What is the Quotient of x² + 7x + 12 and x + 4?

Professor Greenline Explaining Math Concepts

The result we get when we divide one polynomial by another is called the quotient. In polynomial division, the quotient is typically another polynomial, often with a lower degree than the dividend. We will learn about the quotient of x² + 7x + 12 divided by x + 4 below.

What is the Quotient of x² + 7x + 12 and x + 4? for US Students

What is the Quotient of x² + 7x + 12 and x + 4?

To find the quotient of (x² + 7x + 12) ÷ (x + 4), we can use polynomial long division. Follow these steps to simplify the division process.

Step 1: Divide the first term of the dividend (x²) by the first term of the divisor (x), which gives us x.

Step 2: Multiply the entire divisor (x + 4) by this result (x), which gives us x² + 4x.

Step 3: Subtract x² + 4x from the original dividend x² + 7x + 12, resulting in 3x + 12.

Step 4: Divide the first term of the result (3x) by the first term of the divisor (x), which gives us 3.

Step 5: Multiply the entire divisor (x + 4) by 3, resulting in 3x + 12.

Step 6: Subtract 3x + 12 from 3x + 12, resulting in 0.

Therefore, the quotient is x + 3, with a remainder of 0.

Important Glossaries of Quotient of x² + 7x + 12 and x + 4

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

Polynomial: An algebraic expression consisting of variables and coefficients.

Dividend: The polynomial that is being divided.

Divisor: The polynomial by which the dividend is divided.

Remainder: The leftover part of the dividend that is not divisible by the divisor. ```

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Jaskaran Singh Saluja

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Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.