# Let Q(x)=x^4-3x^3+2x^2+x-3. Evaluate Q(x) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. Q(-3)

Let $Q\left(x\right)={x}^{4}-3{x}^{3}+2{x}^{2}+x-3$.
Evaluate Q(x) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. Q(-3)
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Hayden Espinoza
$Q\left(-3\right)={x}^{4}-3{x}^{3}+2{x}^{2}+x-3$ write the function
$=\left(-3{\right)}^{4}-3\left(-3{\right)}^{3}+2\left(-3{\right)}^{2}+\left(-3\right)-3$ substitute the values
=81-3(-27)+2(9)+(-3)-3 evaluate the exponents
=81+81+18-3-3 perform multiplication
=174 remainder
Perform synthetic division to determine the remainder:
polyhorner scheme $\left[x=-3\right]\left\{{x}^{4}-3{x}^{3}+2{x}^{2}+x-3\right\}$
Result:
Q(-3)=174