# Polynomials

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## 5. Degrees of polynomials:

### 5.1. The degree of a polynomial refers to the highest sum of the exponents in a term.

5.1.1. For Example: For the trinomial 3x^2y^2+ 5x+12, the degree will be 2+2= 4

## 7. Finding zeros of a trinomial

### 7.1. The zeroes of a trinomial are taken as alpha, and beta. The addition of these gives: α+β=-b/a in the general expession and αβ=c/a {where a,b,c are taken from the general expression}

7.1.1. thus the equation for the zeroes of a trinomial is x^2 -b/a (x)+c/a

10.1.1. Example:

## 13. Factoring trinomials

### 13.1. When a=1

13.1.1. Look for the constant term, find such pair of numbers that multiply to give the constant term (including the sign) and add up to the middle term

13.1.1.1. For example: x^2+7x+12. in this case, 12= 4*3 and 7= 3+4. So, x^2+3x+4x+12= x(x+3)+4(x+3)= (x+3)(x+4).

### 13.2. When a is not 1

13.2.1. Look for common factors to simplify

13.2.1.1. For example: 3x^2+6x+9. In such a case take out the common factor (3). The common factor can also be a variable. After taking out the common factor, solve the expression as usual if a becomes =1

13.2.2. If there are no common factors, multiple the value of a to the constant term. then find pairs of numbers that multiply to that term and add up to the middle one.

13.2.2.1. For example: 2x^2+5x+2; in this example, multiply 2 by 2= 4. look for such a pair that adds up to 5 i.e. 4x+x= 2x^2+4x+x+2. taking the terms common, 2x(x+2)+(x+2)= (2x+1)(x+2)

## 14. Zeroes of a polynomial

### 14.1. The zeroes of a polynomial are those values which when replace the variables, make the value of the polynomial=0. They are also known as the roots of a polynomial. The number of zeroes in a polynomial can be determined is determined by the number of terms minus 1

14.1.1. For example: 2x-4. Here, the zero of the polynomial is found be equating the expression to zero: 2x-4=0; x=2 is the zero of the polynomial.