Find the product: -6x(-8x^2+x+5)
A)-14x^3-5x^2-x
B)48x^3+x+5
C)48x^3-6x^2-30x
D)48x^2-6x-30
To find the product (-6x)(-8x^2 + x + 5), you need to apply the distributive property. This property states that when multiplying a number or term by a group of terms, you must multiply each term individually and then simplify the expression.
Let's break down the multiplication step by step:
-6x * -8x^2 = 48x^3 (When multiplying the coefficients, -6 * -8 = 48. When multiplying the variables, x * x^2 = x^3, using the exponent rule that states x * x^a = x^(1+a))
-6x * x = -6x^2 (Multiply the coefficients -6 * 1 = -6. Multiply the variables x * x^1 = x^2)
-6x * 5 = -30x (Multiply the coefficients -6 * 5 = -30. Leave the variable x as it is)
Now, let's combine the results:
48x^3 + (-6x^2) + (-30x) = 48x^3 - 6x^2 - 30x
Therefore, the final answer is C) 48x^3 - 6x^2 - 30x.