Answer:
Option 2 is correct
Step-by-step explanation:
We have been given an expression
[tex]5x^3+5x^2-170x+280[/tex]
Since, we have given a factor (x+7) that means at x=-7 the value of given expression will be zero
Similarly we have to check the given points where they are giving values 0.
Let us check at x=-4 that means put x=-4 in given expression we will get
[tex]5(-4)^3+5(-4)^2-170(-4)+280[/tex]
We are getting [tex]f(-4)=720\neq0[/tex]
Hence, x=-4 is dicarded
Hence, option 1 is discarded.
Now, we will check at x=2 we will get
[tex]5(2)^3+5(2)^2-170(2)+280=0[/tex]
Hence, x=2 is factor of given function.
Now, we will check at x=4
[tex]5(4)^3+5(4)^2-170(4)+280=0[/tex]
Hence, x=4 is also a factor of given function.
Option 2 is correct
Answer:
x = –7, x = 2, or x = 4 are factors of f(x).
Step-by-step explanation:
Given : f(x) = 5x³ +5x²-170x +280 and x + 7 is one factor .
To find : What are all the roots of the function.
Solution : f(x) = 5x³ +5x²-170x +280 .
We have given that x + 7 is factor that mean x = -7 is factor of f(x )
When we divide f(x) by x +7 we get
5x² -30x +40 =0
Taking common 5 from equation
5( x² -6x +8) =0
On dividing by 5 both sides
x² -6x +8 = 0
On factoring
x² -2x -4x +8 = 0.
Taking common x from first two terms and -4 from last two terms
x ( x -2) -4 (x -2) = 0
On grouping
(x-2) (x-4) = 0
x -2 =0
x =2
x-4 =0
x = 4
Therefore, x = –7, x = 2, or x = 4 are factors of f(x).
