Find the remainder when polynomial is x^4 2x^3^4 2x^3-3x^2 12x-15 is d...
Division of Polynomials:When we divide one polynomial by another, we get a quotient and a remainder. The remainder is the polynomial left over after dividing as much as possible.
Polynomials to Divide:The given polynomials are:
x4 + 2x3 + 4x2 - 3x + 12
x2 + 5
Long Division:We can use long division to divide the given polynomials. The steps are as follows:
1. Write the dividend and divisor in long division form.
2. Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
3. Multiply the divisor by the first term of the quotient to get the first term of the product.
4. Subtract the product from the dividend to get the first remainder.
5. Bring down the next term of the dividend to get a new dividend.
6. Repeat steps 2 to 5 until the remainder is less than the divisor.
Result:Using long division, we get:
x2 + 3x - 1
Remainder: -8x + 17
Answer:The remainder when the polynomial x
4 + 2x
3 + 4x
2 - 3x + 12 is divided by the polynomial x
2 + 5 is -8x + 17.