Question 1153966: In problems 16-20, describe the mistakes, if any.
16. (-x + 4)(x + 2) solution: x^2 + 2x + 8
AThere should be a "+6" instead of a "+8."
BThere should be a "+6x" instead of a "+2x."
CThere should be a "-8" instead of a "+8"
DThere should be a negative with the x^2
E There should be a "-6" instead of a "+8"
F This solution is correct.
17. (3x^2 + 7)(9 - 8x) solution: 3x^2 - 56x + 63
AThere should be a "3x^3" term in the answer.
BThere should be a "-63" term in the answer instead of "+63".
CThere should be a "+56x" term in the answer instead of "-56x".
DThere should be a "-16" term in the answer.
E There should be a "-24x^3" term in the answer.
F This solution is correct.
18. 9x^2(6 - x)-8x(6 - x)/ x(6 - x)
solution: 1
ABoth of the x's in the 9x^2 term cannot be cancelled, so the answer should be 9x - 8.
BSince we have (6-x), we must multiply through by a negative, so the answer should be 17.
COnly one of the x's in the 9x^2 term can be cancelled, so the answer should be x.
DOnly one of the x's in the numerator can be cancelled, so the answer should be 1x.
E The expression cannot be simplified.
F This solution is correct.
19. [7x^4(x - 7) + 12x^4(x - 7)] / x^4(7- x)
Solution: 19
ATo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -5.
BTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be -19.
CTo cancel (7-x) with (x- 7), a negative must be taken out of the bottom, so the answer should be +5.
D(x-7) will not cancel with (7 - x), so the answer should be [7(x - 7) + 12(x - 7)] / (7 - x)
E The expression cannot be simplified.
F This solution is correct.
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20849)   (Show Source):
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! 16. (-x + 4)(x + 2) solution: x^2 + 2x + 8
(-x + 4)(x + 2)
Use "FOIL"
-x² - 2x + 4x + 8
-x² + 2x + 8
17. (3x^2 + 7)(9 - 8x)
Use FOIL
27x² - 24x³ + 63 - 56x
Arrange in order of descending powers
-24x³ + 27x² - 56x + 63
18. 9x^2(6 - x)-8x(6 - x)/ x(6 - x)
solution: 1
The way you have it typed, going by the standard "PE(MD)(AS)" rule which
does not say "multiplication comes before division", but says
"which comes first, multiplication or division, is determined by which comes
first, going left to right", is
But I'm guessing that you blew the "PE(MD)(AS)" rule in typing that, and the
problem should have been typed with the brackets in red below:
[9x^2(6 - x)-8x(6 - x)]/[x(6 - x)]
instead which was really this:
If so, then factor out x(6 - x) on top:
Cancel the x(6 - x)'s
19. [7x^4(x - 7) + 12x^4(x - 7)] / x^4(7- x)
The way you have it, going by the standard "PEMDAS" rule:
But as above, I'm guessing that you also blew the "PEMDAS" rule in typing that,
and it should have been typed as this, with the brackets in red:
[7x^4(x - 7) + 12x^4(x - 7)] / [x^4(7- x)]
and the problem was really this instead:
The terms in the numerator are like terms since they are exactly alike
except for their numerical coefficients 7 and 14. So we combine them as
Since 7 - x is not in order of descending powers, write it in that order as
-x + 7, then factor out -1 as -1(x - 7), and then write the 1 as understood
as -(x - 7)
Cancel the x4(x - 7)'s
and get:
You really need to learn to do problems of this sort, or you won't be able
to pass your tests.
Edwin
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