Daily Math Guide

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## TRINOMIALS

It is said to be that a trinomial, or polynomial, is an algebraic expression of three terms. Based on the illustration above, it is a trinomial expression. Every term is separated by either plus(+) or minus(-) symbol as an operator. The coefficients a, b and c, are part of every term. The trinomial expression doesn't need to be quadratic, or an equation on the second degree.  Trinomial, from the word itself, is a three-term expression. The binomial expansion may result in trinomial when expanded, and trinomial factoring makes it back to binomial. Some form of trinomials includes an equation of degree higher than second, i.e. 3rd, 4th, and so on. This means that the expression doesn't limit to 2nd degree as in general form.

### Illustration:

Given the following expressions.

$1.) 3x^2-2y+4$

Explanation:  3x2 , 2y, and 4 are separate terms in the expression thus it is trinomial because they are three in the given expression. Here, coefficients a = 3,b = -2, and c = 4.

$2.) 5a^2+2by-2$

Explanation:  5a2 , 2by , and 2 are separate terms in the expression thus it is trinomial because they are three in the given expression. So coefficients, a = 5, b = 2, and c = -2.

$3.) x+y-z$

Explanation:  x , y , and z are separate terms in this expression thus it is trinomial because they are three in the given expression. Here, coefficients a  = 1,b  = 1, and c = 1.

$4.) { x}^2 + 3x+2$

Explanation: based on the illustration above, a = 1, b = 3, c = 2.

### Illustrative  Example

#### Factoring trinomials.

Factor the following trinomials. Write the values of coefficients a, b, and c of the equation. Example was given on number 1.

$1.) { x}^2 + 3x+2$

$a=1, b=3, c=2$

$= (x+2)(x+1)$ , answer

$2.)a^2-9$

$a=$  ____    , $b=$  ____     , $c=$ ____

$=(a+3)(a-3)$ , answer

$3.)4x^2-12x-9$

$a=$  ____    , $b=$  ____     , $c=$ ____

$=(2x-3)(2x+3)$ , answer

$4.) 6a^2+ab-b^2$

$a=$  ____    , $b=$  ____     , $c=$ ____

$=(3a-b)(2a+b)$ , answer

$5.)x^2y^2-z^2$

$a=$  ____    , $b=$  ____     , $c=$ ____

$=(xy+z)(xy-z)$ , answer

#### Problems with partial solution.

Factor the following trinomials. Write the values of a, b, and c of the equation just like in our illustrative example above.

$1.)b^2-4=(b-2)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$2.)3a^2-7a+2=(3a-1)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$3.)4x^2+5x-6=(4x-3)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$4.)6m^2+13m+6=(2m+3)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$5.)4a^2+13ab+3b^2=(a+3b)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$6.) x^2-xy-6y^2=(x+2y)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$7.)n^2-10n+9=(n-1)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$8.)a^2+16a+64=(a+8)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$9.)a^2-13a+40=(a-5)and$

$a=$  ____    , $b=$  ____     , $c=$ ____

$10.)y^2+4y+24=?$

$a=$  ____    , $b=$  ____     , $c=$ ____

#### Simple Quizzes

Factor the given trinomials if applicable. Write "NA" if not.

$1.)7-6x-x^2=$ ________________

$2.)x^2-3x-10=$ ________________

$3.)a^2+ab-6b^2=$ ________________

$4.)3x^2+2x-1=$ ________________

$5.)4-6b+2b^2=$ ________________

$6.)15x^2-8x-1=$ ________________

$7.)2+a-6a^2=$ ________________

$8.)x+3\sqrt{x}+2=$  ________________

$9.)8-20{\sqrt{x}}+4x=$ ________________

$10.)6x-{\sqrt{x}}+3=$ ________________