4x^4+ 3x^2 - 1 = (2x - 1)( ) synthetic division

Answer 1

The equation is .

Use synthetic division to find .

The dividend is , and the root is 1/2.

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown below.

Step 2 : Write the constant r of the divisor (x - r) to the left. In this case, . Bring the first coefficient, 4, down.

Step 3 : Multiply the first coefficient by r : . Write the product under the second coefficient, 0. Then add the product and the second coefficient, 0 : 0 + 2 = 2.

Step 4 : Multiply the sum, 2, by r : .

Write the product under the next coefficient, 3 and add : 3 + 1 = 4.

Step 5 : Multiply the sum, 4, by r : .

Write the product under the next coefficient, 0 and add : 2 + 0 = 2.

Step 6 : Multiply the sum, 2, by r : .

Write the product under the next coefficient, -1 and add : -1 + 1 = 0. The remainder is 0.

The numbers along the bottom row are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend. Thus, the quotient is .

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