Factor f(x) into linear factors given that k is a zero of f(x).

f(x)=x^3+(12-4i)x^2+(32-48i)x-128i, k=4i
In completely factored form, f(x) =____

1. 👍 0
2. 👎 0
3. 👁 196
1. Since you are telling me that 4i = k
then
f(x)=x^3+(12-4i)x^2+(32-48i)x-128i
=x^3 + (12 - k)x^2 + (32 - 12k) - 32k

and since k is a zero, then (x - k) is a factor
by synthetic division:
f(x)=x^3+(12-4i)x^2+(32-48i)x-128i
= (x-k)(x^2 + 12x + 32)
= (x - 4i)(x^2 + 12x + 32)

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### math help

Factor f(x) into linear factors given that k is a zero of f(x). f(x)=x^3+(12-4i)x^2+(32-48i)x-128i, k=4i In completely factored form, f(x) =____ (factor completely. simplify your answer)

asked by Ernie on November 21, 2014
2. ### Math

Davide wants to find the zeros of the polynomial p(x)=x3−2x2−9x+18. His work is shown below. Step 1: p(x)=(x+3)(x−3)(x−2) Step 2: x+3=0 x−3=0 x−2=0 Step 3: x=2, x=3, x=−3 Explain why Davide’s work shows that 2, 3,

asked by London on December 7, 2019
3. ### science help

Two factors which cause global climate change are listed below. Factor 1: Volcanic eruptions. Factor 2: Changes in the amount of Sun’s heat received by the Earth’s atmosphere and surface. Which of these statements is correct

asked by Oscar on March 22, 2016
4. ### algebra

factor f(x)=4x^(3)+19x^(2)-149x+36 into linear factors if f(x)=-9

asked by Anonymous on March 22, 2013
5. ### Algebra

The volume in cubic feet of a box can be expressed as (x)=x^3-6x^2=8x￼ , or as the product of three linear factors with integer coefficients. The width of the box is x-2. Factor the polynomial to find linear expressions for the

asked by Ciaria on March 17, 2015
1. ### Math

1.3x^2+17x+10 2.5y^8-125 3.a^2-2ab-15b^2 *Please help me.You have to factor by completing. Let's look at #1: 3x^2 + 17x + 10 We have 2 and 5 as factors of the last term. What combinations can we do to arrive at the middle term?

asked by Alex on February 4, 2007
2. ### Math

What do we call the numbers that cannot be arranged into 2-row arrays? The question begs for amplification. An array usually contains a set of some sort. There is not a hint in your question of what the set is. My math homework

asked by Ginner on August 21, 2006
3. ### Algebra 1

How to factor 10k^2+35k+15 completely? I would start with the easy: factor five out. 5(5k^2 +7x +3) Now the three tells you that the factors are probably 3,1 and the five tells you that the factors are probably 5,1 5(5k+3)(k+1)

asked by Montie on March 31, 2007
4. ### PRE-CALC

I am having touble understanding: how to factor the polynomial : 8x^4 -6x^3 -57x^2 -6x-65, into its linear factors, given that i is a zero. I tried to use synthetic division, but i keep getting a remainder... please help me

asked by KELLIE on September 26, 2017
5. ### Algebra

What constant must we place in the blank below in order to be able to factor the resulting expression into the product of two linear factors: 2mn - 16m - 7n + ____

asked by XXX on June 16, 2015

More Similar Questions