how many x - intercepts appear on the graph of this polynomial function?\nf(x)=x^{4}-x^{3}+x^{2}-x\n1 x…

how many x - intercepts appear on the graph of this polynomial function?\nf(x)=x^{4}-x^{3}+x^{2}-x\n1 x - intercept\n2 x - intercepts\n3 x - intercepts\n4 x - intercepts

how many x - intercepts appear on the graph of this polynomial function?\nf(x)=x^{4}-x^{3}+x^{2}-x\n1 x - intercept\n2 x - intercepts\n3 x - intercepts\n4 x - intercepts

Answer

Explanation:

Step1: Factor the polynomial

$f(x)=x^4 - x^3+x^2 - x=x(x^3 - x^2+x - 1)=x[x^2(x - 1)+(x - 1)]=x(x - 1)(x^2+1)$

Step2: Find the x - intercepts

Set $f(x)=0$. Then $x(x - 1)(x^2+1)=0$. Since $x^2+1=(x + i)(x - i)$ has no real - roots, and $x=0$ or $x - 1=0$ gives $x = 0$ and $x=1$.

Answer:

2 x - intercepts