Question

Show that (x-2)(2x+3)(x+5) can be written in the form ax³+bx²+cx+d

Answer 1

The expression
`\((x-2)(2x+3)(x+5)\)` can be written in the form (ax³+bx²+cx+d) as follows: "(2x³-11x²-26x-30)".

Step-by-step explanation:

To express the given expression (x-2)(2x+3)(x+5) in the form (ax³+bx²+cx+d), we need to perform the multiplication and simplification. Begin by multiplying the linear factors pairwise. First, multiply (x-2) and (2x+3):

[(x-2)(2x+3) = 2x² - x - 6]

Next, multiply the result by (x+5):

[(2x² - x - 6)(x+5) = 2x³ - 11x² - 26x - 30]

Therefore, the expression ((x-2)(2x+3)(x+5)) can be written in the form (ax³+bx²+cx+d) as "(2x³-11x²-26x-30)".

This cubic polynomial is now in the desired form, where (a = 2), (b = -11), (c = -26), and (d = -30). The coefficients represent the coefficients of the corresponding terms in the polynomial.