Write each polynomial as the product of two binomials.
What's the answers?
(x - 12)9 + x(x - 12)
x(x + 7) + 9(x + 7)
(x - 10)-9 + 7x(x - 10)
in each case I see a common factor.
I will do the first one, you show me how to do the other two ...
(x-12)9 + x(x-12)
= 9(x-12) + x(x-12), the x-12 is a common factor
= (12-x)(9+x)
all done!
Oh, polynomial multiplication, always trying to make things complicated. Alrighty then! Let's break those down for you:
For (x - 12)9 + x(x - 12), we can see that both terms have a common factor of (x - 12). So, we can rewrite it as (x - 12)(9 + x).
Now, for x(x + 7) + 9(x + 7), we notice that both terms also have a common factor of (x + 7). So, we can rewrite it as (x + 7)(x + 9).
Lastly, we have (x - 10)-9 + 7x(x - 10). Here again, both terms have a common factor of (x - 10). So, we can rewrite it as (x - 10)(-9 + 7x).
Ta-da! Those are the answers expressed as the product of two binomials. Now, go forth and conquer those polynomials with the power of factorization! Keep calm and polynomial on!
The answers are:
1. (x - 12)9 + x(x - 12) = (x - 12)(9 + x)
2. x(x + 7) + 9(x + 7) = (x + 7)(x + 9)
3. (x - 10)-9 + 7x(x - 10) = (x - 10)(-9 + 7x)
To write each polynomial as the product of two binomials, we can use a technique called factoring. In factoring, we look for common factors or patterns within the polynomial.
Let's go through each polynomial and find the factors:
1. (x - 12)9 + x(x - 12)
In this polynomial, we see that both terms have a factor of (x - 12). So, we can factor out (x - 12):
(x - 12)9 + x(x - 12) = (x - 12)(9 + x)
Therefore, the answer is (x - 12)(9 + x).
2. x(x + 7) + 9(x + 7)
In this polynomial, we can see that both terms have a factor of (x + 7). So, we can factor out (x + 7):
x(x + 7) + 9(x + 7) = (x + 7)(x + 9)
Therefore, the answer is (x + 7)(x + 9).
3. (x - 10)-9 + 7x(x - 10)
In this polynomial, we observe that both terms have a factor of (x - 10). So, we can factor out (x - 10):
(x - 10)-9 + 7x(x - 10) = (x - 10)(-9 + 7x)
Therefore, the answer is (x - 10)(-9 + 7x).
To get these answers, we looked for common factors in each polynomial and grouped the terms accordingly. Factoring is an essential skill in algebra that helps us express polynomials in simpler forms.