Factor x3 + 9x2 + 27x + 27
Factor 8a3 + 60a2b + 150 ab2+ 125b3
I tried doing them, but I just don't get how; perfect squares didn't work and neither did decomposition... someone please help me.
Factor the following:
a)x4 + 11x2 + 30
b)x4 – 7x2y + 12y2
c)x6 - 3x3 -54
d)3(x – 5)2 + 27(x – 5) – 66
<<Factor x^3 + 9x^2 + 27x + 27 >>
There is no simple general formula for solving cubic equations or factoring cubic poynomials. First look for one root of
x^3 + 9x^2 + 27x + 27 = 0
by graphing or trial and error.
One root is x = -3. That means that x+3 is one of the factors of
x^3 + 9x^2 + 27x + 27. Now use long division to get the quadratic factor. Divide x^3 + 9x^2 + 27x + 27 by (x+3), which will give you (x^2 + 6x + 9). That can be factored to (x+3)^2
The factored form is thus
(x+3)^3
oh, okay, thanks!
To factor the expression x^3 + 9x^2 + 27x + 27, you can use a method called "grouping."
1. Start by grouping the terms into pairs:
(x^3 + 9x^2) + (27x + 27)
2. Factor out the greatest common factor from each pair:
x^2(x + 9) + 27(x + 1)
3. Notice that both terms now have a common factor of (x + 1). Factor it out:
(x + 1)(x^2 + 9x + 27)
So the factored form of the expression is (x + 1)(x^2 + 9x + 27).
To factor the expression 8a^3 + 60a^2b + 150ab^2 + 125b^3, you can use a method called "factoring by grouping" as well.
1. Group the terms in pairs:
(8a^3 + 60a^2b) + (150ab^2 + 125b^3)
2. Find the greatest common factor of each pair:
4a^2(2a + 15b) + 25b^2(6a + 5b)
3. Notice that both terms now have a common factor. Factor it out:
4a^2(2a + 15b) + 25b^2(6a + 5b)
So the factored form of the expression is 4a^2(2a + 15b) + 25b^2(6a + 5b).
If you are struggling with factoring, it might be helpful to review the techniques of factoring, such as factoring by grouping, factoring quadratic expressions, and recognizing perfect squares or difference of squares. Practice and familiarity with these techniques will improve your ability to factor more complicated expressions.