Factor completely
36x2 + 60x + 25
Factor completely
4n2 + 28n + 49
Find what values will multiply to give the last term and first term. Use those values to find what will add to give the middle term.
36 = 36*1 or 9*4 or 6*6
25 = 25*1 or 5*5
36x2 + 60x + 25 = (6x + 5)(6x + 5)
4n2 + 28n + 49 = (2n + 7)(2n + 7)
I hope this helps.
To factorize the quadratic expressions, we can use the factoring method or the quadratic formula. Let's try factoring and see if it works for these equations.
1. Factorizing 36x^2 + 60x + 25:
First, we need to break down the middle term (60x) into two terms whose coefficients multiply to give us the product of the coefficient of x^2 (36) and constant term (25). In this case, we are looking for two numbers whose product is 900 (36 * 25).
The numbers that satisfy this condition are 20 and 45, since 20 * 45 equals 900. Let's rewrite the equation, replacing the term 60x with 20x + 45x:
36x^2 + 20x + 45x + 25
Now, we can factor by grouping:
(36x^2 + 20x) + (45x + 25)
Taking out the common factor from the first group and second group:
4x(9x + 5) + 5(9x + 5)
We can now see that we have a common binomial factor, (9x + 5):
(4x + 5)(9x + 5)
So, the completely factored form of 36x^2 + 60x + 25 is (4x + 5)(9x + 5).
2. Factorizing 4n^2 + 28n + 49:
Similarly, we need to find two numbers that multiply to give us the product of the coefficient of n^2 (4) and constant term (49), which is 196 (4 * 49).
The numbers that meet this criteria are 14 and 14 since 14 * 14 equals 196. Rewrite the equation, replacing the term 28n with 14n + 14n:
4n^2 + 14n + 14n + 49
Factor by grouping:
(4n^2 + 14n) + (14n + 49)
Taking out the common factors:
2n(2n + 7) + 7(2n + 7)
We can see that we have a common binomial factor, (2n + 7):
(2n + 7)(2n + 7) or (2n + 7)^2
So, the completely factored form of 4n^2 + 28n + 49 is (2n + 7)^2.