jerneltelio60
Answered

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use synthetic division to find the quotient of(x³+4x²-x-22)and (x-2).​

Sagot :

Ichigx

PROBLEM:

  • use synthetic division to find the quotient of(x³+4x²-x-22)and (x-2).​

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ANSWER:

  • [tex]\boxed{\green{x^2+6x+11}}[/tex]

==============================

CHECKING:

[tex]\frac{\left(x^3+4x^2-x-22\right)}{\left(x-2\right)}[/tex]

Coefficients of the numerator polynomial

1   4   -1     -22

Find the zeros of the denominator: [tex]x = 2[/tex]

Write the problem in synthetic division format:

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}\end{matrix}[/tex]

[tex]\mathrm{Carry\:down\:the\:leading\:coefficient,\:unchanged,\:to\:below\:the\:division\:symbol}[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}\end{matrix}[/tex]

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

[tex]1\cdot \:2=2[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space}\end{matrix}[/tex]

Add down the column:

[tex]4+2=6[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space\space\space\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space6\space\space\space\space\space\space\space\space\space\space}\end{matrix}[/tex]

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

[tex]6\cdot \:2=12[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space12\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space6\space\space\space\space\space\space\space\space\space\space}\end{matrix}[/tex]

Add down the column:

[tex]-1+12=11[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space12\space\space\space\space\space}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space6\space\space\space11\space\space\space\space\space}\end{matrix}[/tex]

Multiply the carry-down value by the zero of the denominator, and carry the result up into the next column:

[tex]11\cdot \:2=22[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space12\space\space\space22}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space6\space\space\space11\space\space\space\space\space}\end{matrix}[/tex]

Add down the column:

[tex]-22+22=0[/tex]

[tex]\begin{matrix}\texttt{\space\space\space\space2¦\space\space\space\space1\space\space\space\space4\space\space\space-1\space\space-22}\\ \texttt{\space\space\space\space\space¦\underline{\space\space\space\space\space\space\space\space\space2\space\space\space12\space\space\space22}}\\ \texttt{\space\space\space\space\space\space\space\space\space\space1\space\space\space\space6\space\space\space11\space\space\space\space0}\end{matrix}[/tex]

[tex]\mathrm{The\:last\:carry-down\:value\:is\:the\:remainder}[/tex]

0

[tex]\mathrm{Write\:the\:result\:in\:polynom\:format}[/tex]

[tex]\boxed{\green{x^2+6x+11}}[/tex]

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