Question

factor.
$2y^2 - 11y - 21$

Explanation:

Step1: Identify coefficients

For \(2y^2 - 11y - 21\), \(a = 2\), \(b=-11\), \(c = -21\).

Step2: Find \(ac\)

Calculate \(ac=2\times(-21)= - 42\).

Step3: Find factors of \(ac\)

Find two numbers that multiply to \(-42\) and add to \(b=-11\). The numbers are \(-14\) and \(3\) (since \(-14\times3=-42\) and \(-14 + 3=-11\)).

Step4: Split the middle term

Rewrite the middle term: \(2y^2-14y + 3y-21\).

Step5: Group and factor

Group as \((2y^2-14y)+(3y - 21)\). Factor out \(2y\) from first group: \(2y(y - 7)\), factor out \(3\) from second group: \(3(y - 7)\). Now factor out \((y - 7)\): \((2y + 3)(y - 7)\).

Answer:

\((2y + 3)(y - 7)\)