A' factaradh abairtean trì-teirmeach: meudachadh
Co-èifeachd x2 nas motha na 1
Nuair a tha co-èifeachd \({x^2}\) nas motha na 1, tha dòigh eile ann air a dhèanamh.
Seo aon dòigh.
Cuimhnich \(a{x^2} + bx + c\)
Ceum 1: Bheir \(a \times c\) dhut an àireamh a tha a dhìth gus factaran a lorg a bheir dhut b le cur-ris.
Ceum 2: Nuair a bhios na factaran ceart againn, cuir na factaran sin an àite \(bx\).
Ceum 3: Lorg factar cumanta bhon chiad dà theirm agus dèan an uair sin an aon rud airson an dà theirm mu dheireadh.
Ceum 4: Bu chòir gum faic thu gu bheil dà chamaig agad. Tha aon chamag airson do fhreagairt agus tha na factaran cumanta ro na camagan anns a' chamaig eile.
Eisimpleir
Factaraich \(3{x^2} - 7x - 6\)
Freagairt
\(a = 3,b = - 7,c = - 6\)
Ceum 1
\(a \times c = 3 \times - 6 = - 18\)
Feumaidh sinn factaran de -18 a bheir dhuinn -7 le cur-ris.
| Factaran de -18 | A' cur-ris nam factaran |
| \(1x - 18\) | \(- 17\) |
| \(-1 x 18\) | \(17\) |
| \(2x - 9\) | \(- 7\) |
| \(-2 x 9\) | \(7\) |
| \(3x - 6\) | \(- 3\) |
| \(-3 x 6\) | \(3\) |
| Factaran de -18 | \(1x - 18\) |
|---|---|
| A' cur-ris nam factaran | \(- 17\) |
| Factaran de -18 | \(-1 x 18\) |
|---|---|
| A' cur-ris nam factaran | \(17\) |
| Factaran de -18 | \(2x - 9\) |
|---|---|
| A' cur-ris nam factaran | \(- 7\) |
| Factaran de -18 | \(-2 x 9\) |
|---|---|
| A' cur-ris nam factaran | \(7\) |
| Factaran de -18 | \(3x - 6\) |
|---|---|
| A' cur-ris nam factaran | \(- 3\) |
| Factaran de -18 | \(-3 x 6\) |
|---|---|
| A' cur-ris nam factaran | \(3\) |
'S e 2 agus -9 na factaran a tha a dhìth.
Ceum 2
Cuir \(+2x\) agus \(-9x\) an àite \(7x\) anns an òrdugh a chuidicheas sinn a' lorg nam factaran cumanta.
\(3x^{2}-9x+2x-6\)
Ceum 3
\(3x(x-3) +2(x-3)\)
(Lorg factar cumanta dhen chiad dà theirm, agus an uair sin an dà theirm mu dheireadh.)
Ceum 4
\((x - 3)(3x + 2)\)
Question
Factaraich na leanas:
\(4{x^2} + 8x - 5\)
\(a = 4,b = 8,c = - 5\)
Ceum 1
\(a \times c = 4 \times - 5 = - 20\)
| Factaran de -20 | A' cur-ris nam factaran |
| \(1x - 20\) | \(- 19\) |
| \(-1 x 20\) | \( 19\) |
| \(2x-10\) | \(-8\) |
| \(-2 x 10\) | \(8\) |
| \(4x -5\) | \(-1\) |
| \(-4x5\) | \(1\) |
| Factaran de -20 | \(1x - 20\) |
|---|---|
| A' cur-ris nam factaran | \(- 19\) |
| Factaran de -20 | \(-1 x 20\) |
|---|---|
| A' cur-ris nam factaran | \( 19\) |
| Factaran de -20 | \(2x-10\) |
|---|---|
| A' cur-ris nam factaran | \(-8\) |
| Factaran de -20 | \(-2 x 10\) |
|---|---|
| A' cur-ris nam factaran | \(8\) |
| Factaran de -20 | \(4x -5\) |
|---|---|
| A' cur-ris nam factaran | \(-1\) |
| Factaran de -20 | \(-4x5\) |
|---|---|
| A' cur-ris nam factaran | \(1\) |
'S e -2 agus 10 na factaran a tha a dhìth.
Ceum 2
Cuir -2x agus +10x an àite +8x anns an òrdugh a chuidicheas sinn a' lorg nam factaran cumanta.
\(4{x^2} - 2x + 10x - 5\)
(Cuir an àite)
Ceum 3
\(2x(2x - 1) + 5(2x - 1)\)
(Factaran cumanta)
Ceum 4
\((2x - 1)(2x + 5)\)
Question
Factaraich \(10{x^2} + 38x - 8\)
An seo, chì thu gun gabh an abairt seo fhactaradh le bhith a' toirt a-mach factar cumanta de 2.
\(= 2(5{x^2} + 19x - 4)\)
Ceum 1
\(a = 5,b = 19,c = - 4\)
\(a \times c = 5 \times - 4 = - 20\)
A' cleachdadh nam factaran bhon cheist roimhe, a dh'fheumas 19 a thoirt dhut an seo le cur-ris, taghaidh sinn -1 agus 20.
Ceum 2
Cuir –x agus +20 x an àite +19x anns an òrdugh a chuidicheas sinn a' lorg nam factaran cumanta.
\(2(5{x^2} - x + 20x - 4)\)
(Cuir an àite)
Ceum 3
\(2[x(5x - 1) + 4(5x - 1)]\)
(Factaran cumanta)
Ceum 4
\(2(5x - 1)(x + 4)\)