Question

what are the factors of $6x^2 + 37x - 60$?

• $3x - 4$ and $2x + 15$
• $3x + 4$ and $2x - 15$
• $2(x - 2)$ and $3(x + 5)$
• $2(x + 2)$ and $3(x - 5)$

Explanation:

Step1: Recall factoring quadratic

We need to factor \(6x^2 + 37x - 60\). We can also check each option by multiplying the factors.

Step2: Check Option 1: \((3x - 4)(2x + 15)\)

Multiply: \(3x\times2x+3x\times15 - 4\times2x - 4\times15=6x^2 + 45x-8x - 60=6x^2 + 37x - 60\). This matches the quadratic.

Step3: Verify other options (optional)

Option 2: \((3x + 4)(2x - 15)=6x^2-45x + 8x-60=6x^2-37x - 60\) (sign of middle term wrong).
Option 3: \(2(x - 2)\times3(x + 5)=6(x - 2)(x + 5)=6(x^2 + 3x - 10)=6x^2+18x - 60\) (not matching).
Option 4: \(2(x + 2)\times3(x - 5)=6(x + 2)(x - 5)=6(x^2 - 3x - 10)=6x^2-18x - 60\) (not matching).

Answer:

A. \(3x - 4\) and \(2x + 15\)