Remainder And Factor Theorems
Gbogbo ọrọ náà
Dividing one polynomial by another can be slow. The remainder and factor theorems give you a shortcut so powerful it feels like cheating: you can find the remainder of a division, or test whether something is a factor, just by substituting a single number. No long division required.
In this lesson you will meet the remainder theorem, which says the remainder when a polynomial is divided by \((x-a)\) is simply \(f(a)\), and the factor theorem, its special case when that remainder is zero. Together they are the key to factorising and solving cubic equations, a staple of the higher-level syllabus.
Ebumnobi
- Know and use the remainder and factor theorems.
- Find factors of polynomials and solve cubic equations.
Akọmọ Ojú-ẹkọ
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ayẹwo Ẹkọ
Ekele diri gi maka imecha ihe karịrị na Remainder And Factor Theorems. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- What is the remainder when f(x) = x^3 - 2x^2 + 5x - 1 is divided by (x - 2)? A. 0 B. 5 C. 9 D. 11 Answer: C
- By the factor theorem, (x - a) is a factor of f(x) when: A. f(0) = a B. f(a) = 0 C. f(a) = 1 D. f(1) = a Answer: B
- Is (x - 1) a factor of f(x) = x^3 - 6x^2 + 11x - 6? A. Yes, because f(1) = 0 B. No, because f(1) = 6 C. Yes, because f(0) = -6 D. No, because f(1) = 1 Answer: A
- The full factorisation of x^3 - 6x^2 + 11x - 6 is: A. (x - 1)(x - 2)(x - 3) B. (x + 1)(x + 2)(x + 3) C. (x - 1)^3 D. (x - 2)(x - 3)(x - 6) Answer: A
- What is the remainder when f(x) = x^2 + 3x + 2 is divided by (x + 2)? A. 0 B. 2 C. 6 D. 12 Answer: A
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Ọ dị na ngwa Green Bridge
Budata ngwa Green Bridge CBT na ekwentị maọbụ kọmputa gị iji nweta akwụkwọ ndụmọdụ zuru oke, ajụjụ mmụta, na ndị ọzọ.
Àwọn Ìwé Tó Dáa Láti Kà
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Remainder And Factor Theorems? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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