Question

review - factoring quadratics - diamon score: 11/24 answered: 11/24 progress saved done √0 question 12 change f(x) = 4x² - x - 3 to factored form. f(x) =

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\times(-3)= -12\) and add up to \(-1\). The numbers are \(-4\) and \(3\) since \(-4\times3 = -12\) and \(-4 + 3=-1\).

Step2: Rewrite the middle term

Rewrite \(-x\) as \(-4x+3x\) in the quadratic: \(4x^{2}-4x + 3x-3\).

Step3: Group and factor

Group the first two and last two terms: \((4x^{2}-4x)+(3x - 3)\). Factor out the GCF from each group: \(4x(x - 1)+3(x - 1)\).

Step4: Factor out the common binomial

Factor out \((x - 1)\) to get \((4x + 3)(x - 1)\).

Answer:

\((4x + 3)(x - 1)\)