Question

Factoring with Diagrams

Answer 1

Answer:

(x - 7)(x - 4)(x + 4).            

Step-by-step explanation:

A(x) = x3 – 7x² – 16x +112

Dividing by x-7:

      x^2  - 16               <-------- Quotient

     -----------------------------

x-7)x^3 - 7x^2 - 16x + 112

     x^3 - 7x^2

                    0 - 16x + 112

                        - 16x + 112

                          ..............

so A(x) = (x - 7)(x^2 - 16)       x^2 - 16 is the difference of 2 squares so we have:

(x - 7)(x - 4)(x + 4).

Checking by expanding the brackets:  

(x - 7)(x - 4)(x + 4)

= x(x - 4)(x + 4) - 7(x - 4)(x + 4)

= x(x^2 - 16) - 7(x^2 - 16)

= x^3 - 16x - 7x^2 + 114

= x^3 - 7x^2 - 16x + 112