For each cubic function below, one of the zeros is given. Express each cubic function in terms of linear factors.a)f(x)=2x³-9x²-53x-24;f(8)=0b)f(x)=x³+x²+6x+6;f(-1)=0
Accepted Solution
A:
Answer:a)2x³-9x²-53x-24 = (x-8) (2x + 1) ( x +1)b)x³+x²+6x+6 = ( x +1 ) ( x - i√6) ( x + i√6) Step-by-step explanation:a)f(x)=2x³-9x²-53x-24f(8)=0It means that 8 is the root of the function f(x)2x³-9x²-53x-24 = (x-8)(2 x² + 7 x +3)Now find the factor of (2 x² + 7 x +3)2 x² + 7 x +3 = 2 x² + 6 x + x + 3 = 2 x( x + 3)+ 1 (x+3) = ( 2x + 1) ( x +1)So2x³-9x²-53x-24 = (x-8) (2x + 1) ( x +1)b)f(x)=x³+x²+6x+6f(-1)=0It means that -1 is the root of the function f(x)x³+x²+6x+6 = ( x +1 )( x² +6)We know thata² - b² =(a+b)(a-b)i² = - 1So x² +6 = ( x - i√6) ( x + i√6) x³+x²+6x+6 = ( x +1 )( x² +6)x³+x²+6x+6 = ( x +1 ) ( x - i√6) ( x + i√6)