Identify Quadratic Form: Identify the form of the quadratic trinomial. The given quadratic equation y = 3x^2 - 18x + 15 is in the standard form y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.Factor Out GCF: Factor out the greatest common factor (GCF) if there is any. The coefficients 3, -18, and 15 all have a common factor of 3. We can factor out the 3 from the quadratic equation. y = 3(x^2 - 6x + 5)Rewrite in Factored Form: Rewrite the quadratic trinomial in the factored form. We need to find two numbers that multiply to give ac (a times c) and add to give b. In this case, ac = 3 * 5 = 15 and b = -6. The two numbers that meet these criteria are -3 and -2 because (-3) * (-2) = 6 and (-3) + (-2) = -5 (which is incorrect, it should be -5).

Algebra 2

Factor quadratics

Full solution

y=3x^2-18x+15

Identify Quadratic Form: Identify the form of the quadratic trinomial. $\newline$ The given quadratic equation $y = 3x^2 - 18x + 15$ is in the standard form $y = ax^2 + bx + c$ , where $a = 3$ , $b = -18$ , and $c = 15$ .
Factor Out GCF: Factor out the greatest common factor (GCF) if there is any. $\newline$ The coefficients $3$ , $-18$ , and $15$ all have a common factor of $3$ . We can factor out the $3$ from the quadratic equation. $\newline$ $y = 3(x^2 - 6x + 5)$
Rewrite in Factored Form: Rewrite the quadratic trinomial in the factored form. $\newline$ We need to find two numbers that multiply to give $ac$ ( $a \times c$ ) and add to give $b$ . In this case, $ac = 3 \times 5 = 15$ and $b = -6$ . $\newline$ The two numbers that meet these criteria are $-3$ and $-2$ because $(-3) \times (-2) = 6$ and $(-3) + (-2) = -5$ (which is incorrect, it should be $-5$ ).