Worksheet For Quadratics With A Coefficient Greater Than 1 (Page 3 of 4) in pdf

Worksheet For Quadratics With A Coefficient Greater Than 1 Page 3

He then writes (x + 6)(x + 2) and then is lost because 2 divides both 2

and 6. What should the student do to factor with the given method?

Explain. (I do not want you to say that the student should use an-

other method, but rather explain how to use and/or adapt this method

(without factoring out the 2 ﬁrst) to ﬁnish the problem.)

Since 2 6 and 2 2, we can actually use either term. If we

choose the 6 term, then the factorization will give

8x + 6 = (x + 3)(2x + 2)

now factor 2 out

= (x + 3)2(x + 1)

= 2(x + 3)(x + 1).

Alternatively, if we choose the 2 term, we would have

8x + 6 = (2x + 6)(x + 1)

now factor 2 out

= 2(x + 3)(x + 1).

In either case we end up with the same factorization, which is also what

comes out if we factor out a 2 at the beginning.

3. Can the method be adapted to factor 6x

+ 13x + 6? Why or why not?

Yes, using the expanded method above we can now factor,

looking for numbers that add to 13 and multiply to 36, we see that 4

and 9 ﬁt the bill. Now we look for a factorization of 6 such that one

factor divides 4 and the other divides 6. Since 2 and 3 satisfy these

conditions, we have

+ 13x + 6 =

3x +

2x +

= (3x + 2)(2x + 3).

Worksheet For Quadratics With A Coefficient Greater Than 1 Page 3