Which of these standard form equations is equivalent to $(x + 1)(x - 2)(x + 4)(3x + 7)$?

A) $3x^4 + 12x^3 - 19x^2 - 56x - 28$

B) $3x^4 - 12x^3 - 19x^2 + 56x + 28$

C) $3x^4 + 12x^3 + 19x^2 - 56x - 28$

D) $3x^4 - 12x^3 + 19x^2 + 56x + 28$

To find the standard form equation equivalent to (x + 1)(x - 2)(x + 4)(3x + 7), expand the product using the distributive property and then multiply the resulting binomials using the FOIL method. The equivalent standard form equation is 3x⁴ + 12x³ + 19x² - 56x - 28.

Explanation:

To find the standard form equation equivalent to (x + 1)(x - 2)(x + 4)(3x + 7), we need to expand the product using the distributive property.

(x + 1)(x - 2)(x + 4)(3x + 7) = (x² - x + 4x - 4)(3x + 7) = (x² + 3x - 4)(3x + 7)

Next, we can multiply the two binomials using the FOIL method:

(x² + 3x - 4)(3x + 7) = 3x³ + 7x² + 9x² + 21x - 12x - 28

Simplifying further, we get the equivalent standard form equation: 3x⁴ + 12x³ + 19x² - 56x - 28

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Which of these standard form equations is equivalent to \((x + 1)(x - 2)(x + 4)(3x + 7)\)?A) \(3x^4 + 12x^3 - 19x^2 - 56x - 28\)B) \(3x^4 - 12x^3 - 19x^2 + 56x + 28\)C) \(3x^4 + 12x^3 + 19x^2 - 56x - 28\)D) \(3x^4 - 12x^3 + 19x^2 + 56x + 28\)

Answer :

Final answer:

Explanation:

Other Questions

Which of these standard form equations is equivalent to \((x + 1)(x - 2)(x + 4)(3x + 7)\)?

A) \(3x^4 + 12x^3 - 19x^2 - 56x - 28\)

B) \(3x^4 - 12x^3 - 19x^2 + 56x + 28\)

C) \(3x^4 + 12x^3 + 19x^2 - 56x - 28\)

D) \(3x^4 - 12x^3 + 19x^2 + 56x + 28\)