Question

Factorize y²-3 what should we do to factorize this polynomial
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Answer 1

Answer:

What you should be familiar with before this lesson

The GCF (greatest common factor) of two or more monomials is the product of all their common prime factors. For example, the GCF of 6x6x6, x and 4x^24x

2

4, x, squared is 2x2x2, x.

If this is new to you, you'll want to check out our greatest common factors of monomials article.

What you will learn in this lesson

In this lesson, you will learn how to factor out common factors from polynomials.

The distributive property: a(b+c)=ab+aca(b+c)=ab+aca, left parenthesis, b, plus, c, right parenthesis, equals, a, b, plus, a, c

To understand how to factor out common factors, we must understand the distributive property.

For example, we can use the distributive property to find the product of 3x^23x

2

3, x, squared and 4x+34x+34, x, plus, 3 as shown below:

Notice how each term in the binomial was multiplied by a common factor of \tealD{3x^2}3x

2

start color #01a995, 3, x, squared, end color #01a995.

However, because the distributive property is an equality, the reverse of this process is also true!

If we start with 3x^2(4x)+3x^2(3)3x

2

(4x)+3x

2

(3)3, x, squared, left parenthesis, 4, x, right parenthesis, plus, 3, x, squared, left parenthesis, 3, right parenthesis, we can use the distributive property to factor out \tealD{3x^2}3x

2

start color #01a995, 3, x, squared, end color #01a995 and obtain 3x^2(4x+3)3x

2

(4x+3)3, x, squared, left parenthesis, 4, x, plus, 3, right parenthesis.

The resulting expression is in factored form because it is written as a product of two polynomials, whereas the original expression is a two-termed sum.

Answer 2

Step-by-step explanation:

Given polynomial is y²-3

It can be written as y²-(√3)²

it is in the form of a²-b²

Here, a=y and b=√3

We know that:

a²-b²=(a+b)(a-b)

y²-(√3)²= (y+√3)(y-√3)

Therefore,y²-3=(y+√3)(y-√3)

Factorization of y²-3=(y+√3)(y-√3)