Question

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. Explain how to find the factors of the polynomial.

Answer 1

Identify the factor x + 3 from the given root –3.Use synthetic division to divide the polynomial by x + 3.Use the bottom row of the synthetic division as coefficients in the quadratic 2x2 + 3x – 2.Factor the quotient to find the two other factors: x + 2 and 2x – 1.

Answer 2

The factors of the given polynomial are (x+3)(x+2)(2x - 1).

Given that,

• The given polynomial is $f(x) = 2x^3 + 9x^2 + 7x - 6$.
• Also, one root is -3 that means (x+3) = 0.

Based on the above information, the calculation is as follows:

$= 2x^3 + 9x^2 + 7x - 6\\\\= 2x^3 +6x^2+3x^2 +9x - 2x - 6\\\\=2x^2 (x+3)+3x(x+3) -2 (x+3)\\\\= (x+3)(2x^2 +3x - 2)\\\\= (x +3){2x^2 +4x-x-2}\\\\= (x+3)(2x(x +2) -1(x+2))\\\\=(x+3)(x+2)(2x - 1)$

Therefore we can conclude that the factors of the given polynomial are (x+3)(x+2)(2x - 1).

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