Question

describe the mistake made when solving $(x - 1)(3x^2 + 5x - 4)$ if lorrie got an answer of $3x^3 + 2x - x - 4$.
explain:

write the correct product below.

Explanation:

Explain:

To multiply \((x - 1)(3x^2 + 5x - 4)\), we use the distributive property (FOIL for polynomials). Lorrie's answer \(3x^3 + 2x - x - 4\) (assuming a typo, maybe \(3x^3 + 2x^2 - x - 4\) was intended) has a mistake in the middle terms. Let's do the correct multiplication:

1. Distribute \(x\) to each term in \(3x^2 + 5x - 4\):

\(x \cdot 3x^2 = 3x^3\), \(x \cdot 5x = 5x^2\), \(x \cdot (-4) = -4x\).

1. Distribute \(-1\) to each term in \(3x^2 + 5x - 4\):

\(-1 \cdot 3x^2 = -3x^2\), \(-1 \cdot 5x = -5x\), \(-1 \cdot (-4) = 4\).

1. Combine like terms:

\(3x^3 + (5x^2 - 3x^2) + (-4x - 5x) + 4 = 3x^3 + 2x^2 - 9x + 4\).

Lorrie likely made a mistake in distributing \(-1\) to \(5x\) (got \(-x\) instead of \(-5x\)) and missed combining the \(x^2\) terms properly (or misapplied the distributive property to \(5x\) and \(3x^2\)).

Write the correct product below:

To find the correct product of \((x - 1)(3x^2 + 5x - 4)\):

Step 1: Distribute \(x\)

Multiply \(x\) by each term in \(3x^2 + 5x - 4\):
\(x \cdot 3x^2 = 3x^3\), \(x \cdot 5x = 5x^2\), \(x \cdot (-4) = -4x\).

Step 2: Distribute \(-1\)

Multiply \(-1\) by each term in \(3x^2 + 5x - 4\):
\(-1 \cdot 3x^2 = -3x^2\), \(-1 \cdot 5x = -5x\), \(-1 \cdot (-4) = 4\).

Step 3: Combine like terms

Add the results from Step 1 and Step 2:
\(3x^3 + 5x^2 - 4x - 3x^2 - 5x + 4\)
Combine \(x^2\) terms: \(5x^2 - 3x^2 = 2x^2\)
Combine \(x\) terms: \(-4x - 5x = -9x\)

Thus, the correct product is \(3x^3 + 2x^2 - 9x + 4\).

Answer:

Explain:

To multiply \((x - 1)(3x^2 + 5x - 4)\), we use the distributive property (FOIL for polynomials). Lorrie's answer \(3x^3 + 2x - x - 4\) (assuming a typo, maybe \(3x^3 + 2x^2 - x - 4\) was intended) has a mistake in the middle terms. Let's do the correct multiplication:

1. Distribute \(x\) to each term in \(3x^2 + 5x - 4\):

\(x \cdot 3x^2 = 3x^3\), \(x \cdot 5x = 5x^2\), \(x \cdot (-4) = -4x\).

1. Distribute \(-1\) to each term in \(3x^2 + 5x - 4\):

\(-1 \cdot 3x^2 = -3x^2\), \(-1 \cdot 5x = -5x\), \(-1 \cdot (-4) = 4\).

1. Combine like terms:

\(3x^3 + (5x^2 - 3x^2) + (-4x - 5x) + 4 = 3x^3 + 2x^2 - 9x + 4\).

Lorrie likely made a mistake in distributing \(-1\) to \(5x\) (got \(-x\) instead of \(-5x\)) and missed combining the \(x^2\) terms properly (or misapplied the distributive property to \(5x\) and \(3x^2\)).

Write the correct product below:

To find the correct product of \((x - 1)(3x^2 + 5x - 4)\):

Step 1: Distribute \(x\)

Multiply \(x\) by each term in \(3x^2 + 5x - 4\):
\(x \cdot 3x^2 = 3x^3\), \(x \cdot 5x = 5x^2\), \(x \cdot (-4) = -4x\).

Step 2: Distribute \(-1\)

Multiply \(-1\) by each term in \(3x^2 + 5x - 4\):
\(-1 \cdot 3x^2 = -3x^2\), \(-1 \cdot 5x = -5x\), \(-1 \cdot (-4) = 4\).

Step 3: Combine like terms

Add the results from Step 1 and Step 2:
\(3x^3 + 5x^2 - 4x - 3x^2 - 5x + 4\)
Combine \(x^2\) terms: \(5x^2 - 3x^2 = 2x^2\)
Combine \(x\) terms: \(-4x - 5x = -9x\)

Thus, the correct product is \(3x^3 + 2x^2 - 9x + 4\).