Examkin

Question

Difficulty: MediumMultiplying Polynomials

When the algebraic expression (4x−3)(2x2+5x−1)(4x - 3)(2x^2 + 5x - 1) is fully expanded and simplified into standard polynomial form, what is the value of the coefficient of the xx term?

Answer: -19

Answer

-19
The correct answer is −19-19 because the xx term is exclusively formed by the sum of the products (4x)(−1)(4x)(-1) and (−3)(5x)(-3)(5x), which equals −4x−15x=−19x-4x - 15x = -19x.

Step-by-Step Solution

1
Identify the goal.
We need to find the coefficient of the xx term in the product of (4x−3)(4x - 3) and (2x2+5x−1)(2x^2 + 5x - 1).
Focusing only on the terms that produce an xx term saves time compared to expanding the entire polynomial expression.
2
Find the first partial product that results in an xx term.
Multiply the xx term from the binomial (4x4x) by the constant term from the trinomial (−1-1) to get −4x-4x.
An xx term multiplied by a constant results in an xx term.
3
Find the second partial product that results in an xx term.
Multiply the constant term from the binomial (−3-3) by the xx term from the trinomial (5x5x) to get −15x-15x.
A constant multiplied by an xx term results in an xx term.
4
Combine the partial products.
−4x+(−15x)=−19x-4x + (-15x) = -19x
To find the total xx term in the expanded polynomial, all like terms must be combined.
5
Identify the final coefficient.
The coefficient of −19x-19x is −19-19.
The coefficient is the numerical multiplier of the variable.

Key Concept

Multiplying Polynomials and Combining Like Terms
Rate this question

Topics

Multiplying Polynomials

More questions from this topic