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Umnica [9.8K]
2 years ago
13

Subtract the following polynomials. Write answer in a-b-c-d order. From 4a+7b-12c subtract 8a-9b+12d

Mathematics
1 answer:
ozzi2 years ago
4 0

(4a+7b-12c)-(8a-9b+12d)\\4a+7b-12c-8a+9b-12d

Negative multiply negative = Positive

Negative multiply positive = negative

-8a+4a+9b+7b-12c-12d\\-4a+16b-12c-12d

Thus the answer is -4a + 16b - 12c - 12d.

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Consider the following division of polynomials.
Bond [772]

x^4=x^2\cdot x^2. Multiplying the denominator by x^2 gives

x^2(x^2+2x+8)=x^4+2x^3+8x^2

Subtracting this from the numerator gives a remainder of

(x^4+x^3+7x^2-6x+8)-(x^4+2x^3+8x^2)=-x^3-x^2-6x+8

-x^3=-x\cdot x^2. Multiplying the denominator by -x gives

-x(x^2+2x+8)=-x^3-2x^2-8x

and subtracting this from the previous remainder gives a new remainder of

(-x^3-x^2-6x+8)-(-x^3-2x^2-8x)=x^2+2x+8

This last remainder is exactly the same as the denominator, so x^2+2x+8 divides through it exactly and leaves us with 1.

What we showed here is that

\dfrac{x^4+x^3+7x^2-6x+8}{x^2+2x+8}=x^2-\dfrac{x^3+x^2+6x-8}{x^2+2x+8}

=x^2-x+\dfrac{x^2+2x+8}{x^2+2x+8}

=x^2-x+1

and this last expression is the quotient.

To verify this solution, we can simply multiply this by the original denominator:

(x^2+2x+8)(x^2-x+1)=x^2(x^2-x+1)+2x(x^2-x+1)+8(x^2-x+1)

=(x^4-x^3+x^2)+(2x^3-2x^2+2x)+(8x^2-8x+8)

=x^4+x^3+7x^2-6x+8

which matches the original numerator.

3 0
2 years ago
Read 2 more answers
Solve this multistep equation <br>12-5-16+3x=-23-9x
allsm [11]
The answer is x= -6/7<span><span>​​</span></span>
3 0
3 years ago
Three segments of lengths 25 cm, 37 cm, and 62 cm will form a triangle.
Llana [10]
Ok....
What am I supposed to answer here???
6 0
2 years ago
Solving absolute value equation <br> |17(5)|+|3(8)-5|
Alex787 [66]

Answer:

104

Step-by-step explanation:

5 0
3 years ago
A band consists of 3 woodwinds for every 7 members of the band. The independent quantity represents the total members of the ban
IgorC [24]

Answer: k=\frac{3}{7}

Step-by-step explanation:

For this exercise it is important to remember the following:

The constant of proportionality, which is represented as "k", describe  the constant ratio of two quantities that are proportional (the independent and dependent variables).

In this case we know that the independent quantity represents the total members of the band and the dependent quantity represents the woodwind members of the band.

Since the band consists of 3 woodwinds for every 7 members of the band, we can conclude that the constant of  proportionality for this relationship is:

k=\frac{3}{7}

8 0
3 years ago
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