If a is an integer, prove that (14a +3,21a + 4) 1

See explanation below.

Step-by-step explanation:

To prove that the greatest common divisor of two numbers is 1, we use the Euclidean algorithm.

1. In this case, and applying the algorithm we would have:

(14a + 3, 21a + 4) = (14a + 3, 7a + 1)  = (1, 7a + 1) = 1

2. Other way of proving this statement would be that we will need to find two integers x and y such that 1 = (14a + 3) x + (21a + 4) y

Let's make x = 3  and y = -2

Then we would have:

Therefore, (14a + 3, 21a + 4) = 1

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17