-3 plus or minus (i) square root of seven
Over 4
Answer:
- x+3 and x+2
- (
5
x
+
2
)
(
x
2
+
5
)
- 9x^2+16
- 3x2 + 21x + 36
Step-by-step explanation:
- x2 + 5x + 6
Let us try factorizing this polynomial using splitting the middle term method.
Factoring polynomials by splitting the middle term:
We need to find two numbers ‘a’ and ‘b’ such that a + b =5 and ab = 6.
On solving this we obtain, a = 3 and b = 2
Thus, the above expression can be written as:
x2 + 5x + 6
= x2 + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)
Thus, x+3 and x+2 are the factors of the polynomial x2 + 5x + 6.
- For Step 1, you just want to find all combinations of two numbers that multiply together to be 56. Make sure you take negatives into account. Those pairs of numbers are:
(p, q, p+q)
(1, 56, 57)
(-1, -56, -57)
(2, 28, 30)
(-2, -28, -30)
(4, 14, 18)
(-4, -14, -18)
(7, 8, 15)
(-7, -8, -15)
Use those pairs of numbers and their sums to fill in the three columns of your table.
- STEP 2
- Look down your p+q column to find the pair of numbers that add up to equal to -15. That's (p, q) = (-7, -8).
- STEP 3
- Using the information from steps 1 and 2, you can factor the trinomial like this:
- x2 - 15x + 56 = (x + p)(x + q) = (x - 7)(x - 8)
- FOIL that back out if you'd like, to make sure the expressions are equivalent.
- STEP 4
- Hopefully, seeing steps 1 through 3 worked out will help you with step 4. Find all the pairs of numbers that multiply together to be 36 (1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6, and all their negative equivalents), then figure out which pair has a sum of 12. That means you've found your p and q, and can factor the trinomial as (x + p)(x + q).
Y should equal -7/2 or -3.5
Her current balance aftsr adding 60$ 3 times would be -65
