Iipolynomials zii-algebraic expression ezenziwa ngamanani (ii-coefficients) kunye noonobumba (amalungu angokoqobo). Oonobumba be-polynomial bamele amaxabiso angaziwayo entetho.

U mzekelo

a) 3ab + 5
b) x3 + 4xy - 2x2y3
(c) Ngama-25x2 - 9 iminyaka2

## Monomial, iBinomial kunye neTrinomial.

Iipolynomial zenziwe ngamagama. Umsebenzi kuphela phakathi kwezinto zekota kukuphindaphinda.

Xa i-polynomial inekota enye kuphela, ibizwa njalo i-monomial.

U mzekelo

a) 3x
b) 5abc
c) x2y3z4 4

Umnxeba iziqulatho zii-polynomials ezinee-monomials ezimbini kuphela (amagama amabini), ezahlulwe ngokongeza okanye ngokuthabatha.

U mzekelo

kwi2 - b2
b) 3x + y
(c) I-5ab kunye ne-3cd2

El zintathu zii-polynomials ezinee-monomials ezintathu (amagama amathathu), ezahlulwe ngokudibanisa okanye ngokuthabatha imisebenzi.

Umzekelos

a) x2 + 3x + 7
b) 3ab - 4xy-10 iminyaka
i-CM3n + m2 + n4 4

## Isidanga se polynomials

Iqondo le-polynomial linikezelwa ngabakhupheli benxalenye yokoqobo.

Ukufumana inqanaba le-polynomial, kufuneka songeze oonobumba abenza ikota nganye. Esona sixa sikhulu siya kuba liqondo le-polynomial.

U mzekelo

a) 2x3 + kwaye

Ukukhutshwa kwekota yokuqala ngu-3 kwaye ikota yesibini ngu-1. Kuba eyona inkulu ingu-3, ​​isidanga se-polynomial ngu-3.

b) I-4 x2yi +8x3y3 - xy4 4

Masongeze ikota nganye:

4x2y => 2 + 1 = 3
8x3y3 => 3 + 3 = 6
xy4 4 => 1 + 4 = 5

Kuba esona sixa sikhulu siyi-6, inqanaba le-polynomial ngu-6

Qaphela: i-null polynomial yenye yazo zonke ii-coefficients ezilingana no-zero. Xa oku kusenzeka, inqanaba le-polynomial alichazwanga.

## Imisebenzi yePolynomial

Nayi imizekelo yokusebenza phakathi kwepolynomials:

### Yongeza iipolynomials

Senza oku ngokongeza ii-coefficients zamagama afanayo (icandelo elinye lokoqobo).

(7x3 + 5 x2y-xy + 4y) + (- 2x2y + 8xy - 7y)
- 7x3 + 5x2kunye - 2x2y - xy + 8xy + 4y - 7y
- 7x3 + 3x2y + 7xy-3y

### Ukukhutshwa kwePolynomial

Umqondiso wokuthabatha phambi kwabazali ubuyisela umqondiso phakathi kwabazali. Emva kokususa i-parentheses, kufuneka songeze amagama afanayo.

(4x2 - 5xk + 6k) - (3x - 8k)
4x2 - 5xk + 6k - 3xk + 8k
4x2 - 8xk + 14k

### Yandisa iipolynomials

Ukuphindaphinda kufuneka siphindaphinde ixesha. Ukuphindaphindwa koonobumba abalinganayo, ii-exponents ziyaphindwa kwaye zongezwa.

(3x2 - 5x + 8). (-2x + 1)
-6x3 + 3x2 + 10x2 - 5x - 16x + 8
-6x3 + 13x2 - 21x +8

### ICandelo lePolynomial

QaphelaKwisahlulo se polynomials sisebenzisa indlela ephambili. Kuqala, sahlulahlulahlulahlulahlulahlulahlulahlulahlula-hlane zamanani emva koko sahlulahlula-hlula amandla esiseko esinye. Ukulungiselela le nto, isiseko silondoloziwe kwaye izibonisi ziyasuswa.

## Ubungakanani bePolynomial factorization

Ukwenza i-factorization ye-polynomials sinamatyala alandelayo:

### Into eqhelekileyo kubungqina

izembe + bx = x (a + b)

Umzekelo

4x + 20 = 4 (x + 5)

### Iqela

izembe + bx + ay + por = x. (a + b) + y. (a + b) = (x + y). (a + b)

Umzekelo

I-8ax + bx + 8ay + ngo = x (8a + b) + y (8a + b) = (8a + b). (x + y)

### Isikwere esigqibeleleyo setrinomial (ukongeza)

un2 + 2ab + b2 = (a + b) usetyenziso2

Umzekelo

x2 + 6x + 9 = (x + 3)2

### Isikwere esigqibeleleyo setrinomial (umahluko)

un2 - 2ab + b2 = (a - b)2

Umzekelo

x2 - 2x + 1 = (x - 1)2

### Umahluko wezikwere ezibini

(a + b). (a - b) = a2 - b2

Umzekelo

x2 - 25 = (x + 5). (x - 5)

### Ityhubhu egqibeleleyo (ukongeza)

un3 + 3a2b + 3ab2 + b3 = (a + b) usetyenziso3

Umzekelo

x3 + 6x2 + 12x + 8 = x3 + 3. x2 . 2 + 3. x. Mbini2 + 23 = (x + 2)3

### Cube egqibeleleyo (Umahluko)

un3 Okwesithathu2b + 3ab2 - b3 = (a - b)3

## Isonjululwe imithambo

1) Cwangcisa ezi polynomials zilandelayo kwii-monomials, binomials, and trinomials:

a) 3abcd2
b) 3a + bc-d2
c) I-3ab-cd2

2) Chaza inqanaba le-polynomials:

a) xy3 + 8xy + x2y
b) 2x4 4 + 3
c) ab + 2b + a
d) zk7 7 -10z2k3w6 6 + 2x

3) Lithini ixabiso lomjikelezo womzobo ongezantsi?

4) Fumana indawo yomzobo:

5) Iipolynomials

a) 8ab + 2a2b - 4ab2
b) Ama-25 + 10y + y2
c) 9 - k2