Andrew factored the expression 20x^3-12x^2+8x as 4x (5x^2-12x^2+8x). But when Melissa applied the distributive law and multiplied out 4x (5x^2-12x^2+8x), she got 20x^3-48x^3+32x^2; thus, Andrew’s solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

Answer 1

sure, you can take 4x out but do it properly
4x (5 x^2 -3 x + 2)

Answer 2

Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
x2 = 3x – 6