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1. TRINOMIAL
REPORTED BY CLOIE AMIEL B TAN

2. WHAT IS TRINOMIAL???
• A TRINOMIAL IS AN ALGEBRAIC EXPRESSION THAT HAS THREE TERMS. AN ALGEBRAIC EXPRESSION CONSISTS OF
VARIABLES AND CONSTANTS OF ONE OR MORE TERMS. THESE EXPRESSIONS USE SYMBOLS OR OPERATIONS AS
SEPARATORS SUCH AS +, –, ×, AND ÷. A TRINOMIAL ALONG WITH MONOMIAL, BINOMIAL, AND POLYNOMIAL ARE
CATEGORIZED UNDER THIS ALGEBRAIC EXPRESSION. LET US LEARN MORE ABOUT TRINOMIALS, FACTORING
TRINOMIALS, THE FORMULA FOR FACTORING TRINOMIALS ALONG SOLVING A FEW EXAMPLES.
• A TRINOMIAL IS AN ALGEBRAIC EXPRESSION THAT HAS THREE NON-ZERO TERMS AND HAS MORE THAN ONE
VARIABLE IN THE EXPRESSION. A TRINOMIAL IS A TYPE OF POLYNOMIAL BUT WITH THREE TERMS. A POLYNOMIAL
IS AN ALGEBRAIC EXPRESSION THAT HAS ONE OR MORE TERMS AND IS WRITTEN AS A0XN + A1XN-1 + A2XN-2 + ... +
ANX0 IN THE STANDARD FORM. WHERE A0, A1, A2, ..., AN ARE CONSTANTS AND N IS A NATURAL NUMBER. WHEREAS
A TRINOMIAL CAN BE EXPRESSED WITH MULTIPLE VARIABLES AND THREE TERMS. FOR EXAMPLES: X2 + Y2 + XY,
5X2 - 4X2 + Z AND XYZ3 + X2Z2 + ZY3. EXAMPLES OF TRINOMIALS WITH ONE VARIABLE ARE: X2 + 2X + 3, 5X4 - 4X2 +1 AND
7Y - √3 - Y2.
•

3. POLYNOMIAL
• MONOMIAL
NUMBER OF TERMS- 1
EXAMPLE- XY
• BINOMIAL
NUMBER OF TERMS- 2
EXAMPLE – X + Y
• TRINOMIAL
NUMBER OF TERMS- 3
X^2 + XZ + 1

4. PERFECT SQUARE TRINOMIAL
A PERFECT SQUARE TRINOMIAL IS DEFINED AS AN ALGEBRAIC EXPRESSION THAT IS
OBTAINED BY SQUARING A BINOMIAL EXPRESSION. IT IS OF THE FORM AX2 + BX + C.
HERE A, B, AND C ARE REAL NUMBERS AND A ≠ 0. FOR EXAMPLE, LET US TAKE A
BINOMIAL (X + 2) AND MULTIPLY IT WITH (X + 2). THE RESULT OBTAINED IS X2 + 4X + 4. A
PERFECT SQUARE TRINOMIAL CAN BE DECOMPOSED INTO TWO BINOMIALS AND THE
BINOMIALS WHEN MULTIPLIED WITH EACH OTHER GIVES THE PERFECT SQUARE
TRINOMIAL.

5. HOW TO FACTOR TRINOMIAL?
(X+1)(X+3)
BOTH BINOMIAL
FIRST STEP IS USE THE METHOD FOIL OR DISTRIBUTE
Cant be simplified any
further
So in this equation we got 4x
because we added and we got
3 because we multiplied.
Always in trinomial we get the
last 2 numbers by adding and
multiplying

6. EXAMPLE
• X^2+8X+7 BUT THE ANSWER SHOULD BE THE 2 BINOMIAL
FIRST THING YOUR GONNA DO IS PUT THE 2 BINOMIAL
(X+__)(X+__) THE NUMBERS ARE NOT THERE BECAUSE ITS
WHAT WE ARE GONNA ANSWER SO LETS GET THE FACTOR
OF 7 WHICH IS
1,7 OR -1,-7 SO WE GET THE NUMBER 1 AND 7 AND PUT IT
TO THE BLANK AREA IN THE BINOMIAL AND IT WILL BE
(X+1)(X+7) SO THAT WILL BE THE RESULT BUT WE GOT THE
7 BUT NOT THE 8 SO LETS ADD 1 AND 7 U WILL GET 8 AND
THAT’S HOW YOU MAKE THE TRINOMIAL INTO 2 BINOMIAL
ND RD