long divsion to divide the polynomials.
2x^3-5x^2-6x-16/x-4
sythetic division to find the quotient and remainder when the first polynomial is divided by the second.
x^2-2x+5, x-3
can u show me the steps of formula 1/16+7/20= 33/80 please
To divide polynomials using long division, follow these steps:
Step 1: Arrange the dividend and divisor in descending powers of the variable.
2x^3 - 5x^2 - 6x - 16 (dividend)
x - 4 (divisor)
Step 2: Divide the first term of the dividend by the first term of the divisor. Write the result as the first term of the quotient.
The first term of the dividend is 2x^3, and the first term of the divisor is x. So, 2x^3/x = 2x^2.
Write 2x^2 as the first term of the quotient.
Step 3: Multiply the divisor by the term obtained in step 2 and subtract it from the dividend.
Multiply (x - 4) by 2x^2: (x - 4) * 2x^2 = 2x^3 - 8x^2.
Subtract this from the dividend:
(2x^3 - 5x^2 - 6x - 16) - (2x^3 - 8x^2) = -5x^2 + 6x - 16.
Step 4: Bring down the next term of the dividend.
The next term of the dividend is -5x^2. Bring it down.
Step 5: Repeat steps 2 to 4 until there are no more terms left in the dividend.
Following these steps, continue the long division as follows:
2x^2 + (quotient)
x - 4 ) 2x^3 - 5x^2 - 6x - 16
- ( 2x^3 - 8x^2 )
---------------
-5x^2 + 6x - 16 (remainder)
Step 6: Check if there are any remaining terms in the dividend that you can bring down. If not, you have the final quotient and remainder.
In this case, we have -5x^2 + 6x - 16 as the remainder. Since there are no more terms to bring down, the final quotient is 2x^2, and the remainder is -5x^2 + 6x - 16.
Therefore, the division of the polynomial (2x^3 - 5x^2 - 6x - 16) by (x - 4) is:
Quotient: 2x^2
Remainder: -5x^2 + 6x - 16