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QuizMultiple Choice

Factoring Polynomials: Double Grouping

Question 1 • FL-1200700-Mathematics for College Algebra MIS

Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping?

Answer
A
x(x2 + 4) + 5(x2 + 4)
B
x2(x + 4) + 5(x + 4)
C
x2(x + 5) + 4(x + 5)
D
x(x2 + 5) + 4x(x2 + 5)

Explanation

Group the polynomial as (x³ + 4x²) + (5x + 20). Factor each group: x²(x + 4) + 5(x + 4). Both terms share the factor (x + 4), so this is the grouping that leads to the factorization (x + 4)(x² + 5).

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