Question

If (m+1) and (m−3) are factors of m²−km+c, determine the values of k and c.

Answer 1

The values of k and c in the polynomial m²−km+c are determined by multiplying the factors (m+1) and (m−3) and equating the result to the original polynomial. The values are k = 2 and c = −3.

Step-by-step explanation:

The question asks us to determine the values of k and c if (m+1) and (m−3) are factors of m²−km+c. When a polynomial is factored, the product of its factors equals the original polynomial. Given the two factors, we can set up an equation by multiplying them together:

(m+1)(m−3) = m² − 3m + m − 3 = m² − 2m − 3

This product must be equal to the original polynomial m²−km+c. Equating coefficients, we have:

• The coefficient of m in the product m²−km+c must be −2, which gives us k = 2.
• The constant term in the product m²−km+c is −3, which gives us c = −3.