Factor each:
f(x)= x^3 + 7x^2 + 10x
f(x)= 5x^3 -19x^2 - 4x
f(x)=x(x^2+7x+10)
= x(x+5)(x+2)
f(x)=x(5x^2-19x-4)
=x(5x-1)(x+4)
The answers will be correct?
I ment -5,-2 and 1,-4???
No, the solutions are the values of x which make
x = 0
x+5 = 0
x+2 = 0
x = 0, -5, -2
x = 0
5x-1 = 0
x+4 = 0
x = 0, 1/5, -4
To factor each polynomial, we can start by looking for common factors and then using the factoring techniques such as factoring by grouping or using the difference of squares.
Let's start with the first polynomial:
f(x) = x^3 + 7x^2 + 10x
First, we can check if there are any common factors among the terms. In this case, we can see that each term has an x as a common factor. So we can factor out an x:
f(x) = x(x^2 + 7x + 10)
Now, to factor the quadratic expression inside the parentheses, we need to find two binomials that multiply together to give us the quadratic expression.
We're looking for two numbers whose product is 10 and whose sum is 7. The numbers that fit these criteria are 5 and 2.
Therefore, we can rewrite the quadratic expression as:
f(x) = x(x + 5)(x + 2)
Now let's move on to the second polynomial:
f(x) = 5x^3 - 19x^2 - 4x
Again, let's check for any common factors. In this case, the only common factor among the terms is x. So we can factor out an x:
f(x) = x(5x^2 - 19x - 4)
To factor the quadratic expression inside the parentheses, we need to find two binomials that multiply together to give us the quadratic expression.
We're looking for two numbers whose product is -4 and whose sum is -19. The numbers that fit these criteria are -4 and 1.
Therefore, we can rewrite the quadratic expression as:
f(x) = x(5x + 1)(x - 4)
So the factored forms for the given polynomials are:
f(x) = x(x + 5)(x + 2) (for the first polynomial)
f(x) = x(5x + 1)(x - 4) (for the second polynomial)