Question

Which expression is a factor of 10x^2+11x+3

Answer 1

Answer:

The factors are (5x + 3) and (2x + 1)

Step-by-step explanation:

When you need to factor a quadratic, and the coefficient of the x² is not 1, use the slide and divide method.

The general form of a quadratic is ax² + bx + c

Factor:  10x² + 11x + 3

Here a = 10, b = 11, and c = 3

Step 1:  Multiply ac, we SLIDE a over to c.  Notice the 10 is gone for now..

    x² + 11x + 30

Step 2:    Factor this   (this step will always factor)

  x² + 11x + 30 = (x + 5)(x + 6)

So the factors are  (x + 5)(x + 6), but we now need to DIVIDE by a, since we multiplied it into c before.  We divide the constants in the factors...

   (x + 5/10 )(x + 6/10 )  

Now reduce the fractions as much as possible...

(x + 1/2 )(x + 3/5)

*If they don't reduce to a whole number, SLIDE the denominator over as a coefficient of x....

(2x + 1)(5x + 3)        *2 slide over in front of x, 5 slide over in front of x, the fractions are gone!

These are our factors!