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HELP ME PLS IM STRUGGLING

1. If 1(-1) for the polynomial f(z) = 2z+z²-5 is-2, can you use the Factor Theorem to find the other factor?

No, because (x+1) is not a factor of the polynomial f(z) = 22 +2²-5,

Yes, because (x + 1) is a factor of all degree 4 polynomials.

No, because-2 is not an irrational number.

Yes, because-2 is the opposite of the leading coefficient of f(z) = 2x¹ +2²-5.

2 Answers

4 votes

Final answer:

The Factor Theorem states that (x - r) is a factor of a polynomial f(x) if f(r) = 0. Since f(-1) is not equal to 0 for the polynomial in question, (z + 1) is not a factor, and therefore the Factor Theorem cannot be used to find another factor of the polynomial.

Step-by-step explanation:

The question, "If 1(-1) for the polynomial f(z) = 2z+z²-5 is -2, can you use the Factor Theorem to find the other factor?" seems to contain some errors in the polynomial expression. Assuming the correct polynomial is f(z) = z² + 2z - 5 and you've found that f(-1) = -2, the Factor Theorem cannot be used here to find another factor based on this information alone. The Factor Theorem states that for a polynomial f(x), if f(r) = 0 for some number r, then (x - r) is a factor of f(x). Since f(-1) ≠ 0, (z + 1) is not a factor of f(z). Moreover, the other options presented do not provide a valid justification for finding a factor of the polynomial. Therefore, you cannot use the Factor Theorem to find another factor solely based on the information that f(-1) = -2.

User Trenskow
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6 votes

Answer: yes, because -2 is the opposite of the leading coefficient

Step-by-step explanation:

User Tshering
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4.8k points