Question

a quadratic expression is shown.
$3x^2 - 2x - 5$
select an expression for each box to show the factored form of the given quadratic expression.
answer
$3x^2 - 2x - 5 =$

Explanation:

Step1: Identify coefficients

For $3x^2 - 2x - 5$, $a = 3$, $b = -2$, $c = -5$.

Step2: Find $ac$ product

Calculate $ac = 3\times(-5) = -15$.

Step3: Find factors of $ac$

Find two numbers that multiply to $-15$ and add to $b = -2$. The numbers are $-5$ and $3$ (since $-5\times3 = -15$ and $-5 + 3 = -2$).

Step4: Rewrite middle term

Rewrite $-2x$ as $-5x + 3x$: $3x^2 - 5x + 3x - 5$.

Step5: Group and factor

Group terms: $(3x^2 - 5x) + (3x - 5)$. Factor out GCF from each group: $x(3x - 5) + 1(3x - 5)$.

Step6: Factor out common binomial

Factor out $(3x - 5)$: $(3x - 5)(x + 1)$.

Answer:

$(3x - 5)(x + 1)$