Question

x^4-7x^3+14x^2-38x-60, zero given:1+3i
I gotten that factored (x-(1-3i)(x-(1+3i) then got (x^2-2x+10). I don't know what to factor with it

Answer 1

there is an important rule

complex zeroes come in conjugate pairs, always.
so if 1 +3i is a zero, then so is (1 - 3i )

Answer 2

Yeah I understand that

Answer 3

so first expand

( x - (1 + 3i)) ( x - ( 1 - 3i))

Answer 4

( x - (1 + 3i)) ( x - ( 1 - 3i))
= ( x - 1 - 3i ) ( x - 1 + 3i )
= ( (x-1) - 3i) ( (x-1) + 3i )
= ( x-1)^2 - 3i*(x-1) + 3i(x-1) - 3i^2

Answer 5

with me so far

Answer 6

= (x-1)^2 -3*-1
= x^2 -2x + 1 + 9
= x^2 -2x + 10

Answer 7

now do long division

Answer 8

I don't understand what you did in the third line. I multiplied the second line together and that's how I got x^2-2x+10

Answer 9

that was just a trick to rearrange parentheses, it doesn't matter. we got the same answer

Answer 10

Oh okay, then I don't know what I would factor with that to get back to the original polynomial with that