SOLUTION: Hello,I have a question on polynomials..I've spent much time trying to figure out what to do,but I keep getting answers that don't add up in the end..Here is the question:
The p
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: Hello,I have a question on polynomials..I've spent much time trying to figure out what to do,but I keep getting answers that don't add up in the end..Here is the question:
The p
Log On
Question 1049745: Hello,I have a question on polynomials..I've spent much time trying to figure out what to do,but I keep getting answers that don't add up in the end..Here is the question:
The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b.
Please help,I'm so stuck.. Found 2 solutions by stanbon, advanced_Learner:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b.
-------------
Using synthetic division::
(-1/4)....4....a..........b..............2
.........4...a-1..-(1/4)a+(1/4)+b....|(1/16)a-(1/16)-(1/4)b+b
-------
1st equation:: (1/16)a - (1/16) + (3/4)b = 0
=====================================
1)....4.....a......b......2
......4....a+4...a+b+4...|.. a + b + 6
----------------
2nd equation:: a+b+6 = 20
-----------------------------
Solve 2nd eq for "a" and substitute in 1st to solve for "b"::
a = 14-b
----
(1/16)(14-b) - (1/16) + (12/16)b = 0
----
14-b - 1 + 12b = 0
----
11b = -13
b = -13/11
----
a = 14-b = 14+13/11 = 167/11
---------------
Cheers,
Stan H.
--------------
You can put this solution on YOUR website! Hello,I have a question on polynomials..I've spent much time trying to figure out what to do,but I keep getting answers that don't add up in the end..Here is the question:
The polynomial f(x) is given by f(x) =4x^3 +ax^2 + bx+2. (4x+1) is a factor of f(x).When f(x) is divided by (x-1) there is a remainder of 20. Find a and b.
Please help,I'm so stuck
---------------------------------------------------------------------------
The polynomial f(x) is given by f(x) =. is a factor of f(x).When f(x) is divided by there is a remainder of . Find and .
solution
first step
when f(x) is evaluated at x= the remainder is 0 Because is a factor of f(x).
f(x) =
x= =
simplify to get =
second step
what happens when f(x) is evaluated at x=
f(x) =
this expression equals the remainder which we know to be = = = = =
Solve: We'll use substitution. After moving 1*b to the right, we get: , or . Substitute that
into another equation: and simplify: So, we know that b=9. Since , a=5.
Answer: .
answer = =
the polynomial is
f(x) =
check that
/ gives off a remainder of meaning is a factor of f(x).
when / the remainder is which is the same as evaluating the expression at x=
(
