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- https://math.libretexts.org/Courses/Cosumnes_River_College/Corequisite_Codex/04%3A_Simplifying_Expressions/4.05%3A_Dividing_Polynomials_-_Long_Division\(\qquad \begin{array}{r}x+\phantom{0}4\hspace{.5em}\\[-3pt] x+5\enclose{longdiv}{x^2+\phantom{00}9x+20\phantom{0}}\\[-3pt] \underline{{\color{red}-}x^2+({\color{red}-}5x)}\hspace{2.1em}\\[-3pt] 4x+20...\(\qquad \begin{array}{r}x+\phantom{0}4\hspace{.5em}\\[-3pt] x+5\enclose{longdiv}{x^2+\phantom{00}9x+20\phantom{0}}\\[-3pt] \underline{{\color{red}-}x^2+({\color{red}-}5x)}\hspace{2.1em}\\[-3pt] 4x+20\hspace{.5em}\\[-3pt] \underline{{\color{red}-}4x+({\color{red}-}20)}\\[-3pt] 0\hspace{.33em}\end{array}\) \(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\)
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_104_Intermediate_Algebra/5%3A_Polynomial_and_Polynomial_Functions/5.5%3A_Dividing_Polynomials\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\)...\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\), the value of the function at \(c\), \(f(c)\), is the same as the remainder from the division problem. In function notation we could say, to get the dividend \(f(x)\), we multiply the quotient, \(q(x)\) times the divisor, \(x−c\), and add the remainder, \(r\).
- https://math.libretexts.org/Courses/Coastline_College/Math_C045%3A_Beginning_and_Intermediate_Algebra_(Tran)/07%3A_Polynomial_and_Polynomial_Functions/7.05%3A_Dividing_Polynomials\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\)...\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\), the value of the function at \(c\), \(f(c)\), is the same as the remainder from the division problem. In function notation we could say, to get the dividend \(f(x)\), we multiply the quotient, \(q(x)\) times the divisor, \(x−c\), and add the remainder, \(r\).
- https://math.libretexts.org/Courses/Highline_College/Math_098%3A_Intermediate_Algebra_for_Calculus/03%3A_Chapter_3_-_Rationals/3.03%3A_Divide_Polynomials\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\)...\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\), the value of the function at \(c\), \(f(c)\), is the same as the remainder from the division problem. In function notation we could say, to get the dividend \(f(x)\), we multiply the quotient, \(q(x)\) times the divisor, \(x−c\), and add the remainder, \(r\).
- https://math.libretexts.org/Workbench/Intermediate_Algebra_2e_(OpenStax)/05%3A_Polynomial_and_Polynomial_Functions/5.05%3A_Dividing_PolynomialsFor functions f ( x ) = x 3 + x 2 − 7 x + 2 f ( x ) = x 3 + x 2 − 7 x + 2 and g ( x ) = x − 2 , g ( x ) = x − 2 , find ⓐ ( f g ) ( x ) ( f g ) ( x ) ⓑ ( f g ) ( 2 ) ( f g ) ( 2 ) For functions f ( x )...For functions f ( x ) = x 3 + x 2 − 7 x + 2 f ( x ) = x 3 + x 2 − 7 x + 2 and g ( x ) = x − 2 , g ( x ) = x − 2 , find ⓐ ( f g ) ( x ) ( f g ) ( x ) ⓑ ( f g ) ( 2 ) ( f g ) ( 2 ) For functions f ( x ) = x 3 + 2 x 2 − 19 x + 12 f ( x ) = x 3 + 2 x 2 − 19 x + 12 and g ( x ) = x − 3 , g ( x ) = x − 3 , find ⓐ ( f g ) ( x ) ( f g ) ( x ) ⓑ ( f g ) ( 0 ) ( f g ) ( 0 )
- https://math.libretexts.org/Workbench/Hawaii_CC_Intermediate_Algebra/05%3A_Polynomial_and_Polynomial_Functions/5.04%3A_Dividing_Polynomials\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\)...\(\begin{array} {ll} {\text{Multiply the quotient by the divisor.}} &{(x+4)(x+5)} \\ {\text{You should get the dividend.}} &{x^2+9x+20\checkmark}\\ \end{array}\) When the divisor is written as \(x−c\), the value of the function at \(c\), \(f(c)\), is the same as the remainder from the division problem. In function notation we could say, to get the dividend \(f(x)\), we multiply the quotient, \(q(x)\) times the divisor, \(x−c\), and add the remainder, \(r\).
