SOLUTION: Factor f(x) into linear factors given that k is a zero of f(x). f(x) = x^3 - 75x - 250; k = -5 (multiplicity 2)

Algebra.Com
Question 1155941: Factor f(x) into linear factors given that k is a zero of f(x).
f(x) = x^3 - 75x - 250; k = -5 (multiplicity 2)
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Consider f(x) = x³ - 75x - 250 as 

f(x) = 1x³ +0x² - 75x - 250 to perform synthetic division on with -5.

-5|1  0 -75 -250
  |  -5  25  250   
   1 -5 -50    0

So we have factored

f(x) = x³ - 75x - 250

as

f(x) = (x+5)(x²-5x-50)

which factors further as

f(x) = (x+5)(x+5)(x-10)

or

f(x) = (x+5)²(x-10)

Edwin
RELATED QUESTIONS

factor f(x) into linear factors given that k is a zero of f(x) f(x)=... (answered by josgarithmetic)
Factor f(x) into linear factors given that k is a zero of f(x) f(x)=x^3-3x^2-36x+108;... (answered by edjones)
Factor​ f(x) into linear factors given that k is a zero of​ f(x). f(x)=... (answered by stanbon)
Factor f(x) into linear factors given that k is a zero of f(x) f(x)=3x³-10x²-37x+60; k=5 (answered by Edwin McCravy)
Factor f(x) into linear factors given that k is a zero of f(x).... (answered by MathLover1)
Can I please get assistance with the following problem? factor f(x) into linear... (answered by jim_thompson5910)
Factor​ f(x) into linear factors given that k is a zero of​ f(x).... (answered by Alan3354)
It says factor f(x) into linear factors given that k is a zero of f(x),... (answered by rothauserc)
Show that the number is a zero of f(x) of the given multiplicity and express f(x) as a... (answered by josgarithmetic)