IDNLearn.com makes it easy to find the right answers to your questions. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.

What Made Me?

Directions: Factor the given polynomials.

1. [tex]y^2 - 10y[/tex]
2. [tex]4x^2 - 12x[/tex]
3. [tex]6s^2 + 18s[/tex]
4. [tex]y^2 + 2y + 1[/tex]
5. [tex]x^2 - 3x - 10[/tex]


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]