I need help factoring... I refuse to just sit there and play little games in my head trying to get numbers that fit... I'd rather thing of it as solving for X then going in backwards as that makes much more sense to me...
So I'm given
16c^2 - 64 and i'm asked to factor... instead of playing games in my head I'd rather solve for the C and go in backwards per say...
so C= plus or minus 2 now what????
Can someone please tell me how to do this wihout doing some crazy mind game guess and checking method my teach like drew what seemed to me to be like a pundent square in biology and pluged in numbers and I almost laughed and also drew a big X and placed numbers in the slots inbetween the lines and I didn't understand it all...
after taking many math classes that I most likely shouldn't have been in I refuse to just sit there and factor and look at it... please help me factor that equation wihout going oh what number plus what number equalls this number times this number or anything of the sort i want to see equations and stuff of the sorty pleasae!!!! no more pundent biology squares to factor show me how to factor without playing games lol
what do I do when I have this also....
X^4-13X^2+36
"so C= plus or minus 2 now what????"
If a polynomial P(x) has its zeroes at x= x1, x2, x3,..., then P(x) has the factorization:
P(x) = K (x-x1)(x-x2)(x-x3).....
So, if you know the x1, x2, x3,... then you can determine K by taking some arbitrary value for x, computing P(x) and computing the product (x-x1)(x-x2)... and dividing these two numbers.
I do not understand i appologize could you maybe please explain more
It boils down to that from the solutions C = ±2, you know that:
16c^2 - 64 = K(C+2)(C-2)
Then you find that K = 16. You can see that by comparing the coefficient of C^2, or just by inserting some value for C in bith sides...
To factor the expression 16c^2 - 64, you can approach it by solving for c and then going backwards. Here's how to do it step by step:
1. Start with the expression 16c^2 - 64.
2. Notice that both terms have a common factor of 16. So, we can rewrite the expression as 16(c^2 - 4).
3. Now, focus on the expression within the parentheses, c^2 - 4. It is a difference of squares.
4. To factor a difference of squares, use the formula (a^2 - b^2) = (a + b)(a - b). In this case, let a = c and b = 2.
5. Apply the formula to the expression c^2 - 4: (c + 2)(c - 2).
6. Finally, substitute the value of c that you found earlier, which is ±2. This gives you two possible factorizations: (2 + 2)(2 - 2) and (-2 + 2)(-2 - 2).
7. Simplifying each expression further, you get (4)(0) and (0)(-4).
8. The final factorization of 16c^2 - 64 is 16(c + 2)(c - 2).
Now, let's tackle the expression X^4 - 13X^2 + 36:
1. Start with the expression X^4 - 13X^2 + 36.
2. Notice that it's a quadratic trinomial in the form of X^2 - 13X^2 + 36.
3. Try to factor this trinomial by searching for two numbers that multiply to 36 (the constant term) and add up to -13 (the coefficient of the X term).
4. In this case, the numbers are -9 and -4 because (-9) + (-4) = -13 and (-9) * (-4) = 36.
5. Now, rewrite the middle term -13X^2 as -9X^2 - 4X^2.
6. Group the terms: X^4 - 9X^2 - 4X^2 + 36.
7. Factor by grouping: X^2(X^2 - 9) - 4(X^2 - 9).
8. Notice that (X^2 - 9) appears as a common factor in both terms.
9. Factor out (X^2 - 9) from each group: (X^2 - 9)(X^2 - 4).
10. Simplify further by factoring the difference of squares X^2 - 9 as (X + 3)(X - 3).
11. The final factorization of X^4 - 13X^2 + 36 is (X + 3)(X - 3)(X^2 - 4).
By following these steps, you can factor expressions without relying on guess and check methods or visualizing patterns.