Math, asked by devasaravanakumar5, 4 hours ago

find theGCD of 6x3 -30x2 + 60x -48 and 3 x 3-12x2 +21x -18.​

Answers

Answered by komalpatel7286
0

Answer:

These is the right answer

Attachments:
Answered by hukam0685
0

Step-by-step explanation:

Given:6 {x}^{3} - 30 {x}^{2} + 60x - 48 and 3 {x}^{3} - 12 {x}^{2} + 21x - 18 \\

To find: GCD of both polynomial.

Solution:

Step 1: Assume one as f(x) and other as g(x)

Let

f(x) = 6 {x}^{3} - 30 {x}^{2} + 60x - 48 and g(x) = 3{x}^{3} - 12{x}^{2} + 21x - 18

Step 2: Take 3 common from f(x) by g(x)

f(x) = 3(2 {x}^{3} - 10 {x}^{2} + 20x - 16)

g(x) = 3({x}^{3} - 4{x}^{2} + 7x - 6)

Now,Divide f(x) and g(x)

 {x}^{3} - 4 {x}^{2} + 7x - 6 )2 {x}^{3} - 10 {x}^{2} + 20x - 16(2 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 {x}^{3} - 8 {x}^{2} + 14x - 12\\ ( - ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - - - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2 {x}^{2} + 6x - 4 \\ or \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2( {x}^{2} - 3x + 2) \\

Step 3: Divide   {x}^{3} - 4 {x}^{2} + 7x - 6 by x²-3x+2

 {x}^{2} - 3x + 2) \:  {x}^{3} - 4 {x}^{2} + 7x - 6(x - 1\\ {x}^{3} - 3 {x}^{2} + 2x \\ ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - \\ -{x}^{2} + 5x - 6 \\ - {x}^{2} +3x - 2 \\ ( - ) \\ - - - - - - - - - \\ 2x - 4 \\ or \\ 2(x - 2) \\

Step 4: Divide x²-3x+2 by (x-2)

x - 2) {x}^{2} - 3x + 2( x - 1 \\ {x}^{2} - 2x \\ ( - ) \\ - - - - - - \\ -x + 2 \\ - x + 2 \\ ( - ) \\ - - - - - - - \\ 0 \\ - - - - - - - -

Step 5: Remainder is 0 now,Thus (x-2) is a common factor of f(x) and g(x).

Final answer:

GCD of 6 {x}^{3} - 30{x}^{2} + 60x - 48 and 3 {x}^{3} - 12 {x}^{2} + 21x - 18 is 3(x-2).

Hope it helps you.

Note*: After every division leave the constant term.

To learn more on brainly:

find the GCD of the polynomials45(x4-x³-x²) and 75(8x5+x²) https://brainly.in/question/43783839

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