factor the following expression completely 75x^4+35x^3-10x^2
75x^4 + 35x^3 - 10x^2
See your first post below for an example of how this is done.
Hint, factor out 5x^2 first, then factor the remaining expression.
You will never learn without practice :)
75x^4+35x^3-10x^2=(5x^2)*(15x^2+7x-2)
Factoring:
15x^2+7x-2
Using the factor pair (-3, 10) whose sum is 7, rewrite your equation replacing the term 7 x with
-3 x and 10 x.
15x^2+7x-2=15x^2-3x+10x-2
Now group the first two terms and the last two terms on the left hand side:
(15x^2-3x)+(10x-2)
Within each group, factor out common factors.
(15x^2-3x)+(10x-2)=3x*(5x-1)+2*(5x-1)
Notice that the two quantities in parentheses are the same. This means that the quantity, (5x-1), is a common factor and we can factor it out.
3x*(5x-1)+2*(5x-1)=(5x-1)*(3x+2)
15x^2+7x-2=(5x-1)*(3x+2)
75x^4+35x^3-10x^2=(5x^2)*(15x^2+7x-2)=
(5x^2)*(5x-1)*(3x+2)
Hvala
To factor the expression 75x^4 + 35x^3 - 10x^2 completely, we can first look for the greatest common factor (GCF) of all the terms. In this case, all terms have a common factor of 5x^2. Factoring it out, we get:
5x^2(15x^2 + 7x - 2)
Now we need to factor the quadratic expression (15x^2 + 7x - 2), which can be done using various methods like factoring, completing the square, or using the quadratic formula. In this case, let's try factoring.
First, we need to find two numbers that multiply to give the constant term (-2) and add up to give the coefficient of the middle term (7). The two numbers that fit these requirements are 8 and -1. Therefore, we can rewrite the quadratic expression as:
5x^2(15x^2 + 8x - x - 2)
Next, we group the terms and factor out the common factors:
5x^2[(15x^2 + 8x) + (-x - 2)]
Now we can factor out the GCF from each group:
5x^2(8x + 15x) - (x + 2)
After factoring, we get:
5x^2(8x + 15) - (x + 2)
So, the completely factored expression is:
5x^2(8x + 15) - (x + 2)