Question

1. when factored, the expression ( x^3 - 25x ) is equivalent to

a. ( (x + 5)(x - 5) )
b. ( x(x + 5)(x - 5) )
c. ( (x + 25)(x - 25) )
d. ( x(x + 25)(x - 25) )

1. what is the constant term of the polynomial ( 3x^3 + 6 + x - 4x^2 )?

a. ( x )
b. ( 6 )
c. ( 3 )
d. ( -4 )

1. which expression is equivalent to ( (6x^2 - x + 2) - (4x^2 + 5x - 3) )?

a. ( 2x^2 - 6x + 5 )
b. ( 10x^2 - 6x - 1 )
c. ( 2x^2 + 4x - 1 )
d. ( 10x^4 - 5x^3 + 5 )

Explanation:

Question 5

Step1: Factor out GCF

Factor $x$ from $x^3 - 25x$:
$x^3 - 25x = x(x^2 - 25)$

Step2: Factor difference of squares

Use $a^2-b^2=(a+b)(a-b)$ for $x^2-25$:
$x(x^2 - 25) = x(x+5)(x-5)$

Question 6

Step1: Rearrange polynomial terms

Sort $3x^3 +6 +x -4x^2$ by degree:
$3x^3 -4x^2 +x +6$

Step2: Identify constant term

The constant term is the term without $x$: $6$

Question 7

Step1: Distribute the negative sign

Expand $-(4x^2 +5x -3)$:
$-(4x^2 +5x -3) = -4x^2 -5x +3$

Step2: Combine like terms

Add to $6x^2 -x +2$:
$(6x^2 -x +2) + (-4x^2 -5x +3) = (6x^2-4x^2)+(-x-5x)+(2+3) = 2x^2 -6x +5$

Answer:

1. B. $x(x + 5)(x - 5)$
2. B. 6
3. A. $2x^2 -6x + 5$