I need help finding the x and y intercepts

[jgarcia]

I need to figure this out,

f(x)=x³+3x²+x+1

I need to find the x and y intercepts. Here is my work:

y-int

y=(0)³+3(0)²+(0)+1
y=1

done!

x-int

x³+3x²+x+1=0

Here is where I struggle, simplifying this. I am not very good at factoring or knowing what to do when. It's like I am dyslexic or something. No offence with those are affected by it.

x²(x+3) + 1(x+1)=0
(x²+1)(x+3)(x+1)=0
(x²+1²)(x+3)(x+1)=0
x²=-1² x=–3 x=–1
√x²=√-1² x=–3 x=–1
x=±1x=–3 x=–1
x=1x=–3 x=–1

∴ my y-int is y=1 and my x-int arex=–3 x=–1 x=1

Yes? No? Maybe?

Thanks in advance!

 

[HallsofIvy]

I need to figure this out,

f(x)=x³+3x²+x+1

I need to find the x and y intercepts. Here is my work:

y-int

y=(0)³+3(0)²+(0)+1
y=1

done!

x-int

x³+3x²+x+1=0

Here is where I struggle, simplifying this. I am not very good at factoring or knowing what to do when. It's like I am dyslexic or something. No offence with those are affected by it.

Since ab+ ac has "common factor", a, we can "factor" it: a(b+ c).

x²(x+3) + 1(x+1)=0
(x²+1)(x+3)(x+1)=0
(x²+1²)(x+3)(x+1)=0

No, you cannot "factor" x+ 3 and x+ 1 because they are not in both terms. IF you had \(\displaystyle x^2(x+ 3)+ 1(x+ 3)\) then you could write is as \(\displaystyle (x^2+ 1)(x+ 3)\).
If you multiply out \(\displaystyle (x^2+1)(x+ 3)(x+ 1)\) it would have highest power \(\displaystyle x^4\), not \(\displaystyle x^3\).

x²=-1² x=–3 x=–1
√x²=√-1² x=–3 x=–1
x=±1x=–3 x=–1
x=1x=–3 x=–1

\(\displaystyle x^2+1= 0\) gives \(\displaystyle x^2= -1= -(1^2)\) NOT \(\displaystyle (-1)^2\). \(\displaystyle (1)^2+ 1= 2\ne 0\)

∴ my y-int is y=1 and my x-int arex=–3 x=–1 x=1

Yes? No? Maybe?

Thanks in advance!

You may check this by evaluating the function. If \(\displaystyle f(x)= x^3+ 3x^2+ x+ 1\), what is f(1)? What is f(-3)? What is f(-1)?