Question

(4x^4 + 3x^2 - 1) + (mx^3 + 2)(3x^2 + 1). The expression is simplified to 15x^5 + 4x^4 + 5x^3 + 9x^2 + 1. What is the value of m?

a) -3
b) 3
c) 5
d) 15

Answer 1

To find the value of m in the given expression, compare the coefficients of the terms with the same exponent, setting up the equation 3m = 15, which simplifies to m = 5. Hence the correct answer is option C

Step-by-step explanation:

To find the value of m, we can compare the coefficients of the terms with the same exponent on both sides of the equation. The term with the highest exponent on the simplified side is 15x⁵, so we need to find the term with the same exponent on the original equation.

The term that has x⁵ as the exponent is mx³(3x²). So, we have the equation mx³(3x²) = 15x⁵. By comparing coefficients, we can set up the equation 3m = 15, which simplifies to m = 5 (Option c).