Question

simplify.
(3x³ + x + 2)(5x² − 3x + 1)
the simplified product of the expression has a as the coefficient of the x²-term.
13
10
7
5
reset next

Explanation:

Step1: Identify terms for \(x^2\)

To find the coefficient of \(x^2\), we need to multiply terms from each polynomial that result in \(x^2\).

• Multiply \(3x^3\) (from first polynomial) with \(-3x\) (from second polynomial): \(3x^3\times(-3x)= -9x^4\) (not \(x^2\), skip).
• Multiply \(x\) (from first polynomial) with \(5x^2\) (from second polynomial): \(x\times5x^2 = 5x^3\) (not \(x^2\), skip).
• Multiply \(x\) (from first polynomial) with \(-3x\) (from second polynomial): \(x\times(-3x)= -3x^2\) (contributes to \(x^2\)).
• Multiply \(2\) (from first polynomial) with \(5x^2\) (from second polynomial): \(2\times5x^2 = 10x^2\) (contributes to \(x^2\)).
• Multiply \(3x^3\) with \(1\), \(x\) with \(1\), \(2\) with \(1\) don't give \(x^2\), skip.

Step2: Sum the coefficients

Now sum the coefficients of the \(x^2\) terms: \(-3 + 10 = 7\).

Answer:

7