64y^3-125
9y^4+42y^3+49y^2
I need help I cannot get the right answer. factor complete, or state that the polynomial is prime.
are they 2 different problems?
Yes they are two different problem.
factor complete, or state that the polynomial is prime.
To factor the given polynomials, we'll use the factoring formulas for special products. Let's factor each polynomial one by one:
1. 64y^3 - 125:
This polynomial can be recognized as a difference of cubes. The difference of cubes formula is a^3 - b^3 = (a - b)(a^2 + ab + b^2). In this case, a = 4y and b = 5. So, we have:
64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)
2. 9y^4 + 42y^3 + 49y^2:
This polynomial is not as straightforward as the first one, so we'll factor it by grouping. To do this, we'll group the terms of the polynomial in pairs, and then find the greatest common factor (GCF) of each pair. Here, we have:
9y^4 + 42y^3 + 49y^2 = (9y^4 + 21y^3) + (21y^3 + 49y^2)
Now, we factor out the GCF from each pair:
9y^4 + 21y^3 = 3y^3(3y + 7)
21y^3 + 49y^2 = 7y^2(3y + 7)
Notice that we have a common factor in both terms: (3y + 7). Factoring it out, we get:
9y^4 + 42y^3 + 49y^2 = (3y + 7)(3y^3 + 7y^2)
Therefore, the factored form of the given polynomials are:
1. 64y^3 - 125 = (4y - 5)(16y^2 + 20y + 25)
2. 9y^4 + 42y^3 + 49y^2 = (3y + 7)(3y^3 + 7y^2)