Can you Solve. 3x^2+10x+3
2 answers:
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Answer:
0
Step-by-step explanation:
We are given the following:
(equ. 1)
(equ. 2)
We are asked:
(equ. 3) , what is
?
The 's represent the quotients you get.
is the remainder of dividing
by 5.
We know that is a number in {0,1,2,3,4}.
(I got this by multiplying both sides of equ 1. by 5.)
(I got this by multiplying both sides of equ 2. by 5.)
Let's add these equations together:
Factoring the 5 out for the 's part and simplify 4+1 gives:
So can't be the remainder of dividing something by 5 but see that we can factor this right hand expression more as:
So while there is no remainder (the remainder is 0).
Let's do an example if you are not convinced at this point that the remainder will be 0.
So choose x=9 since 9/5 gives a remainder of 4.
And choose y=16 since 16/5 gives a remainder of 1.
x+y=9+16=25 and 25/5 gives a remainder of 0.
Given:
The polynomial function is
To find:
The possible roots of the given polynomial using rational root theorem.
Solution:
According to the rational root theorem, all the rational roots and in the form of , where, p is a factor of constant and q is the factor of leading coefficient.
We have,
Here, the constant term is 10 and the leading coefficient is 4.
Factors of constant term 10 are ±1, ±2, ±5, ±10.
Factors of leading term 4 are ±1, ±2, ±4.
Using rational root theorem, the possible rational roots are
Therefore, the correct options are A, C, D, F.