Question

Find the lcm of 1345 and 3215 by using synthetic division method.

answer this guyss..

Answer 1

Synthetic division is a method of dividing polynomials.

When given 3x3 + 2x2 + 4 divided by x-2, you first must solve for x.

So set x-2=0, then x=2

To use this with synthetic division, we must take the coefficients in the polynomial and make sure all powers of x are accounted for. So, 3x3 + 2x2 + 0x1 + 4 (notice there was no coefficient for x1, so we use 0 as a place holder).

Then we are ready to use synthetic division. The x value goes on the outside the box and the polynomial coefficients inside.

sd1

We bring the first number down,

sd2

then multiply it by our divisor (3 x 2 = 6) and place this value under our next coefficient.

sd2

Add these 2 numbers (2+6=8). The answer is placed vertically below

sd2

and used as our next number to be multiplied by the divisor (8 x  2 = 16),

sd2

continue this process 'till you run out of coefficients.

sd2

The number left over in the bottom right corner is your remainder. The numbers to the left of this are your quotient. (remember we are going down by one power)

ie. (3x3 + 2x2 + 4) over (x - 2) = 3x2 + 8x1 + 16 remainder: 36

Hope this helps.

Answer 2

Using Euclid's division lemma
3215=1345×2+525
1345=525×2+295
525=295×1+230
295=230×1+65
230=65×3+35
65=35×1+30
35=30×1+5
30=5×6+0
the hcf is 5