\[
\left(3 y^{3}+2 y^{2}+7 y+4\right) \div(y-4)
\]
Use synthelic susion to sivize the polynominals

Answer

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Answer

\( 3y^{3} + 2y^{2} + 7y + 4 = (y - 4)(3y^{2} + 42y - 28) + 48y^{2} - 78y + 184 \)

Steps

Step 1 ：\( 3y^{3} +2y^{2} +7y +4 = \frac{(3y^{3} + 2y^{2} + 7y + 4)(y - 4) + c}{y - 4} \)

Step 2 ：\( c = 48y^{2} - 78y + 184 \)

Step 3 ：\( 3y^{3} + 2y^{2} + 7y + 4 = (y - 4)(3y^{2} + 42y - 28) + 48y^{2} - 78y + 184 \)