Question

( 2x + 1)( x - 5) = ___
a. 2x² - 9x - 4
b. 2x² + 11x - 4
c. 2x² - 4x - 5
d. 2x² - 9x - 5
a
c
b
d

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
$$(2x + 1)(x - 5)=2x\cdot x+2x\cdot(-5)+1\cdot x + 1\cdot(-5)$$

Step2: Simplify each term

Calculate the products:
$$2x\cdot x = 2x^{2}, \quad 2x\cdot(-5)=-10x, \quad 1\cdot x = x, \quad 1\cdot(-5)=-5$$
So the expression becomes:
$$2x^{2}-10x + x-5$$

Step3: Combine like terms

Combine the $x$ terms:
$$-10x + x=-9x$$
So the simplified form is:
$$2x^{2}-9x - 5$$

Answer:

D. \(2x^{2}-9x - 5\)