In your own words, explain the process of factoring a trinomial with a leading coefficient that is not equal to one. Why is this process more difficult than when the leading coefficient is equal to one? Give an example.

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When the leading coefficient is not one, it adds an additional dimension of complexity to the problem of factoring. The problem lies in the fact that more than one number's factors must be included in order to solve the problem, which generates a greater number of possibilities that must be checked. Since brute-force "guess and check" is the most common method of factoring, adding extra possibilities can ...

Solution Summary

Factoring is simple enough when you only have to worry about factoring the third term, but how do you factor a trinomial when the first term has a coefficient not equal to one? It adds some complexity! This solution will help you on your way to understanding this concept in 257 words.

Choose three integers a, b, and c? Feel free to choose negative numbers. Use a, b, and c to create a trinomial ax2 + bx + c. Can you factor this trinomial? How would you create a trinomial that will factor?

1. b^2-2b+1-64t^2=Factor completely
2. 3125x^4-5y^4= factor completely
3. Factor the trinomial 25b^2+10b+1= type p if prime
4. 15(x+1)^3-50(x+1)^2-125(x+1)
5. Factor by grouping 9t^4-3t-6t^3+2
6. 3t^2=22t+16
7. Solve the equation (4x+5)(x-5)=8x+10

Please see the attached file for full problem description.
1. Find the greatest common factor of 12x and 27x = The GCF is
2. Find the greatest common factor of 28a b,8a b , and 36ab
3. Factor. Check the multiplying.
3x +6x =
4. Factor. Check the multiplying.
9x y +45x y +_18xy=
5. Factor: x (x+2)+5(

1. Find the GCF of the set of monomials of 252, 468
2. Factor the polynomial 35 y + 14, if possible.
3. Factor the polynomial 7 a ^6 b ^7 c^ 5 - 35 a ^7 b ^5 c ^6, if possible.
4. Factor the expression 2(x + y) - 19 t(x + y).
5. Factor 17 x ^2 + 17 x y + 2 x + 2 y by grouping.
6. Factor the polynomial.
25

1. When simplifying like terms, how do you determine the like terms?
2. How do you determine the common factors in an expression?
3. What is factoring by grouping? When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms?
4. What is a common factor? Where do you use the common fac

Choose three integers a, b, and c. (Negative numbers are welcome.) Now use a, b, and c to create a trinomial ax2+bx+c. Can you factor this trinomial? How would you create a trinomial that will factor? Show work.

How would you use this procedure (factoring a quadratic expression with leading coefficient a = 1) to determine if a given polynomial is prime, that is, determine that it cannot be factored into a product of two linear polynomials

A^2- 6a +9=0
Use the even -root property to solve each question
x^2= 9/4
(x-3)^2=16
(w-3/2)^2=7/4
(w+2/3)^2=5/9
Find the perfect square trinomial whose first two terms are given.
w^2-5w
p^2+6/5p
factor each perfect square trinomial.
y^2-5y+25/4
t^2+3/5t+9/100
solve by complteing the square