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Using synthetic division, find the root of x^3-3x+2

User Noitidart
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The root of x³ - 3x + 2 is x = 1.

Further factoring reveals that the complete factorization is (x - 1)²(x + 2).

Here's how to find the root using synthetic division:

Set up the synthetic division tableau:

Write the coefficients of the polynomial in descending order: 1, 0, -3, 2.

Place a potential root (we'll start with 1) outside the tableau to the left.

Bring down the first coefficient:

Bring down the 1 to the first row of the quotient.

Multiply and add:

Multiply the root (1) by the first number in the quotient (1) and write the result (1) below the second coefficient (0).

Add the numbers in the second column (0 + 1) and write the result (1) in the third row.

Repeat for remaining coefficients:

Multiply 1 by 1 and write the result (1) below -3.

Add -3 + 1 to get -2.

Multiply 1 by -2 and write the result (-2) below 2.

Add 2 - 2 to get 0.

Interpret the resultt

The quotient is 1x² + 1x - 2.

The remainder is 0.

Since the remainder is 0, 1 is a root of the polynomial.

Therefore, the root of x³ - 3x + 2 is x = 1.

Further factoring reveals that the complete factorization is (x - 1)²(x + 2).

User IanC
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