Answer:
2
Step-by-step explanation:
Subtract 1 from 7, and then divide 6 by 3.
Answer:
P(x) = (
)x(x + 3)(x - 1)²
Step-by-step explanation:
Given - The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,256)
To find - Formula for P(x) ?
Proof -
Given that,
P(x) has a root of multiplicity 2 at x=1
So,
(x - 1)² is a factor.
Now,
Given that, there is roots of multiplicity 1 at x=0 and x=-3
So,
(x - 0) and ( x - (-3) are also factor
So,
P(x) can be written as
P(x) = Ax(x + 3)(x - 1)² .........(1)
where A is a constant.
Now,
Given that, It goes through the point (5,256)
⇒At x = 5, P(x) = 256
So,
Put the values of x and P(x) in equation (1), we get
P(x) = Ax(x + 3)(x - 1)²
⇒256 = A(5)(5 + 3)(5 - 1)²
⇒256 = 5A(8)(4)²
⇒256 = 40A(16)
⇒256 = 640 A
⇒A = 
=
∴ we get
P(x) = ()x(x + 3)(x - 1)²
Answer:
Step-by-step explanation:
Looking at our particular problem...let's identify everything that's going on here. What's inside the box are the coefficients from the original polynomial, with the last number being the constant. If we have 3 numbers there, which we do, then the first number is a coefficient on x², the second number is the coefficient on x, and the third number is the constant. So from that we know that our original polynomial was a 2nd degree, namely:
3x² + 7x - 20
The number outside the box is the number we are dividing into this original polynomial. This is a number in solution form. That means that x = -4. If
x = -4 is a solution, then the factor is (x + 4) = 0.
The numbers in the very bottom row are the coefficients of what is called the depressed polynomial, and this depressed polynomial is one degree less than the degree with which we started. So this depressed polynomial is a linear one (first degree, which is a line). The very last number in this bottom row is the remainder. If the remainder is 0, then -4 is a solution of the polynomial, it is also a 0, and (x + 4) is a factor of the polynomial. Our remainder is a 0.
So putting that all together gives us the answers as A, C, and E are our choices.
