Further Pure Mathematics - 4PM1 PearsonEdexcel

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

  1. Perform algebraic division by (x + a), (x - a), (ax + b) or (ax - b)

Akọ̀wé Ẹ̀kọ́

Factorising a quadratic is second nature by now, but what about a cubic or a quartic? When you know one factor, polynomial long division lets you peel it away and reduce the degree by one, turning a hard problem into a simpler one. The technique mirrors numerical long division so closely that, once you see the parallel, the steps feel natural.

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Oriire fun ipari ẹkọ lori Simple Algebraic Division. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.

Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.

Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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

O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
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O wa lori ohun elo Green Bridge

Gba ohun elo Green Bridge CBT sori foonu tabi kọmputa rẹ lati ri awọn akọsilẹ ẹkọ ni kikun, awọn ibeere adaṣe, ati diẹ sii.

Awọn akọsilẹ ẹkọ ni kikun pẹlu awọn aworan apejuwe
Oluranlọwọ ẹkọ ti AI ṣe agbara rẹ
Kọ ẹkọ laisi intanẹẹti, nigbakugba, nibikibi
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