QuestionApril 20, 2026

Select all factors of the polynomial x^3+5x^2-3x-15 x-3 x-5 x+5 x^2-3 x^2+3

Select all factors of the polynomial x^3+5x^2-3x-15 x-3 x-5 x+5 x^2-3 x^2+3
Select all factors of the polynomial
x^3+5x^2-3x-15
x-3
x-5
x+5
x^2-3
x^2+3

Solution
4.1(280 votes)

Answer

x+5, x^{2}-3 Explanation 1. Test x-3 as a factor Substitute x=3: 3^3+5(3^2)-3(3)-15 = 27+45-9-15 = 48 \neq 0. Not a factor. 2. Test x-5 as a factor Substitute x=5: 125+125-15-15 = 220 \neq 0. Not a factor. 3. Test x+5 as a factor Substitute x=-5: -125+125+15-15 = 0. Factor. 4. Test x^{2}-3 as a factor Substitute x=\sqrt{3}: (\sqrt{3})^3+5(\sqrt{3})^2-3(\sqrt{3})-15 = 3\sqrt{3}+15-3\sqrt{3}-15=0. Factor. 5. Test x^{2}+3 as a factor Substitute x=i\sqrt{3}: (i\sqrt{3})^3+5(i\sqrt{3})^2-3(i\sqrt{3})-15 = -3i\sqrt{3}-15-3i\sqrt{3}-15 \neq 0. Not a factor.

Explanation

1. Test $x-3$ as a factor <br /> Substitute $x=3$: $3^3+5(3^2)-3(3)-15 = 27+45-9-15 = 48 \neq 0$. Not a factor. <br /><br />2. Test $x-5$ as a factor <br /> Substitute $x=5$: $125+125-15-15 = 220 \neq 0$. Not a factor. <br /><br />3. Test $x+5$ as a factor <br /> Substitute $x=-5$: $-125+125+15-15 = 0$. Factor. <br /><br />4. Test $x^{2}-3$ as a factor <br /> Substitute $x=\sqrt{3}$: $(\sqrt{3})^3+5(\sqrt{3})^2-3(\sqrt{3})-15 = 3\sqrt{3}+15-3\sqrt{3}-15=0$. Factor. <br /><br />5. Test $x^{2}+3$ as a factor <br /> Substitute $x=i\sqrt{3}$: $(i\sqrt{3})^3+5(i\sqrt{3})^2-3(i\sqrt{3})-15 = -3i\sqrt{3}-15-3i\sqrt{3}-15 \neq 0$. Not a factor.
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