Step-by-step explanation:
P(x)= x⁴-5x³+6x²+4x-8
y-intercept
plug in 0 in every x
P(x)= 0⁴-5(0)³+6(0)²+4(0)-8
y= 0 -5(0) +6(0)+4(0)-8
y= 0-0+0+0-8
y= -8
zeros
P(x)= x⁴-5x³+6x²+4x-8
0= x⁴+x³-6x³+12x²-6x²-8x+12x-8
0= x³(x+1) -6x²(x+1) +12x(x+1) -8(x+1)
0= (x+1) (x³-6x²+12x-8)
0= (x+1) (x³-3(2)(x²)+3(2²)(x)-2³) {optional to write}
0= (x+1) (x-2)³
0= (x+1) (x-2) (x-2) (x-2)
x+1 = 0
x=-1
x-2=0
x= 2
the zeros are {-1, 2, 2, 2}
note: it depends on the teacher if he allows repetition on zeros
