Perform the indicated operations and simplify your answer 2x

Perform the indicated operations and simplify your answer: (2x - 9)(5x^2 - 4x - 7) Factor completely and show the check by re-multiplication. If the polynomial is not factorable, write \"prime.\" 12x^3 - 20x^2 - 8x Factor completely and show the check by re-multiplication. If the polynomial is not factorable, write \"prime.\" 42x^2 - 23x - 5

Solution

7) (2x-9)( 5x² – 4x- 7) = 2x(5x² – 4x- 7) -9(5x² – 4x- 7) =2x*5x² -2x*4x-2x*7 - 9*5x² + 9*4x +9*7 = 10x³ -8x²- 14x – 45x²+36x + 63 = 10x³ – (8x²+ 45x²) +(36 -14)x+63 = 10x³- 53x² + 22x + 63.

8) 12x³ -20x² -8x = 4x(3x² -5x -2)= 4x( 3x² -6x + x -2) = 4x[ 3x(x – 2) +1(x -2)] = 4x(x-2)(3x+1)

     Also, 4x(x-2)(3x+1) = 4x[ x(3x+1) -2(3x+1)] = 4x[ 3x² + x - 6x -2] = 4x( 3x² -5x -2) = 12x³ -20x² -8x

9)   42x² -23x -5 = 42x² -30x +7x -5 = 6x(7x -5) + 1 (7x -5) = (7x -5)(6x +1)

     Also, (7x -5)(6x +1) = 7x(6x +1) -5(6x +1) = 42x² +7x -30x -5 = 42x² -23x -5.