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marta [7]
3 years ago
9

The amount of space in the dog carrier shown can be found by multiplying it's width length and height write the amount of space

in cubic units using an exponent then evaluate please show the work so I know

Mathematics
1 answer:
Leokris [45]3 years ago
4 0
Given:
Length = 2 ft
Width = 2 ft
Height = 2 ft

Volume = Length * Width * Height
V = 2 ft * 2 ft * 2 ft 
V = 8 ft³ or 8 cubic feet

In exponential form:
V = (2ft)³
V = 8 ft³
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Write the polynomial in factored form. <br><br> p(x)=(x+5)(x-___)(x+___)
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Answer:


Step-by-step explanation:

Given : p(x)=x^{3} +6x^{2} -7x-60

Solution :

Part A:

First find the potential roots of p(x) using rational root theorem;

So, \text{Possible roots} =\pm\frac{\text{factors of constant term}}{\text{factors of leading coefficient}}

Since constant term = -60

Leading coefficient = 1

\text{Possible roots} =\pm\frac{\text{factors of 60}}{\text{factors of 1}}

\text{Possible roots} =\pm\frac{1,2,3,4,5,6,10,12,15,20,60}{1}

Thus the possible roots are  \pm1, \pm2, \pm 3, \pm4, \pm5,\pm6, \pm10, \pm12, \pm15, \pm20, \pm60

Thus from the given options the correct answers are -10,-5,3,15

Now For Part B we will use synthetic division

Out of the possible roots we will use the root which gives remainder 0 in synthetic division :

Since we can see in the figure With -5 we are getting 0 remainder.

Refer the attached figure

We have completed the table and have obtained the following resulting coefficients: 1 , 1,−12,0.  All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus the quotient is x^{2} +x-12

And remainder is 0 .

So to get the other two factors of the given polynomial we will solve the quotient by middle term splitting

x^{2} +x-12=0

x^{2} +4x-3x-12=0

x(x+4)-3(x+4)=0

(x-3)(x+4)=0

Thus x-3 and x+4 are the other two factors

So , p(x)=(x+5)(x-3)(x+4)





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3 years ago
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ehidna [41]
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