What I Have Learned About Grade 9 Polynomials

Things to know about Grade 9 Polynomials that I have learned:

Monomial- has only 1 term

Binomial- has 2 terms

Trinomial- has 3 terms

A term is when there’s a coefficient (number), variable(s), and an exponent.

Example: $4x^2$

A coefficient is when a number is in front of the variable. (4)

A variable is a letter(s) in a term, and when solving an equation, it serves as a symbol of a number that is unknown yet. (x)

An exponent is a small number on the top right of the variable. (2)

Constant is when there’s no variable and exponent, just a number itself. (zero degree)

A degree is the largest exponent of a variable.

Example: $4x^2$

Degree = 2

Example: $4x^2 + 6x^5$

Degree = 5 (largest exponent)

Adding Polynomials using algebra tiles:

When adding polynomials, it’s always important to group the like terms together like this: (The variables and exponents should always be the same when grouping like terms)

Before moving to the next step, make sure to sort the terms from biggest to smallest:

Then take off the zero pairs, and all the terms that are left are the simplified answer.

Algebraically:

( $2x^2 + x - 1$ ) + ( $1x^2 + 5x +3$ )

$2x^2$ + $x^2$ = $3x^2$

$x$ + $5x$ = 6x

-1 + 3 = +2

$3x^2$ + $6x$ + 2

Subtracting polynomials is quite similar to adding polynomials but the only difference is that if there’s a (-) minus sign before the second bracket, you flip the tiles or you do the opposite of each terms like this:

( $x^2$ – 4x +3) – ( $3x^2$ + 2x – 2)

Algebraically:

( $x^2$ – 4x +3) – ( $3x^2$ + 2x – 2)

$x^2$ – $3x^2$ = $-2x^2$

-4x – 2x = -6x

3 + 2 = 5

$-2x^2$ – 6x + 5

Multiplying Polynomials

When multiplying polynomials, it’s straightforwardly you just multiply the coefficients, but since there are variables and exponents that applies to the multiplication law which means you add the exponents together but make sure the variable is the same.

2x x 2x

= $4x^2$