1. What is the remainder when x2³ - 4x² + x + 6 is divided by x - 1?
2. What is the value of k such that x + 2 is a factor of 2x³ + x² + kx - 6?
pa help with solution po plsss.
2. What is the value of k such that x + 2 is a factor of 2x³ + x² + kx - 6?
pa help with solution po plsss.
Answers & Comments
Answer:
1. If (x-a) is a factor of any polynomial p(x), then p(a) should be =0 [remainder theorem]
x-1=0
x=1
Now substitute 1 for x in the equation. x^3+4x^2+x-6
=> (1)^3+[4×(1)^2]+(1)-6 on solving gives 0
So yes, (x-1) is a factor of the given polynomial.
2. K=13
Step-by-step explanation:
P(3) = 2(3)³-(3)²-k(3) -6
P(3) = 2(27) - 9 -k(3) -6
P(3) = 54 -9 -k(3) -6
54 - 9 - 6= 39
39/3=k(3)/3
k=13
P(3) = 54 - 9 - 13(3) -6
P(3) = 54- 9 - 39 - 6
P(3) = 0
Therefore, the value of k is equal to 13; and x-3 is a factor