Question

question 4 of 5

select the correct location on the image.

david simplified a polynomial expression as shown.

select the step where david made a mistake.

\\((4-x^2)(3x+2)+(5x^3-4x^2-7)\\)

step 1: \\((12x+8-3x^3-2x^2)+(5x^3-4x^2-7)\\)

step 2: \\((-3x^3+5x^3)+(-2x^2-4x^2)+(12x)+(8-7)\\)

step 3: \\(2x^3-6x^2+12x+1\\)

david did not make a mistake.

Explanation:

Expand the first term of the expression

$$ (4 - x^2)(3x + 2) = 4(3x) + 4(2) - x^2(3x) - x^2(2) = 12x + 8 - 3x^3 - 2x^2 $$

Compare expansion with Step 1

$$ (12x + 8 - 3x^3 - 2x^2) + (5x^3 - 4x^2 - 7) $$

This matches Step 1 exactly.

Compare grouping with Step 2 and simplification with Step 3

$$
LATEXBLOCK0
$$

All steps are correct.

Answer:

• Step 1
• Step 2
• Step 3
• David did not make a mistake. (Correct answer)