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

will mark brainliest

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

.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8