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Learn how to write a polynomial from factored form to standard form with a couple of good examples.
Example #1
Write the expression (x + 2)(x + 3)(x + 4) as a polynomial in standard form
Multiply (x + 3) and (x + 4)
(x + 2)(x + 3)(x + 4) = (x + 2)(x2 + 4x + 3x + 12)
Simplify
(x + 2)(x + 3)(x + 4) = (x + 2)(x2 + 7x + 12)
Use the distributive property
(x + 2)(x + 3)(x + 4) = x(x2 + 7x + 12) + 2(x2 + 7x + 12)
Multiply
(x + 2)(x + 3)(x + 4) = x3 + 7x2 + 12x + 2x2 + 14x + 24
Combine like terms
(x + 2)(x + 3)(x + 4) = x3 + 7x2 + 2x2 + 12x + 14x + 24
Simplify
(x + 2)(x + 3)(x + 4) = x3 + 9x2 + 26x + 24
The expression (x + 2)(x + 3)(x + 4) is the factored form of x3 + 9x2 + 26x + 24
Example #2
Write the expression (x - 5)(x + 1)(x + 1) as a polynomial in standard form
Multiply (x + 1) and (x + 1)
(x - 5)(x + 1)(x + 1) = (x - 5)(x2 + x + x + 1)
Simplify
(x - 5)(x + 1)(x + 1) = (x - 5)(x2 + 2x + 1)
Use the distributive property
(x - 5)(x + 1)(x + 1) = x(x2 + 2x + 1) + -5(x2 + 2x + 1)
Multiply
(x - 5)(x + 1)(x + 1) = x3 + 2x2 + x + -5x2 + -10x + -5
Combine like terms
(x - 5)(x + 1)(x + 1) = x3 + 2x2 + -5x2 + x + -10x + -5
Simplify
(x - 5)(x + 1)(x + 1) = x3 + -3x2 + -9x + -5
The expression (x - 5)(x + 1)(x + 1) is the factored form of x3 + -3x2 + -9x + -5
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