Factor completley
12r^2 +36rf +27f^2
5x^5-20x^4+30x^3
Can anyone please help me with these two problems. I have to get them done and do not understand them. Please help me.
12r^2 +36rf +27f^2
= 3(4r^2 + 12rf + 9f^2)
= 3(2r+3f)(2r+3f) or 3(2r+3f)^2
5x^5-20x^4+30x^3
= 5x^3(x^2 - 4x + 6)
Of course, I'd be happy to help you with these factoring problems!
Let's start with the first problem: 12r^2 + 36rf + 27f^2.
To factor this expression completely, we need to look for common factors in each term. In this case, we can see that all three terms have a factor of 3. Let's factor out 3:
3(4r^2 + 12rf + 9f^2)
Now, let's focus on factoring the expression inside the parentheses: 4r^2 + 12rf + 9f^2.
To factor this quadratic expression, we need to find two binomials where the product of their first terms gives us 4r^2, the product of their last terms gives us 9f^2, and the sum of the products of their outer and inner terms gives us 12rf.
To factor the expression 4r^2 + 12rf + 9f^2, we can use the following factors:
(2r + 3f)(2r + 3f)
Therefore, the completely factored form of 12r^2 + 36rf + 27f^2 is:
3(2r + 3f)(2r + 3f)
Now let's move on to the second problem: 5x^5 - 20x^4 + 30x^3.
Similar to the first problem, we need to look for common factors in each term. Here, we have a common factor of 5x^3. Let's factor it out:
5x^3(x^2 - 4x + 6)
Now, let's focus on factoring the expression inside the parentheses: x^2 - 4x + 6.
Since this quadratic expression doesn't have easy-to-find factors, we can use the quadratic formula or complete the square. However, in this case, the expression does not factor further using whole numbers.
Therefore, the completely factored form of 5x^5 - 20x^4 + 30x^3 is:
5x^3(x^2 - 4x + 6)
I hope this explanation helps you understand how to factor these expressions. If you have any further questions, feel free to ask!