Respuesta :
Answer:
Step-by-step explanation:
(a) p(2)=(2+2) (2+5) (2-4)
=4*7*-2
=-56
So this is not the polynomial
(b) p(2)=(4-4) (2+5) (2+5)
=0*7*7
0
p(5)=(10-4)(5+5)(5+4)
6*10*9
=540
So this is also not the polynomial
(c)p(2)=(6-2)(2-5)(2-4)
4*-3*-2
24
so this is also not the polynomial
(d)p(2)=(4-4)(2-3)(2+4)
=0
p(5)=(10-4)(5-5)(5+4)
=0
p(-4)=(-8-4)(-4-5)(-4+4)
=0
so this is the polynomial
The polynomial has zeros of 2, 5, and -4 is option (d) (2x - 4)(x - 5)(x + 4).
What is polynomial?
A polynomial is a mathematical equation made up of indeterminates and coefficients and uses only addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
How to find the correct polynomial?
To find a polynomial that has zeros 2, 5, and -4 substituted x = 2, 5, and -4 in a polynomial.
By substituted x = 2, 5, and -4 in a polynomial (2x - 4)(x - 5)(x + 4).
(a) For x=2.
The polynomial is
(2(2) - 4)(2- 5)(2 + 4) = (4- 4)(-3)(6)
= 0×-3×6
= 0
(b) For x=5.
The polynomial is
(2(5) - 4)(5 - 5)(5 + 4) = (10-4)(0)(9)
= 6×0×9
= 0
(c) For x=-4.
The polynomial is
(2(-4) - 4)(-4 - 5)(-4 + 4) = (-8-4)(-9)(0)
= -`12×-9×0
= 0
Since (2x - 4)(x + 5)(x + 4) has zeros of 2, 5, and -4
For incorrect options
By substituted x = 2, 5, and -4 in a polynomial (x + 2)(x + 5)(x - 4), (2x - 4)(x + 5)(x + 4) and (6x - 2)(x - 5)(x - 4) is not equal to zero therefore (a), (b) and (c)is not correct option.
Learn more about polynomial here: https://brainly.com/question/11536910
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