9-5 F ACTORING T RINOMIALS type ax 2 + bx +cand a = 1.

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Presentation transcript:

9-5 F ACTORING T RINOMIALS type ax 2 + bx +cand a = 1

In this section, you will be factoring polynomials like: Technically these can all be written as: when a = 1

Remember that factoring means breaking it down into two expressions which are being multiplied. For many of these problems, you will use guess and check… The first part is easy! When you multiply, the first term will be x 2, and the other terms will both be positive.

Now for the guess and check part… The two numbers I need have a sum of 4 and a product of 3. Well = 4, but 2 * 2 =4, doesn’t work… How about, = 4, and 3 * 1 = 3 That works! So the answer is ( x + 3)( x + 1)

Try this one… The two numbers I need have a sum of 8 and a product of 15.

The signs can change… The two numbers I need have a difference of 2 and a product of -8. There are 4 ways to get a product of -8 – 8 * 1 8 * –1 –4 * 2 4 * –2 Which set has a difference of 2? So the solution is (x+4)(x –2) 4 * –2 Notice now one is plus and one is minus!

Try this one… The two numbers I need have a difference of 10 and a product of – 24.

The signs can change again… The two numbers I need have a sum of –11 and a product of 24. There are lots of ways to get 24, but since the sum is negative, I must be adding two negative numbers! – 1 * –24 –2 * –12 –3 * –8 – 4 * –6 Which set has a sum of –11? So the solution is (x – 3)(x –8) –3* –8 now they are both minus!

Try this one… The two numbers I need have a difference of 10 and a product of – 24.

The signs can change again… The two numbers I need have a difference of –3 and a product of –28. There are 6 ways to get – 28, – 1 * 28 1 * –28 –2 * 14 2 * –14 – 4 * 7 4 * –7 Which set has a difference of –3? So the solution is (x – 7)(x + 4) –7* 4 Notice now one is plus and one is minus!

Try this one… The two numbers I need have a difference of –3 and a product of – 40.