The polynomial A(x) is divisible by (x+3).
What is factor?
A factor is a number or expression that divides another number or expression leaving no remainder.
What is factor theorem?
If p(x) be the polynomial, then p(x) is divisible by q if q is the factor of p(x).
According to the given question
we have different polynomials
[tex]A(x) = x^{3} +4x^{2} -9[/tex]
When we divide A(x) by (x+3) we get remainder 0.
⇒ (x+3) is a factor of A(x).
Hence, the polynomial A(x) is divisible by (x+3).
[tex]B(x) = x^{3} -22 -18[/tex]
⇒ [tex]B(x) = x^{3} -30[/tex]
When we divide B(x) by (x+3) we get remainder -57.
⇒ (x+3) is not a factor of B(x)
Hence, the polynomial B(x) is not divisible by (x + 3).
[tex]C(x) =x^{3} -6x -9[/tex]
By dividing C(x) by (x +3) we get remainder -18
⇒ (x+3) is not a factor of C(x).
Hence, C(x) is not divisible by (x+3).
[tex]D(x) = x^{3} + 3x + 3[/tex]
By dividing D(x) by (x+3), we get remainder -33.
⇒ (x+3) is not a factor of D(x).
Hence, D(x) is not divisible by (x+3).
Thus, the polynomial A(x) is divisible by (x+3).
Learn more about factor theorem here:
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