can u help me to find the product of -4x^2 and x^3 + 2x^2 - 5x + 3
and the solution to the equation of x^2 + 30x = 1000...I came up with -20 and 50 but i don't think it is right..can u help
also can you help me to do the factorization of 6x^2 - 2x - 20.....Help please help
Assistance needed.
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For the first problem, just multiply each terms by -4x^2 (e.g., -4x^2 * x^3 = -4x^5). (When multiplying two like terms with exponents, you add the exponents, e.g., -4x^2 * x^3 = -4x * x * x * x *x. )
x^2 + 30x = x(x+30) = 1000 This should help.
What two numbers have a product of -20? Will they give you -2, if 6 times one minus the other gives you -2?
I hope this helps. Thanks for asking.
Of course! I'd be happy to help you with these problems.
To find the product of -4x^2 and x^3 + 2x^2 - 5x + 3, we can use the distributive property. We multiply -4x^2 by each term in the second expression separately and then combine the like terms. Here's how you can do it step by step:
-4x^2 * x^3 = -4x^5
-4x^2 * 2x^2 = -8x^4
-4x^2 * (-5x) = 20x^3
-4x^2 * 3 = -12x^2
Now, we can combine all of these terms together:
-4x^5 + (-8x^4) + 20x^3 + (-12x^2)
Simplifying further, we get:
-4x^5 - 8x^4 + 20x^3 - 12x^2
Now let's move on to the equation x^2 + 30x = 1000. To find the solution(s) of this equation, we need to solve for x. Here's how you can do it step by step:
First, let's move all the terms to one side of the equation to set it equal to zero:
x^2 + 30x - 1000 = 0
To factorize this quadratic equation, we need to find two numbers whose product is -1000 and whose sum is 30. We can do this by trial and error or by using the quadratic formula.
By factoring or using the quadratic formula, we can find that the two solutions to this equation are x = -50 and x = 20. So, your initial solution of -20 and 50 is incorrect.
Finally, let's factorize the expression 6x^2 - 2x - 20. Here's how you can do it step by step:
First, check if there's a common factor among all the terms. In this case, the common factor is 2:
2(3x^2 - x - 10)
Now, let's focus on factoring the quadratic expression within the parentheses, 3x^2 - x - 10. We need to find two numbers whose product is -30 (3 * -10) and whose sum is -1 (coefficient of x). These numbers are -6 and 5:
2(3x^2 - 6x + 5x - 10)
Now, we can group the terms:
2((3x^2 - 6x) + (5x - 10))
Factor out the common factors within each group:
2(3x(x - 2) + 5(x - 2))
Now, we can notice that (x - 2) is a common factor within both groups, so we can factor it out:
2(x - 2)(3x + 5)
So, the expression 6x^2 - 2x - 20 can be factorized as 2(x - 2)(3x + 5).
I hope this explanation helps you understand how to approach these problems! If you have any further questions, feel free to ask.