Rewrite each polynomial as the product of two binomials.
1. y^2 + 6y + 9
2. 25x^2 - 10x + 1
3. 36 - y^2
Can someone please help me do these correctly?
Duplicate post, already answered
y^2+6y+9
Sure! To rewrite each polynomial as the product of two binomials, we can use a technique called factoring. Here's how you can do it for each of the given polynomials:
1. y^2 + 6y + 9:
To factor this polynomial, we need to find two binomials in the form (ay + b)(cy + d) that multiply to give us the given polynomial. Let's start by finding the factors of 9 (the constant term) that add up to 6 (the coefficient of the middle term).
The factors of 9 are 1 and 9, or -1 and -9. Among these factors, the pair that adds up to 6 is 3 and 3.
Therefore, we can rewrite the polynomial as (y + 3)(y + 3), which simplifies to (y + 3)^2.
2. 25x^2 - 10x + 1:
To factor this polynomial, we need to find two binomials in the form (ax + b)(cx + d) that multiply to give us the given polynomial. Let's start by multiplying the leading coefficient (25) with the constant term (1) to get 25.
Now, we need to find two numbers that multiply to 25 and add up to -10 (the coefficient of the middle term).
The factors of 25 are 1 and 25, or -1 and -25. Among these factors, the pair that adds up to -10 is -5 and -5.
Therefore, we can rewrite the polynomial as (5x - 1)(5x - 1), which simplifies to (5x - 1)^2.
3. 36 - y^2:
To factor this polynomial, we need to use a special factoring formula called the difference of squares. The formula states that a^2 - b^2 can be factored as (a + b)(a - b).
In the given polynomial, we have 36 (which is 6^2) minus y^2 (which is (sqrt(y))^2).
So we can rewrite the polynomial as (6 + y)(6 - y).
Remember, factoring polynomials may not always be straightforward, and sometimes trial and error is required. I hope this explanation helps you understand how to approach factoring polynomials!