We write the polynomial in its factored form first.
We have then:
(x + 2) * (x + 1) * (x-4) * (x-5)
We now rewrite the polynomial:
(x ^ 2 + x + 2x + 1) * (x ^ 2-5x-4x + 20)
(x ^ 2 + 3x + 1) * (x ^ 2-9x + 20)
x ^ 4 - 9x ^ 3 + 20x ^ 2 + 3x ^ 3 - 27x ^ 2 + 60x + x ^ 2 - 9x + 20
We now add terms of the same degree:
x ^ 4 + (-9 + 3) x ^ 3 + (20-27 + 1) x ^ 2 + (60-9) x + (20)
x ^ 4 + (-6) x ^ 3 + (-6) x ^ 2 + (21) x + (20)
x ^ 4 - 6x ^ 3 - 6x ^ 2 + 21x + 20
Answer:
The polynomial sought is:
x ^ 4 - 6x ^ 3 - 6x ^ 2 + 21x + 20
The answer to that is (x^4 y^6+1)(x^8 y^12-x^4 y^6+1
<h3>
Answer:</h3>
(2x + 1)(x + 3)
<h3>
Step-by-step explanation:</h3>
It is probably easier to try the answer choices than to try to factor the expression yourself.
(2x + 2)(x + 1) = 2x² +4x +2
(2x + 3)(x + 1) = 2x² +5x +3
(2x + 1)(x + 3) = 2x² +7x +3 . . . . . correct choice
_____
<em>Constructed solution</em>
If you want to factor this yourself, you can look for factors of "ac" that add to give "b". That is, you want factors of 2·3 = 6 that add up to give 7. You don't have to look very far.
... 6 = 1·6 = 2·3 . . . . . . the first factor pair adds to give 7
Now, rewrite the x term using the sum of these numbers.
... 2x² +(1 +6)x +3
... 2x +x +6x +3 . . . . eliminate parentheses
... (2x +x) +(6x +3) . . . . group pairs of terms
... x(2x +1) +3(2x +1) . . . . factor each pair
... (x +3)(2x +1) . . . . . . matches the last selection
Answer:
Emily has a 1 in 9 chance of rolling an odd number for all 3 rolls
Step-by-step explanation:
