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kevinvalencia01
18.01.2020 •
Mathematics
must show work
problem 3 and problem 5
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Ответ:
#3. (x-7)(x-4) #5. (2k+7)(k-2)
Step-by-step explanation:
For #3 you have to first get all the terms on one side of the equals sign and set it equal to 0. So that gives us
Our a value is 1 and our c value is 28, so the product of those is 28. Find the factors of 28 and the combination of those factors that add up to equal the linear term -11x is the combination we need for our problem. The factors of 28 are: 1, 28; 2, 14; 4, 7. 4 and 7 give us 11 when we add them, but since we need a -11, we have to use the negative of both the factors since -7 + -4 = -11. Set up your equation now using the -7 and the -4, "larger" number first (the absolute value which makes the 7 larger):
Group the terms in groups of 2 to get:
Now factor out whatever is common from each set of parenthesis:
Now the common term is the factor (x-7) so that can be factored out now, leaving behind:
(x-7)(x-4). That's the answer for #3.
Now for #5:
We will start by getting everything on one side (I am changing the k's to x's):
The product of our a value and c value is again 28. Find the combination of the factors of 28 that will add to give us the middle (linear) term of 3: That is again 7 and 4, with the 7 needing to be positive and the 4 needing to be negative since 7 - 4 = 3. Set up our expanded quadratic as follows, "larger" number (the absolute value of) first:
Group them into groups of 2 again:
Again, notice the necessary sign change so when we distribute the negative back into the parenthesis we get the -14 we started with in the original problem.
Now factor out what is common from each set of parenthesis:
What's common now is the factor (2x+7) so that can be factored out leaving behind
(2x+7)(x-2)=0
And you're done!!!
Ответ: