can someone please help me with my math?(algebra 2 and polynomial factoring)

Question

AddieroniAndCheese · Answer

yeah sure, I'm in precalc

Krissyy2025 · Answer

ME

Aratox · Answer

She provided us with the problem in All Subjects earlier, it is

$$a^3-b^3=(a-b)(a^2+b^2)$$

lanaa · Answer

$$125x^4-1=0$$

lanaa · Answer

i meant 3*

adrianluvvsyouu2 · Answer

@lanaa wrote:

i meant 3*

125x^3 - 1 = 0?

Gdub08 · Answer

I got no clue what this means.

lanaa · Answer

@adrianluvvsyouu2 wrote:

@lanaa wrote:

i meant 3*

125x^3 - 1 = 0?

yes

surjithayer · Answer

$$a^3-b^3=\left( a-b \right)\left( a^2+ab+b^2 \right)$$
$$125x^3-1=0$$
$$\left( 5x \right)^3-1^3=0$$
$$\left( 5x-1 \right)^3\left[ \left( 5x \right) ^2+\left( 5x \right)\left( 1 \right)+1^2\right]=0$$
$$\left( 5x-1 \right)^3\left[ 25x^2+5x+1 \right]=0$$
either
5x-1=0
5x=1
$$x=\frac{ 1 }{ 5}$$
or
$$5x^2+5x+1=0$$
$$x=\frac{ -5\pm \sqrt{5^2-4(5)(1)} }{ 2(5) }$$
$$x=\frac{ -5 \pm \sqrt{25-20} }{ 10}$$
$$x=\frac{ -5\pm \sqrt{5} }{ 10 }=-\frac{ 5 }{ 10}\pm \frac{ \sqrt{5} }{ 10}$$

lanaa · Answer

@surjithayer wrote:

$$a^3-b^3=\left( a-b \right)\left( a^2+ab+b^2 \right)$$ $$125x^3-1=0$$ $$\left( 5x \right)^3-1^3=0$$ $$\left( 5x-1 \right)^3\left[ \left( 5x \right) ^2+\left( 5x \right)\left( 1 \right)+1^2\right]=0$$ $$\left( 5x-1 \right)^3\left[ 25x^2+5x+1 \right]=0$$ either 5x-1=0 5x=1 $$x=\frac{ 1 }{ 5}$$ or $$5x^2+5x+1=0$$ $$x=\frac{ -5\pm \sqrt{5^2-4(5)(1)} }{ 2(5) }$$ $$x=\frac{ -5 \pm \sqrt{25-20} }{ 10}$$ $$x=\frac{ -5\pm \sqrt{5} }{ 10 }=-\frac{ 5 }{ 10}\pm \frac{ \sqrt{5} }{ 10}$$

i just need like the factoring like how would i write a^3−b^3=(a−b)(a^2+ab+b^2) with the equation

adrianluvvsyouu2 · Answer

@lanaa wrote:

@adrianluvvsyouu2 wrote:

@lanaa wrote:

i meant 3*

125x^3 - 1 = 0?

yes

You can write 125 as 5^3 (5*5*5) so that it has the same power as the x.. Now it's 5^3 * x^3 - 1 If you have two things to the same power being multiplied, you can simplify and write it as... (5x)^3 - 1 1 is the same as 1^3 So then you have (5x)^3 - 1^3 Now we have your original expression in the form a^3 - b^3 which equals (a - b)(a^2 + ab + b^2). So, 5x = a 1 = b (5x - 1) is the first part, then [(5x)^2 + 5x * 1 + 1^2] is your second term All together it should look like: (5x-1)((5x)^2 + 5x + 1) Theres no way to factor out the second part further without using the quadratic formula and making it look ugly, this is the most simplified version, and is factored. Hope this helps!

surjithayer · Answer

write 5x-1 in 3rd and 4th line.
by mistake written (5x-1)^3