Simple Algebraic Division
Akopọ
When you learned to divide numbers at school, you started with short division and moved on to long division for bigger divisors. Polynomial division works the same way: given a cubic or quartic expression, you can split it into a simpler quotient and a remainder, just as 17 divided by 5 gives 3 remainder 2.
This topic teaches you the long division algorithm for polynomials, a skill you will use throughout Further Pure Mathematics. It connects directly to the factor theorem and to finding roots of higher-degree equations, making it one of the most practical algebraic tools in your toolkit.
Awọn Afojusun
- Perform algebraic division by (x + a), (x - a), (ax + b) or (ax - b)
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- When x^3 + 3x^2 - 10x - 24 is divided by (x - 3), the remainder is: A) 0 B) 6 C) -24 D) 12 Answer: A
- What must you do before dividing x^4 - 16 by (x - 2)? A) Factor x^4 - 16 first B) Insert 0x^3 + 0x^2 + 0x placeholders C) Multiply by -1 D) Nothing special is needed Answer: B
- When a polynomial f(x) is divided by (x + 1), the quotient is x^2 - x + 3 and the remainder is -2. What is f(x)? A) x^3 + 2x - 5 B) x^3 + 0x^2 + 4x + 1 C) x^3 + 0x^2 + 4x - 5 D) x^3 - 2x + 1 Answer: B
- If (x - 4) is a factor of x^3 - 6x^2 + 11x - 4, the remainder when dividing is: A) 4 B) -4 C) 1 D) 0 Answer: D
- When 6x^3 + 5x^2 - 3x - 2 is divided by (2x + 1), the leading term of the quotient is: A) 6x^2 B) 3x^2 C) 2x^2 D) x^2 Answer: B
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Ẹ̀kọ́ síwájú láti àwọn orísun ṣíṣí
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Abala ìwé ẹ̀kọ́
Dividing Polynomials
Use long division to divide polynomials.
"College Algebra: Dividing Polynomials" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/5-4-dividing-polynomials. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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