Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the re

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Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the re

lationship between the values of m and n? Explain.

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-04-05T21:12:51+03:00

The condition is that m must surpass n. The multiplication of binomials results in the middle term from the summation of the outside and inside products. Accordingly, bx becomes –nx + mx, revealing b as –n + m. When combining numbers with opposing signs, their absolute values are subtracted, retaining the positive sign associated with the larger absolute value. Given that b is positive, it follows that m must have the greater absolute value.

AnnZ [12.3K] · Answer 2 · 2026-04-05T21:10:29+03:00

It is necessary for the value of m to exceed that of n. When binomials are multiplied, the middle term emerges from combining the outside and inside products. Thus, bx = –nx + mx, simplifying further leads to b = –n + m. When adding numbers that have opposite signs, we subtract their absolute values and retain the sign of the number with the larger absolute value. Since b is positive, m must indeed possess a greater absolute value.