Jika P(x) = 3x ^ 4 - 5x ^ 3 - 14x ^ 2 + 5x + 16 dibagi dengan (3x + 1) maka hasil bagi dan sisanya berturut-turut adalahSee answer

Daftar Isi

Jika P x 3x 4 5x 3 14x 2 5x 16 dibagi dengan 3x 1 maka hasil bagi dan sisanya berturut turut adalah

Question

Basic Answer

Step 1: Polynomial Long Division Setup

We will perform polynomial long division to divide P(x) = 3x⁴ – 5x³ – 14x² + 5x + 16 by (3x + 1).

Step 2: Divide the leading terms

Divide the leading term of the dividend (3x⁴) by the leading term of the divisor (3x): 3x⁴ / 3x = x³. This is the first term of the quotient.

Step 3: Multiply and Subtract

Multiply the divisor (3x + 1) by x³: x³(3x + 1) = 3x⁴ + x³.
Subtract this result from the dividend: (3x⁴ – 5x³ – 14x² + 5x + 16) – (3x⁴ + x³) = -6x³ – 14x² + 5x + 16

Step 4: Repeat the process

Now, divide the leading term of the new dividend (-6x³) by the leading term of the divisor (3x): -6x³/3x = -2x². This is the next term of the quotient.

Multiply the divisor by -2x²: -2x²(3x + 1) = -6x³ – 2x².
Subtract: (-6x³ – 14x² + 5x + 16) – (-6x³ – 2x²) = -12x² + 5x + 16

Step 5: Repeat again

Divide -12x² by 3x: -12x²/3x = -4x. This is the next term of the quotient.

Multiply the divisor by -4x: -4x(3x + 1) = -12x² – 4x.
Subtract: (-12x² + 5x + 16) – (-12x² – 4x) = 9x + 16

Step 6: Final division

Divide 9x by 3x: 9x/3x = 3. This is the last term of the quotient.

Multiply the divisor by 3: 3(3x + 1) = 9x + 3.
Subtract: (9x + 16) – (9x + 3) = 13

Step 7: Result

The quotient is x³ – 2x² – 4x + 3 and the remainder is 13.

Final Answer

Hasil bagi: x³ – 2x² – 4x + 3, Sisa: 13