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2 years ago

Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.

1 answer:

5 0

You can find the remainder right away by simply plugging in $x=3$ . The polynomial remainder theorem guarantees that the value of $p(3)$ is the remainder upon dividing $p(x)$ by $x-3$ , but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to

$\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}$

(and note that $p(3)=2(3)^3-11(3)^2+18(3)-15=-6$ , as expected)

You might be interested in

Is the function even, odd or neither? y=x^2-2x-8

mestny [16]

It is neither.

To be even, f(x) must equal f(-x).

If you substitute -x for x, you'd get

y = (-x)^2 - 2(-x) -8

y = x^2 +2x -8

This is not the same as the original, so this is not even.

To be odd, f(x) must equal -f(-x).

If you take the -x substitution from the last step and then multiply it by -1, you'd have:

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

y = -x^2 -2x +8

This is not the same as the original either.

The function is neither even nor odd.

5 0

2 years ago

Read 2 more answers

Example 24 In a school there are 20 teachers who teach mathematics or physil

Trava [24]

Answer:

The number of teachers who teach physics n(P) = 12

Step-by-step explanation:

Step(i):-

Given that the number of teachers who teach mathematics or physics

n(MUP) = 20

Given that the number of teachers who teach mathematics

n(M) = 12

Given that the number of teachers who teach both mathematics and physics

n(M∩P) = 4

Step(ii):-

By using n(A∪B) = n(A) + n(B) - n(A∩B)

n(M∪P) = n(M) +n(P) - n(M∩P)

20 = 12 + n(P) - 4

20 -12 +4 = n(P)

n(P) = 12

Final answer:-

The number of teachers who teach physics n(P) = 12

3 0

3 years ago

Read 2 more answers

(05.08A)Triangle ABC is transformed to similar triangle A′B′C′ below:

Romashka-Z-Leto [24]

Answer:

1st option is correct i.e., 1 over 2

Step-by-step explanation:

Given that Triangle ABC transformed to Triangle A'B'C'.

Coordinated of Triangle ABC are A(2,6) , B(2,4) and C(4,4)

Coordinated of Triangle A'B'C' are A'(1,3), B'(1,2) and C'(2,2)

Scale factor of Dilation is the no. of times coordinates of vertices of a figure increase or decrease.i.e.,

if A(a,b) ⇒ A'(c,d)

where, a.k=c & b.k=d then k is scale factor of dilation.

Value of k is same for all vertices.

For coordinates of A & A' ,we have $2.k=1\implies k=\frac{1}{2} \:\: and \:\: 6.k=3\implies k=\frac{1}{2}$

For coordinates of B & B' ,we have $2.k=1\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}$

For coordinates of C & C' ,we have $4.k=2\implies k=\frac{1}{2} \:\: and \:\: 4.k=2\implies k=\frac{1}{2}$

Therefore, the scale factor of dilation is $\:\frac{1}{2}\:$ since in all cases $k=\frac{1}{2}$

1st option is correct i.e., 1 over 2

3 0

3 years ago

If the bird is dircelty above the fish how far apart

yulyashka [42]

-3 -2 -1 0 1 2 3. If that’s confusing, it’s 0.

8 0

2 years ago

Andre owned a 1/4 acre lot. He wanted to construct a 120’ x 80’ tennis court on the lot. How many square feet will remain uncove

OLga [1]

The area of the tennis court is computed by multiplying the dimensions given,

A = 120' x 80'

A = 9600 ift

Then, we convert the area in ft² to acres,

A = (9600 in²)(2.3 x 10^-5/ 1 in²)

A = 0.24 acre

The portion of land remaining is,

A of remaining = 0.25 acre - 0.24 acre

= 0.1 acre

The remaining portion is for Andre's studies.

This, 0.1 ft² is equal to the 4% of the given area of the court.

3 0

3 years ago