8. Write each of the following as a product of the polynomial's greatest common factor (gcf) and another polynomial. [2 points each]
(a) \( 15 y ^ { 2 } - 40 y \) (b) \( 16 m ^ { 3 } - 24 m ^ { 2 } - 56 m\)
Pregunta
Answer
Factor \( 15 y ^ { 2 } - 40 y : 5 y ( 3 y - 8 ) \)
Steps
\( 15 y ^ { 2 } - 40 y \)
Apply exponent rule: \( a ^ { b + c } = a ^ { b } a ^ { c } = 0 ^ { - } \)
\( y ^ { 2 } = y y \)
\( = 15 y y - 40 y \)
Rewrite \( 15 \) as \( 5 \cdot 3 \)
Rewrite \( 40 \) as \( 5 \cdot 8 \)
\( = 5 \cdot 3 y y - 5 \cdot 8 y \)
Factor out common term \( 5 y \)
\( = 5 y ( 3 y - 8 )\)
Factor \( 16 m ^ { 3 } - 24 m ^ { 2 } - 56 m : 8 m ( 2 m ^ { 2 } - 3 m - 7 ) \)
Steps
\( 16 m ^ { 3 } - 24 m ^ { 2 } - 56 m \)
Apply exponent rule: \( a ^ { b + c } = a ^ { b } a ^ { c } \cdot 0 ^ { - } \)
\( m ^ { 2 } = m m ^ { 3 } = m ^ { 2 } m \)
\( = 16 m ^ { 2 } m - 24 m m - 56 m \)
Rewrite \( 16 \) as \( 8 \cdot 2 \)
Rewrite \( 24 \) as \( 8 \cdot 3 \)
Rewrite \( 56 \) as \( 8 \cdot 7 \)
\( = 8 \cdot 2 m ^ { 2 } m - 8 \cdot 3 m m - 8 \cdot 7 m \)
Factor out common term \( 8 m \)
\( = 8 m ( 2 m ^ { 2 } - 3 m - 7 )\)
Related Questions
Q:
Calculate the maximum value of \( 4 x + 6 y \) subject to the constraints below:
\( 3 x + y \leq 16 \)
\( x + 3 y \leq 16 \)
\( y \geq 1 \)
\( x \geq 0\)
Q:
Jse the equation of the polynomial function \( f ( x ) = - 2 ( x - 1 ) ( x ^ { 2 } - 4 ) \) to complete the followin (a) State the degree and the leading coefficient. (b) Describe the end behavior of the graph of the function. (c) Support your answer by graphing the function. (a) The degree of the polynomial is \( \square \) and the leading coefficient is \( \square \) .