Quotient of 5x² + 22x + 8 divided by x + 4

To find the quotient of (5x² + 22x + 8) ÷ (x + 4), we can follow the steps given below.

These steps simplify the polynomial division process.

Step 1: Set up the division like a long division problem with 5x² + 22x + 8 as the dividend and x + 4 as the divisor.

Step 2: Divide the first term of the dividend (5x²) by the first term of the divisor (x) to get the first term of the quotient, which is 5x.

Step 3: Multiply the entire divisor (x + 4) by this term (5x) and subtract the result from the original dividend.

Step 4: Bring down the next term from the dividend and repeat the process.

Step 5: Continue this process until all terms of the dividend have been divided. The remainder, if any, will be a polynomial of lower degree than the divisor.

Step 6: If needed, verify your result by multiplying the quotient by the divisor and adding any remainder to see if you get back to the original dividend.

• Quotient: The result obtained after dividing one polynomial by another.

• Dividend: The polynomial that is being divided.

• Divisor: The polynomial by which the dividend is divided.

• Remainder: The leftover part of the dividend after division which cannot be divided further by the divisor.

• Polynomial: An algebraic expression consisting of variables and coefficients, involving terms in powers of variables.