Unit 7 Preview (Polynomials)

• Monomial
• Binomial
• Trinomial
• Polynomial

• Monomial
• Binomial
• Trinomial
• Polynomial

Classify

• Monomial

• Binomial

• Trinomial

• Polynomial

Answer explanation

A trinomial is a polynomial with exactly three terms. It differs from a monomial (one term), binomial (two terms), and polynomial (any number of terms). Therefore, the correct classification is trinomial.

Answer explanation

To find the product, distribute $2x$ across $3x^2 - 5x$: $2x \cdot 3x^2 = 6x^3$ and $2x \cdot -5x = -10x^2$. Thus, the result is $6x^3 - 10x^2$, which matches the correct answer.

Answer explanation

To simplify, distribute 6t across the polynomial: 6t * 5t^3 = 30t^4, 6t * -2t^2 = -12t^3, and 6t * 3t = 18t^2. Thus, the correct answer is 30t^4 - 12t^3 + 18t^2.

Add the polynomial (-3x + 4) + (8x - 5)

• 5x - 9

• 5x - 1

• 11x - 1

• 11x - 9

• None of these

Answer explanation

To add the polynomials, combine like terms: (-3x + 8x) + (4 - 5) = 5x - 1. Thus, the correct answer is 5x - 1.

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

Answer explanation

To simplify (2x + 5y - z) + (-6x - 4y + 7z), combine like terms: (2x - 6x) + (5y - 4y) + (-z + 7z) = -4x + y + 6z. Thus, the correct answer is -4x + y + 6z.

Subtract

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Answer explanation

To subtract, distribute the negative sign: (4n^4 - 8n + 4) - (8n^2 + 4n^4 + 1) = 4n^4 - 8n + 4 - 8n^2 - 4n^4 - 1. Combine like terms: (4n^4 - 4n^4) + (-8n^2) + (-8n) + (4 - 1) = -8n^2 - 8n + 3. Thus, the correct answer is -8n^2 - 8n + 3.

Subtract

(5x + x² - 4) - (4x - x² + 6)

• 2x² + x + 2

• x + 2

• 2x² + x - 10

• x - 10

Answer explanation

To subtract, distribute the negative: (5x + x^2 - 4) - (4x - x^2 + 6) = 5x + x^2 - 4 - 4x + x^2 - 6. Combine like terms: 2x^2 + (5x - 4x) + (-4 - 6) = 2x^2 + x - 10. Thus, the correct answer is 2x^2 + x - 10.

Subtract

(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x

• 7x⁵ - 6x

• -5x³ + 2x² - 6x

• -5x⁵ - 6x

Answer explanation

To simplify, distribute the negative sign: (x^5 + x^3) - (6x - x^3 + 6x^5) = x^5 + x^3 - 6x + x^3 - 6x^5. Combine like terms: (1 - 6)x^5 + (1 + 1)x^3 - 6x = -5x^5 + 2x^3 - 6x, which matches the correct answer.