Adding binomials and trinomials

  • MHB
  • Thread starter CSCI MARIO
  • Start date
In summary, the example in the book solved for the numerator by factoring the denominators and then finding a common denominator. This resulted in a simplified numerator of 2x^3 - 6x^2 - 27x + 67.
  • #1
CSCI MARIO
1
0
( x - 3/ x^2- 7x + 10 ) + ( x + 4 / x ^ 2 - 9 )
i have to add these and put the denominator in a factored form

(x-5)(x-2)(x-3)(x+3)

but the example in my book came up with

2x^3 - 6x^2 - 27x + 67 as the numerator.
This is what i don't understand.
can someone explain how the numerator was solved.
 
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  • #2
CSCI MARIO said:
( x - 3/ x^2- 7x + 10 ) + ( x + 4 / x ^ 2 - 9 )
i have to add these and put the denominator in a factored form

(x-5)(x-2)(x-3)(x+3)

but the example in my book came up with

2x^3 - 6x^2 - 27x + 67 as the numerator.
This is what i don't understand.
can someone explain how the numerator was solved.

$$x^2- 7x + 10=0 \Leftrightarrow (x-2) (x-5)=0$$

$$\frac{ x - 3}{ x^2- 7x + 10} + \frac{ x + 4 }{ x^2 - 9}= \frac{x-3}{(x-2)(x-5)}+\frac{x+4}{(x-3)(x+3)} \\ =\frac{(x-3)(x-3)(x+3)}{(x-2)(x-5)(x-3)(x+3)}+\frac{(x+4)(x-2)(x-5) }{(x-3)(x+3) (x-2)(x-5)} \\ =\frac{(x-3)(x-3)(x+3)+(x+4)(x-2)(x-5) }{(x-3)(x+3) (x-2)(x-5)} \\ =\frac{(x^2-9)(x-3)+ (x^2+2x-8)(x-5)}{(x-3)(x+3) (x-2)(x-5)}\\ =\frac{x^3-3x^2-9x+27+x^3-3x^2-18x+40}{(x-3)(x+3) (x-2)(x-5)}$$
 

FAQ: Adding binomials and trinomials

What is the difference between a binomial and a trinomial?

A binomial is an algebraic expression containing two terms, while a trinomial is an algebraic expression containing three terms. In other words, a binomial has two parts that are separated by a plus or minus sign, while a trinomial has three parts.

How do you add binomials and trinomials?

To add binomials or trinomials, you simply combine like terms. This means that you add the coefficients of terms with the same variables and exponents. For example, in the expression (2x + 3y) + (4x + 2y), you would combine the coefficients of x and y to get 6x + 5y. When adding trinomials, it may be helpful to rearrange the terms so that like terms are next to each other before combining them.

Do you have to follow any specific order when adding binomials and trinomials?

No, you do not have to follow a specific order when adding binomials and trinomials. As long as you combine like terms correctly, the order in which you add them does not matter. However, it may be helpful to rearrange the terms in a specific order before adding to make the process easier.

Can you add a binomial and a trinomial together?

Yes, you can add a binomial and a trinomial together. The same rules apply - you simply combine like terms. For example, in the expression (2x + 3y) + (4x + 2y + 5), you would combine the coefficients of x and y to get 6x + 5y + 5.

Are there any shortcuts or tricks for adding binomials and trinomials?

Yes, there are some shortcuts and tricks that can make adding binomials and trinomials easier. One trick is to use the FOIL method when multiplying two binomials, which stands for First, Outer, Inner, Last. Another trick is to use the distributive property to simplify expressions before adding them. Additionally, memorizing common binomial and trinomial patterns can help you add them more quickly.

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