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3 years ago

11

If p-1 is a factor of p⁴+p²+p-k what is the value of k

1 answer:

laila [671]3 years ago

7 0

Answer:

k = 3

Step-by-step explanation:

If p-1 is a factor of p⁴+p²+p-k, then we can express the polynomial in form

p⁴+p²+p-k = (p-1) * (ap³ + bp² + cp + d)

where a,b,c,d are constants. The important thing is that we can subst in p = 1 to make the polynomial zero. We can do this for original polynomial. WE must have to equal to 0 when we use p = 1 substitution...

1⁴+1²+1-k = 0

3 - k = 0

k = 3

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Mikaela placed a frame around a print that measures 10 inches by 10 inches. The area of just the frame itself is 69 square inche

olchik [2.2K]

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1.5 in

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Let x be the width of the frame.

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By using the formula

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3 years ago

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3 years ago

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2. Which of the following are terms of the series with nth term T-3n +17? a) 80 b) 170 c)217 d) 312 e) 278 f) 3566

pishuonlain [190]

Answer:

The correct options are a,b,e and f.

Step-by-step explanation:

It is given that the nth terms of the series is defined as

$T_n=3n+17$

Subtract 17 from both the sides.

$T_n-17=3n$

Divide both sides by 3.

$\frac{T_n-17}{3}=n$

The term Tₙ is a term of given series if n is a positive integer.

(a) The given term is 80.

$n=\frac{80-17}{3}=21$

Since n is a positive integer, therefore 80 is a term of given series.

(b) The given term is 170.

$n=\frac{170-17}{3}=51$

Since n is a positive integer, therefore 170 is a term of given series.

(c) The given term is 217.

$n=\frac{217-17}{3}=66.67$

Since n is not a positive integer, therefore 217 is a term of given series.

(d) The given term is 312.

$n=\frac{312-17}{3}=98.33$

Since n is not a positive integer, therefore 312 is a term of given series.

(e) The given term is 278.

$n=\frac{278-17}{3}=87$

Since n is a positive integer, therefore 278 is a term of given series.

(f) The given term is 3566.

$n=\frac{3566-17}{3}=1183$

Since n is a positive integer, therefore 3566 is a term of given series.

Thus, the correct options are a, b, e and f.

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3 years ago