Question
Evaluate the following polynomial when \( x=-3 \) and when \( x=0 \). \[ -3 x^{3}+6 x^{2}-2 x+4 \] When \( x=-3 \), the value of the polynomial is 145 . (Type an integer or a simplified fraction.) When \( \mathrm{x}=0 \), the value of the polynomial is \( \square \). (Type an integer or a simplified fraction.)
Ask by Norris Coleman. in the United States
Feb 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When \( x = 0 \), the value of the polynomial is 4.
Solution
To evaluate the polynomial -3x³ + 6x² - 2x + 4 when x = 0, substitute 0 for x:
-3(0)³ + 6(0)² - 2(0) + 4 = 0 + 0 + 0 + 4 = 4.
Thus, when x = 0, the value of the polynomial is 4.
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Simplify this solution Extra Insights
To evaluate the polynomial \(-3x^3 + 6x^2 - 2x + 4\) at \(x = 0\), we simply substitute \(0\) for \(x\): \[ -3(0)^3 + 6(0)^2 - 2(0) + 4 = 0 + 0 + 0 + 4 = 4. \] So, when \(x = 0\), the value of the polynomial is \(4\).
