Answer :
Final answer:
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
Learn more about Standard Form Equations here:
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