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Factor completely the polynomial 6x5 + 5.4 + 20r3 + 1522 +61 + 1 _Hint:66 = (a _ b)(a + b)(a? + ab + 62)(a2 ab + 62) _...

Question

Factor completely the polynomial 6x5 + 5.4 + 20r3 + 1522 +61 + 1 _Hint:66 = (a _ b)(a + b)(a? + ab + 62)(a2 ab + 62) _

Factor completely the polynomial 6x5 + 5.4 + 20r3 + 1522 +61 + 1 _ Hint: 66 = (a _ b)(a + b)(a? + ab + 62)(a2 ab + 62) _



Answers

Factor each polynomial by grouping.
$$
a b+3 a+2 b+6
$$

All right. So to solve this problem, we're going to be using factoring by grouping. So we see our first moment 60 squared on our second element. You have easy, but five is not. Ah does not share any denominator with fixed. So we're going to break it up into three and two. This will really We can rewrite this expression than six D squared Z squared plus three z from our five plus the other two z from the five plus one. So now this is the part where the Group six and three both both of those have ese and they're both multiples of three. We're going to use those as a group and then we're gonna have the two z plus one is our other group. So we pull out their common denominator. Three z. It's multiplied by de cause. That's what's left behind Three z times. He gives us the 60 squared one. Oh, sorry. It's a to Z to Z in here because three z times to Z gives us the actual six plus one three z times. One gives us the three C that's going to be plus one times what's left over here to Z plus one. This is essentially the same thing as just putting parentheses around this. So now we can see this to Z plus one that both are three z and R one or being multiplied by this allows us to rewrite our expression as three Z plus one. All of that still needs to be multiplied by what's underlined in red, the two Z plus one and the Sir solutions the factored form of our expression.

In this cushion you have perfected, uh, suspicion. He is there. The six c Let's g are taking tea, woman Oh, from or comes in the expression you got See my lab. I is that that's way less one I'm here in the bosom is a sphere And for one of my peoples that provided some is one So vigils one and one. So that product is what and summits. So we can write Double expression is teamwork. Clever, aimless One birdie fly. But even this one, we'll all go big team I d Grab it. That's one. And a final Lonza is You might be glad when a plus one all this back.

All right. 60 squared plus five plus one. First is in my starting point of knowing the only way you can get the one is one times one second. If everything's positive, that means these air both positive as well. And so now we just have to think about six. It's certainly not six times one, because I would get us to seven a. But if it was three times two, that would give us a five day. So I put a three a here in a two way here, and I'm gonna get a to eight times one of 38 times one, though, get us to five. So this is that tryingto meal factor.

The case room when we multiply fractions with this multiplier crossed with the enumerators and then with their denominators. So when we do up top, we have a plus three times a plus three. Or we could even write this if you want it to, depending on how you're tall, a plus three squared B the way out. That just depends on your teachers preference. And then down low. We have a plastic time a minus one and this is your final answer because all we need to produce put in factory farm.


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