Find the missing factor in each of the following.1. x3 - 8 = (x-2)(____)2. 2x3 + x2 - 23x + 20 = (x+4)(___)3. 3x2 + 2x2 – 37x + 12 = (x-3)(___)4.x3 - 2x2 - x + 2 = (x-2) (____)5.2x3 – x2 - 2x + 1 = (2x - 1) (___)
Answer (1)
Answer:( x^3 - 8 = (x-2)(____) ) To find the missing factor, we can use polynomial division or recognize that ( x^3 - 8 ) is a difference of cubes: [ x^3 - 8 = (x-2)(x^2 + 2x + 4) ] So, the missing factor is ( x^2 + 2x + 4 ).( 2x^3 + x^2 - 23x + 20 = (x+4)(___) ) Using polynomial division or synthetic division: [ 2x^3 + x^2 - 23x + 20 = (x+4)(2x^2 - 7x + 5) ] So, the missing factor is ( 2x^2 - 7x + 5 ).( 3x^3 + 2x^2 - 37x + 12 = (x-3)(___) ) Using polynomial division or synthetic division: [ 3x^3 + 2x^2 - 37x + 12 = (x-3)(3x^2 + 11x - 4) ] So, the missing factor is ( 3x^2 + 11x - 4 ).( x^3 - 2x^2 - x + 2 = (x-2)(____) ) Using polynomial division or synthetic division: [ x^3 - 2x^2 - x + 2 = (x-2)(x^2 - 1) ] Since ( x^2 - 1 ) can be factored further: [ x^2 - 1 = (x-1)(x+1) ] So, the missing factor is ( (x-1)(x+1) ).( 2x^3 - x^2 - 2x + 1 = (2x-1)(___) ) Using polynomial division or synthetic division: [ 2x^3 - x^2 - 2x + 1 = (2x-1)(x^2 - \frac{1}{2}x - 1) ] So, the missing factor is ( x^2 - \frac{1}{2}x - 1 ).Step-by-step explanation:
