Question

possible points 7.14
desmos | graphing calculator | texas version
if the product from the factors $(4x - 1)(5x + 3)$ is represented by the expression $20x^{2}+kx - 3$, what is the value of $k$?

Explanation:

Step1: Expand the binomial product

Use FOIL method: $(a+b)(c+d)=ac+ad+bc+bd$
$$(4x-1)(5x+3) = 4x\cdot5x + 4x\cdot3 + (-1)\cdot5x + (-1)\cdot3$$

Step2: Calculate each term

Simplify individual products
$$=20x^2 + 12x -5x -3$$

Step3: Combine like terms

Add the linear terms
$$=20x^2 + (12-5)x -3 = 20x^2 +7x -3$$

Step4: Match coefficients

Compare to $20x^2 +kx -3$ to find $k$

Answer:

$k=7$