Step-by-step explanation:
1 * (-5) = -5 a = -5
6 + (-5) = 1 b = 1
1 * (-5 ) = -5 c = -5
-7 + -5 = -12 d = -12
The divisor of the polynomial in the synthetic long division is linear factor
The correct values are;
Reason:
[tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex]
The divisor in the division is (x - (-5)) = (x + 5)
By synthetic long division, we have;
Carry down the 1 representing the leading coefficient
Multiply the 1 brought down by the zero value of x which is -5, and take the result into the second line of the division symbol
-5 × 1 = -5
Add the coefficient 6 to -5, and bring down the result
Repeat the above steps again to get;
-5 × 1 = -5
-5 × (-12) = 60
By comparison to the given synthetic long division, [tex]-5 \underline{\left \lfloor{ \begin{matrix}1 & 6 & -7 &-60 \\ &a & c & 60\end{matrix}}} \underset \hspace {} \hspace {0.6 cm} 1 \ \ b \hspace {0.25 cm} d \hspace {0.25 cm} 0[/tex], we have;
a = -5, c = -5, b = 1, and d = -12
Learn more about synthetic long division here:
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