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).
Answer:
x=
Step-by-step explanation:
Answer:
495-75=m m=420
Step-by-step explanation:
He needs to save 495 dollars, and hes already saved 75
and needs to find out how much more he needs to save to have 495 dollars
To do this, take 495 and subtract 75. This is how we get the inequality
495-75=m
From here it is simple, just subtract 75 from 495 to get 420
Answer:
0
Step-by-step explanation:
The zero is in the "hundred-thousands" place. Zero hundred thousands has a value of zero.