Find the remaining factors for x4 - 10x3 + 35x2 - 50x + 24 if two factors are x - 1, and x - 3 Polynomial Functions.

Question

triciaal · Answer

@ziqbal103

campbell_st · Answer

well this is a quick and dirty solution... and involves equating coefficients. 

$$(x -1)(x -3_ = x^2 - 4x + 3 $$

then the other quadratic factor is 

$$(x + a)(x + b) = x^2 + (a + b)x + ab$$

then product of the 2 quadratic is 

= x^4 + (-4 + a + b)x^3 +(3 +ab -4(a+b))x + (-4ab+3(a+b))x + 3ab\]

comparing coeffiecients 

constant       24 = 3ab       so ab = 8

the coefficient of x^3      -10 = -4 + a + b     a + b = -6

you can check the  values of ab and a + b by substituting into the coefficients of x and x^2

so the 2nd quadratic is 

$$x^2 -6x + 8$$

factor this for the other binomial factors.

anonymous · Answer

$$x^4-10 x^3+35 x^2-50 x+24=(x-4) (x-3) (x-2) (x-1)  $$