The factor of the polynomial [tex]f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35[/tex] is (a) 2x - 7
The polynomial function is given as:
[tex]f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35[/tex]
To determine if 2x - 7 is a factor, we start by setting it to 0
[tex]2x - 7 = 0[/tex]
Add 7 to both sides
[tex]2x = 7[/tex]
Divide both sides by 2
[tex]x =3.5[/tex]
Substitute 3.5 for x in f(x)
[tex]f(3.5) = 6(3.5)^4 - 21(3.5)^3 - 4(3.5)^2 + 24(3.5) - 35[/tex]
[tex]f(3.5) =0[/tex]
Because f(3.5) equals 0, then 2x - 7 is a factor of the polynomial
Read more about polynomial factors at:
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