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NISA [10]
2 years ago
13

for the polynomial P(x)=4x^2-5x+6 and c =1, find p(c) by (a. direct substitution and (b. the remainder theorem

Mathematics
1 answer:
nata0808 [166]2 years ago
8 0
p(x)=4x^2-5x+6

c=1\implies p(c)=4(1)^2-5(1)+6=5

By the remainder theorem, the remainder upon dividing a polynomial p(x) by a linear binomial x-c is equal to p(c). Via synthetic division, we get

1   |  4   -5   6
.    |        4  -1
- - - - - - - - - - -
.    |  4   -1   5

which translates to

\dfrac{4x^2-5x+6}{x-1}=4x-1+\dfrac5{x-1}

or

4x^2-5x+6=(4x-1)(x-1)+5

Indeed, when x=1, the first term on the right hand side vanished and we're left with 5.
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<u>Given</u>:

The given expression to find the nth term of the sequence is d(n)=d(n-1) \cdot (-5)

The first term of the sequence is d(1)=8

We need to determine the third term of the sequence.

<u>Second term:</u>

The second term of the sequence can be determined by substituting n = 2 in the nth term of the sequence.

Thus, we have;

d(2)=d(2-1) \cdot (-5)

d(2)=d(1) \cdot (-5)

d(2)=8 \cdot (-5)

d(2)=-40

Thus, the second term of the sequence is -40.

<u>Third term:</u>

The third term of the sequence can be determined by substituting n = 3 in the nth term of the sequence.

Thus, we have;

d(3)=d(3-1) \cdot (-5)

d(3)=-40 \cdot (-5)

d(3)=120

Thus, the third term of the sequence is 120.

7 0
3 years ago
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The measure of an angle is 2.8.what is the measure of its complementary angle
german

Answer:

87.2º

Step-by-step explanation:

Complimentary angles total 90º

c + 2.8 = 90

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Dorji thought of a number. He first multiplied the number by 3 and then subtracted 12
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Answer

The answer is 24

Step-by-step explanation

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6 0
2 years ago
In class, 5/9 of the students have blue Eyes. if 10 students have blue eyes, how many students are in the class in total?
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Let us cross multiply.

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90 <u />÷ 5= 5x <span>÷ 5

18=x

So, the answer is 18. I hope this helped you, since I just learned cross multiplication last week.</span>
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