how do you factor 3x^3-6x^2-24x
I know that it becomes 3x(x^2-2x-8), but you can still factor it more. how?
Try distributing. I'm pretty sure that 3x times x^2 would be 3x^3, because you add the exponents. You'd do it with the rest of the stuff in the parentheses, too. :)
after you get 3x(x^2-2x-8), look at what is in the parenthesis.
x^2-2x-8
what are 2 numbers that add to the constant, 8?
at the same time, these 2 numbers must equal -2
the two numbers should be -4 and 2
so the final answer would be..
3x(x-4)(x+2)
hope this helps. =)
To factor the expression 3x^3 - 6x^2 - 24x further, you can use the method of factoring by grouping. Here's how:
Step 1: Group the terms in pairs.
3x(x^2 - 2x - 8)
Step 2: Factor out the greatest common factor from each pair.
3x(x^2 - 2x - 8) = 3x(1x^2 - 2x - 8)
Step 3: Now, we focus on factoring the quadratic expression inside the parentheses, which is 1x^2 - 2x - 8.
To factor a quadratic expression, we need to find two binomial expressions whose product equals the original quadratic. In this case, the product of the binomials should have a first term of x^2, the last term of -8, and a middle term of -2x.
Step 4: Determine two numbers whose product is -8 and whose sum is -2. The two numbers are -4 and 2.
Step 5: Rewrite the middle term -2x as the sum of -4x and 2x.
3x(1x^2 - 4x + 2x - 8)
Step 6: Group the terms again, this time with the binomials.
3x[(1x^2 - 4x) + (2x - 8)]
Step 7: Factor out the greatest common factor from each pair separately.
3x[x(1x - 4) + 2(1x - 4)]
Step 8: Notice that we have a common binomial factor, (1x - 4), in both pairs. Factor it out.
3x(1x - 4)(x + 2)
Finally, the factored form of the expression 3x^3 - 6x^2 - 24x is 3x(1x - 4)(x + 2).