Question
For . each of the 3 following characteristic equations:Equation 1:1313112Equation 2:1341229 124Factor the polynomial on the left-hand side down into 3 smaller product termsHint #1: If you recall from Algebra Il, the key to synthetic division is to know all possible factors of the constant term in our polynomial !! For instance, for Equation #2, you want to focus on the factors associated with the constant "24-Hint #2: If it's been @ while since you've seen factors of a number, che
For . each of the 3 following characteristic equations: Equation 1: 13 131 12 Equation 2: 13 412 29 1 24 Factor the polynomial on the left-hand side down into 3 smaller product terms Hint #1: If you recall from Algebra Il, the key to synthetic division is to know all possible factors of the constant term in our polynomial !! For instance, for Equation #2, you want to focus on the factors associated with the constant "24- Hint #2: If it's been @ while since you've seen factors of a number, check out this reminder https:/ /www.mathsisfun com/numbers/factors-all-tool html (b) Find the roots of each polynomial
Answers
Factor each polynomial completely. See Examples 1 through 12. $$ 3 a^{2}+12 a b+12 b^{2} $$
It's the West to find a polynomial with these fall in with Well, we see that they're all real numbers, so we can just write them out. We have X minus *** one. That's one X minus two and X minus Negative three, which is exposed.
So I am three x where Line six plus three. So I have three common to everything's gonna factor out a ready which leaves me with X squared minus two x plus one inside my parentheses Now inside my parentheses send going to factor x times X He was the X squared The signs are both the same They're both negative and one times one multiplies getting wanted ads to give me too. It could also write this as three times x minus one wanted these weird.
Four x Where minus 39 x less 27 Nothing. Common doll three terms. Four times 27 or 10 78 four times two is eight plus 208 Now saying what multiplies Give me 108 and heads. Give me 39. One of 108 two and 54 three and 36. There we go. I have four x squared minus 36 minus three x plus 27. So factoring out my 1st 2 terms is gonna factor out, or X, which gives me X minus. Factoring out of three out of the 2nd 2 terms, use me X minus nine that I, in fact, around my X minus nine. And I know four x minus. I agree.
Way Have the try No meal three x where it was 13 x plus 12. We have a trying only with leading coefficient. That is not once we multiply the A and C terms together. Three times 12 is 36 that's our target number. What factors of 36 multiplied? 36 An ad. 13. Well, what most wives in 36 2 in 18. We're not gonna get a 13 out of that. Three and 12 were not getting the 13 out of that four and nine. There is our 13 for post minus 13 so we break apart the 13 with a four x and a nine x The other two terms filed down so that we have turned our trying amulet into four terms so that we can group in greatest common. Factor. Each group to take out an X from the first group. Left with three X plus four. We can take a three out of the second group left with three X plus four. Now we have the common groups. Three. Expose four and what we took out experts. Three. That's what's left from each term, so three X plus four