Rewrite x^2+9 as a product using complex numbers and the polynomial identity below.
a. (x+3)(x-3)
b. (x+3i)(x-3i)
c. (3x)(3i)
d. (x+9i)(x-9i)
I'm not sure if it's b or d, if I'm on the right path. Please help? Thanks
You are on the right track! To rewrite x^2 + 9 as a product using complex numbers, you can use the polynomial identity (x^2 + a^2) = (x + ai)(x - ai), where "a" is a real number.
In this case, a=3 because we have x^2 + 9. So, using the identity, we can expand it as (x + 3i)(x - 3i).
Therefore, the correct answer is b. (x+3i)(x-3i).
To rewrite x^2 + 9 as a product using complex numbers, we can use the polynomial identity called the difference of squares. The difference of squares states that a^2 - b^2 can be factored as (a + b)(a - b).
In this case, x^2 is the perfect square of x, and 9 is the perfect square of 3. So, we can rewrite x^2 + 9 as (x + 3i)(x - 3i), where i is the imaginary unit.
Therefore, the correct answer is b. (x + 3i)(x - 3i).
9 = 3^2, so it's (b)
which you could have verified by actually doing the multiplication, guy.