Can someone help me with this please.
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 thus Andrews solution does not appear to check. Why is that? Please help Andrew to understand this better. Explain your answer reasoning and correctly factor the original expression if possible. If the expression is prime so state.
Andrew divided only the first term by 4x.
Should have been
4x(5x^2 - 3x + 2)
The mistake that Andrew made while factoring the expression is that he didn't distribute the 4x properly to each term inside the parentheses. Andrew factored out the common factor of 4x correctly, but he didn't distribute it correctly to each term.
To correctly factor the expression 20x^3 - 12x^2 + 8x, we need to distribute the 4x to each term inside the parentheses:
4x(5x^2 - 12x + 8)
Now, let's focus on the terms inside the parentheses: 5x^2 - 12x + 8.
To factor this trinomial, we need to find two numbers whose product is equal to the product of the coefficient of the squared term (5) and the constant term (8), and whose sum is equal to the coefficient of the linear term (-12).
The product of 5 and 8 is 40. We need to find two numbers whose product is 40 and whose sum is -12. Since there are no such numbers, we can conclude that the trinomial 5x^2 - 12x + 8 cannot be factored further using integers.
Therefore, the correctly factored expression is 4x(5x^2 - 12x + 8).
It's important to remember that when factoring, we need to apply the distributive law correctly. In this case, Andrew made a mistake by not distributing the common factor properly.