is equal to the polynomial 2x⁴ + 5x³ - 8x - 20. To find which of the given expressions is equivalent to this polynomial, we need to either factor the polynomial or expand the given options and compare them to the original expression. Let's try to factor the given polynomial:

2x⁴ + 5x³ - 8x - 20 = x³(2x + 5) - 4(2x + 5) = (x³ - 4)(2x + 5).

This factored form is not listed as one of the options, so let's try option (a) which is in a factored form similar to factoring by grouping:

2(x⁴ + 2x³ - 4x - 10) = 2x⁴ + 4x³ - 8x - 20.

This is exactly the same as the original polynomial after distributing the 2. Therefore, option (a) is the correct expression that is equal to the given polynomial.