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juin [17]
3 years ago
8

Is -2/3(12b - 6 + 9b - 18) equivalent to 2b(b + 8)? Show your work.

Mathematics
2 answers:
AURORKA [14]3 years ago
8 0

Answer:

No, they are not equivalent

Step-by-step explanation:

\frac{-2}{3}(12b - 6 + 9b - 18) = \frac{-2}{3}(12b + 9b - 6 - 18)\\\\=\frac{-2}{3}(21b - 24)\\\\  = \frac{-2}{3}*21b -24*\frac{-2}{3}\\\\= -2*7b + 8*2\\\\= 2( -7b + 8)

masha68 [24]3 years ago
4 0

Answer:

This is NOT equivalent to 2b(b + 8).

Step-by-step explanation:

Start with -2/3(12b - 6 + 9b - 18).  Simplify this.  First, combine the like terms inside the set of parentheses:

(-2/3)(21b - 24)

Simplify this by applying the distributation property of multiplication:

-14b + 16

Finally, factor out 2:  2(-7b + 8)

This is NOT equivalent to 2b(b + 8).

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Need Help! 10 points!
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5 0
2 years ago
Use synthetic division and remainder theorem p(x) = 3x^3 - 5x^2 - x + 2. p(-1/3)=
Alik [6]

Answer:

5/3

Step-by-step explanation:

-1/3 goes on the outside and since we have our polynomial in standard form with no in between terms missing, 3,-5,-1,2 go inside because they are the coefficients of our polynomial.

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

First step bring the 3 down inside. (3+0=3)

-1/3   |   3      -5          -1          2

       |

         -------------------------------------

           3

Whatever goes below the bar, must be multiplied by outside number and put directly below next number inside.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3

The numbers lined up vertically are added to get the numbers underneath the bar.

-1/3   |   3      -5          -1          2

       |             -1

         -------------------------------------

           3        -6

Again any number below the bar gets multiply to the number outside.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6

Again the numbers lined up vertically above the bar get added to get the number that goes underneath the bar there.

-1/3   |   3      -5          -1          2

       |             -1          2

         -------------------------------------

           3        -6          1

Multiply to outside number 1(-1/3)=-1/3.

This goes under the 2 inside.

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1

The last number we are fixing to be put is the remainder of (3x^3-5x^2-x+2)/(x+1/3) or you could say it is the value of p(-1/3) since:

P(x)/(x-c)=Q(x)+R/(x-c)

Multiply both sides by (x-c):

P(x)=Q(x)(x-c)+R

If you evaluate P at x=c, we get R:

P(c)=Q(c)(c-c)+R

P(c)=Q(c)*0+R

P(c)=R.

Let's finish:

-1/3   |   3      -5          -1          2

       |             -1          2          -1/3

         -------------------------------------

           3        -6          1         5/3

This means p(-1/3)=5/3.

We could have also got this by directly plugging in (-1/3) for x into 3x^3-5x^2-x+2.

7 0
3 years ago
Factor out the coefficient of the variable 1.7j-3.4
Ad libitum [116K]
Here you would factor out a 1.7 because that is the coefficient in front of the j. When you factor, you are essentially dividing each term by the value you are factoring out
1.7j/1.7=j
-3.4/1.7=-2

So the final answer is 1/7(j-2)

Hope this helps<span />
6 0
3 years ago
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