Zeros of polynomials (with factoring
2 answers:
Answer:
x = -5/2 x=1 x = -1
Step-by-step explanation:
p(x) = 2x^3 + 5x^2 – 2x – 5
Use factor by grouping
p(x) = 2x^3 + 5x^2 – 2x – 5
Factor x^2 from the first group and -1 from the second group
x^2(2x +5) -1( 2x+5)
Then factor out 2x+5
p(x) = (2x+5) (x^2-1)
Factor x^2 -1 as the difference of squares
p(x) = (2x+5)(x-1)(x+1)
Set to zero to find the x intercepts
0 = (2x+5)(x-1)(x+1)
Using the zero product property
2x+5 =0 x-1 =0 x+1 =0
2x = -5 x=1 x=-1
x = -5/2 x=1 x = -1
Answer:
The zeroes are (-1,0), (1, 0) and (-5/2, 0)
Step-by-step explanation:
We can find the zeroes by factoring:
2x^3 + 5x^2 - 2x - 5 = 0
x^2(2x + 5) - 1(2x + 5) = 0
(x^2 - 1)(2x + 5) = 0
(x - 1)(x + 1)(2x + 5) = 0
So x = -1, 1, -5/2.
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