Question

3x^3-x^2-3x+1 solve cubic polynomial ​

Answer 1

hi mate,

solution:

3x^3-x^2-3x+1

Factoring: 3x³-x²-3x+1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -3x+1

Group 2: 3x³-x²

Pull out from each group separately :

Group 1: (-3x+1) • (1) = (3x-1) • (-1)

Group 2: (3x-1) • (x²)

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Add up the two groups :

(3x-1) • (x²-1)

Which is the desired factorization

Trying to factor as a Difference of Squares :

Factoring: x²-1

Theory : A difference of two perfect squares, A² - B² can be factored into

(A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B²=

A² - AB + AB - B² =

A²- B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x² is the square of x¹

Factorization is : (x + 1) • (x - 1)

Final result :

(x + 1) • (x - 1) • (3x - 1)

i hope it helps you..