List all possible rational zeros, find all rational zeros, and factor f (x). f (

Question

List all possible rational zeros, find all rational zeros, and factor f (x). f (x) = x^3 + 13 x^2 + 47x + 35 Choose the possible rational zeros for f (x) = x^3 + 13x^2 + 47x + 35 A. -1, -5, -7 B. plusminus 1, plusminus 5, plusminus 7, plusminus 35 C. plusminus 1, plusminus 5, plusminus 7 D. 1, 5, 7, 35 Choose the rational zeros for f (x) = x^3 +13x^2 + 47x + 35 A. -1 B. 1, -5, -7 C. plusminus 1, plusminus 5, plusminus 7, plusminus 35 D. 1, 5, 7 Choose the factored form of f (x) = x^3 +13x^2 +47x + 35 A. (x - 1) (x - 5) (x - 7) B. (x + 1) (x^2 + 12x + 35) C. (x + 1) (x + 5) (x + 7) D. (x - 1) (x + 1) (x - 2)

Explanation / Answer

x3+13x2+47x+35

Find all factors of constant 35= 1,5,7,35

use remainder theorem

substitute 1 for x , if we are getting 0 (x-1) is a factor

when x=1 f(x)=13+13(12)+47*1+35 which is not equal to 0 so (x-1) is not a factor.

x=-1 f(x)=(-1)^3+13(-1)^2+47*-1+35

=-1+13-47+35=0 so (x-(-1)) =(x+1) is a factor

using remainder theorem we got one factor of x3+13x2+47x+35   

next polynomial division   

  

12x2+47x+35

12x2+12x

35x+35

35x+35

0

so    x3+13x2+47x+35=(x+1)(x2+12x+35)

   =(x+1)(x+7)(x+5)

to find rational zeros equate each factor to 0 and solve for x

x+1=0 x+7=0 x+5=0

x=-1 x=-7 x=-5

Answer:

a)choose the possible rational zeros of f(x)

A(-1,-5,-7).

b) choose the rational zeros of f(x)

B) (-1,-5,-7)

c) factored form of f(x)=(x+1)(x+7)(x+5)

C)(x+1)(x+7)(x+5)

Thanks :)

x2+12x+35 (x+1)   x3+13x2+47x+35 x3+x2

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.