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Which of the following expressions, 5(p+6)(q-4), has exactly 3 factors?
a. Yes
b. No

User Tamon
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1 Answer

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Final answer:

No, the expression 5(p+6)(q-4) does not have exactly 3 factors because it is a polynomial that typically expands to a form with more than three factors.

Step-by-step explanation:

The student asked whether the expression 5(p+6)(q-4) has exactly 3 factors. The answer to this question is No. An expression in the form of a product of binomials, such as 5(p+6)(q-4), represents a polynomial which will typically have more than three factors when expanded and simplified. Factors in this context refer to numbers or expressions that divide the expression without leaving a remainder. Since the expression 5(p+6)(q-4) can be expanded and can have factors including 5, p+6, q-4, and any factors of the simplified polynomial, it usually has more than three factors.

Furthermore, an expression will only have exactly three factors if it represents a prime number or a prime number raised to a power. Since 5(p+6)(q-4) is an algebraic expression that depends on the values of p and q for its evaluation, and it consists of more than one term, it does not fit the criteria of having exactly three factors.

User Deumaudit
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