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sukhopar [10]
3 years ago
5

Identify a value k that makes (x+5) a factor of x^3+kx^2-x+45 will mark brainliest

Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

Answer:

We should attempt synthetic division to find when

x

3

−

k

x

2

+

2

k

x

−

15

x

−

3

has a remainder of

0

, which would signify that it is a factor of the polynomial.

The synthetic substitution would be set up as:

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

−−−

−−−

−−−

|

0

Treating the synthetic division like any other synthetic division problem, we see that

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

3

−−−−−−−−

−

3

k

+

9

−−−−−−−−

−

3

k

+

27

−−−−−−−−−

1

−

k

+

3

−

k

+

9

|

0

If the remainder equals

0

, then we know that

−

3

k

+

27

+

(

−

15

)

=

0

Solve this to see that

k

=

4

.

Thus,

(

x

−

3

)

is a factor of

x

3

−

4

x

2

+

8

x

−

15

.

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Answer:

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Step-by-step explanation:

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