Question

the fundamental theorem of algebra practice
complete this assessment to review what youve learned. it will not count toward your grade.
the greatest value of the root of $p(x) = x^3 + 4x^2 - 7x - 10$ is 2. calculate the remaining roots and enter them in ascending order. (1 point)
the roots are \boxed{} and \boxed{}.
check answer remaining attempts 3

Explanation:

Step1: Use Factor Theorem

Since \( x = 2 \) is a root, \( (x - 2) \) is a factor of \( p(x)=x^{3}+4x^{2}-7x - 10 \). We perform polynomial division or use synthetic division to factor \( p(x) \). Using synthetic division with root 2:

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So, \( p(x)=(x - 2)(x^{2}+6x + 5) \).

Step2: Factor Quadratic

Factor the quadratic \( x^{2}+6x + 5 \). We need two numbers that multiply to 5 and add to 6. Those numbers are 1 and 5. So, \( x^{2}+6x + 5=(x + 1)(x + 5) \).

Step3: Find Remaining Roots

Set each factor equal to zero: \( x + 1 = 0 \) gives \( x=-1 \), and \( x + 5 = 0 \) gives \( x=-5 \).

Answer:

-5, -1