$$x^{4}+3x^{3}-2x^{2}+4x-3; x=-5$$
$y=177$
$$y=\left(-5\right)^{4}+3\left(-5\right)^{3}-2\left(-5\right)^{2}+4\left(-5\right)-3$$
$$y=625+3\left(-5\right)^{3}-2\left(-5\right)^{2}+4\left(-5\right)-3$$
$$y=625+3\left(-125\right)-2\left(-5\right)^{2}+4\left(-5\right)-3$$
$$y=625-375-2\left(-5\right)^{2}+4\left(-5\right)-3$$
$$y=250-2\left(-5\right)^{2}+4\left(-5\right)-3$$
$$y=250-2\times 25+4\left(-5\right)-3$$
$$y=250-50+4\left(-5\right)-3$$
$$y=200+4\left(-5\right)-3$$
$$y=200-20-3$$
$$y=180-3$$
$$y=177$$
$$x=-5$$ $$y=177$$
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