Answer :
Answer:
Let’s factor each of these polynomials step by step:
(8y + 64):
First, notice that both terms have a common factor of 8.
Factor out the common factor: (8(y + 8)).
(4mn - 48m):
Again, both terms have a common factor of 4m.
Factor out the common factor: (4m(n - 12)).
(2x^3 + 6x^2 + 14x):
This polynomial doesn’t have a common factor, so we’ll look for other factorization methods.
Let’s group the terms: (2x^2(x + 3) + 14x).
Factor out the common factor from the first two terms: (2x^2(x + 3)).
The last term doesn’t have a common factor with the first two, so we can’t factor it further.
(4xy^2 - 7x^2y + x):
Notice that all terms have a common factor of x.
Factor out the common factor: (x(4y^2 - 7xy + 1)).
(9x^2 + 36x - 72):
Let’s first divide all coefficients by 9 to simplify: (x^2 + 4x - 8).
Now we’ll look for factors of -8 that add up to 4.
The factors are 6 and -2.
Rewrite the middle term: (x^2 + 6x - 2x - 8).
Factor by grouping: (x(x + 6) - 2(x + 6)).
Factor out the common factor: ((x - 2)(x + 6)).
(9a^2 - 3ab + 6a - 2b):
Group the terms: ((9a^2 - 3ab) + (6a - 2b)).
Factor out the common factor from each group:
First group: (3a(3a - b))
Second group: (2(3a - b))
Combine the common factor: ((3a - b)(3a + 2)).
Feel free to ask if you need further clarification or have additional questions!
