223k views
1 vote
Find the value of the constant K if 4x³ + kx² + 7x - 23 have a remainder 7 when divided by 2 x - 5​

User DBoyer
by
8.5k points

1 Answer

1 vote

Final answer:

The value of the constant K is -5.2.

Step-by-step explanation:

We can use the factor theorem to find the value of the constant K. According to the factor theorem, if a polynomial f(x) has a remainder of c when divided by the binomial (ax - b), then f(b/a) = c. In this case, the polynomial is 4x³ + kx² + 7x - 23 and the binomial is 2x - 5. So, we set f(5/2) = 7 and solve for K:

f(5/2) = 4(5/2)³ + k(5/2)² + 7(5/2) - 23 = 7

Simplifying this equation:

(125/2) + (25/2)*k + (35/2) - 23 = 7

125/2 + (25/2)*k + 35/2 - 46/2 = 7

(125 + 25k + 35 - 46)/2 = 7

(144 + 25k)/2 = 7

144 + 25k = 14

25k = -130

k = -5.2

User Ccamacho
by
8.7k points

Related questions

asked Feb 27, 2022 146k views
RedYeti asked Feb 27, 2022
by RedYeti
8.2k points
1 answer
0 votes
146k views
1 answer
5 votes
119k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories