IDNLearn.com: Your trusted source for finding accurate and reliable answers. Get the information you need from our community of experts, who provide detailed and trustworthy answers.
Sagot :
Let's go through the process of factoring each of the given polynomials step by step:
### 1. [tex]\( y^2 - 10y \)[/tex]
We start by factoring out the greatest common factor (GCF) from the polynomial:
[tex]$ y^2 - 10y = y(y - 10) $[/tex]
Thus, the factored form is:
[tex]$ y(y - 10) $[/tex]
### 2. [tex]\( 4x^2 - 12x \)[/tex]
Again, we factor out the GCF from the polynomial:
[tex]$ 4x^2 - 12x = 4x(x - 3) $[/tex]
So the factored form is:
[tex]$ 4x(x - 3) $[/tex]
### 3. [tex]\( 6s^2 + 18s \)[/tex]
First, we factor out the GCF:
[tex]$ 6s^2 + 18s = 6s(s + 3) $[/tex]
Thus, the factored form is:
[tex]$ 6s(s + 3) $[/tex]
### 4. [tex]\( y^2 + 2y + 1 \)[/tex]
This quadratic polynomial resembles a perfect square trinomial. It can be written as:
[tex]$ y^2 + 2y + 1 = (y + 1)(y + 1) = (y + 1)^2 $[/tex]
Thus, the factored form is:
[tex]$ (y + 1)^2 $[/tex]
### 5. [tex]\( x^2 - 3x - 10 \)[/tex]
For this quadratic polynomial, we look for two numbers that multiply to [tex]\(-10\)[/tex] (the constant term) and add up to [tex]\(-3\)[/tex] (the coefficient of the linear term). These numbers are [tex]\(-5\)[/tex] and [tex]\(2\)[/tex]. Therefore, we can factor the polynomial as follows:
[tex]$ x^2 - 3x - 10 = (x - 5)(x + 2) $[/tex]
So the factored form is:
[tex]$ (x - 5)(x + 2) $[/tex]
### Summary
Here are the factored forms of the given polynomials:
1. [tex]\( y(y - 10) \)[/tex]
2. [tex]\( 4x(x - 3) \)[/tex]
3. [tex]\( 6s(s + 3) \)[/tex]
4. [tex]\( (y + 1)^2 \)[/tex]
5. [tex]\( (x - 5)(x + 2) \)[/tex]
### 1. [tex]\( y^2 - 10y \)[/tex]
We start by factoring out the greatest common factor (GCF) from the polynomial:
[tex]$ y^2 - 10y = y(y - 10) $[/tex]
Thus, the factored form is:
[tex]$ y(y - 10) $[/tex]
### 2. [tex]\( 4x^2 - 12x \)[/tex]
Again, we factor out the GCF from the polynomial:
[tex]$ 4x^2 - 12x = 4x(x - 3) $[/tex]
So the factored form is:
[tex]$ 4x(x - 3) $[/tex]
### 3. [tex]\( 6s^2 + 18s \)[/tex]
First, we factor out the GCF:
[tex]$ 6s^2 + 18s = 6s(s + 3) $[/tex]
Thus, the factored form is:
[tex]$ 6s(s + 3) $[/tex]
### 4. [tex]\( y^2 + 2y + 1 \)[/tex]
This quadratic polynomial resembles a perfect square trinomial. It can be written as:
[tex]$ y^2 + 2y + 1 = (y + 1)(y + 1) = (y + 1)^2 $[/tex]
Thus, the factored form is:
[tex]$ (y + 1)^2 $[/tex]
### 5. [tex]\( x^2 - 3x - 10 \)[/tex]
For this quadratic polynomial, we look for two numbers that multiply to [tex]\(-10\)[/tex] (the constant term) and add up to [tex]\(-3\)[/tex] (the coefficient of the linear term). These numbers are [tex]\(-5\)[/tex] and [tex]\(2\)[/tex]. Therefore, we can factor the polynomial as follows:
[tex]$ x^2 - 3x - 10 = (x - 5)(x + 2) $[/tex]
So the factored form is:
[tex]$ (x - 5)(x + 2) $[/tex]
### Summary
Here are the factored forms of the given polynomials:
1. [tex]\( y(y - 10) \)[/tex]
2. [tex]\( 4x(x - 3) \)[/tex]
3. [tex]\( 6s(s + 3) \)[/tex]
4. [tex]\( (y + 1)^2 \)[/tex]
5. [tex]\( (x - 5)(x + 2) \)[/tex]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.