Answer:
3(2x^2-3x+14)
Step-by-step explanation:
6x^2-9x+42
All three terms have a common factor of 3
3(2x^2-3x+14)
Now let's focus on 2x^2-3x+14 and bring down the factor 3 later
so a=2
b=-3
c=14
Let's try to find two factors for ac that multiply to be a*c and add up to be b.
ac=28
b=-3
-----
ac=7(4)=14(2)=8(2)
Even if I made these pairs with both negatives nothing would give me -3
So you can only go as far as 3(2x^2-3x+14)
Here is another thing to help you if you have ax^2+bx+c and b^2-4ac<0 then it can't be factored (over reals)
Answer:
y = -(5/2)x -2
Explanation:
The general formula for a straight line is y – mx + b.
The image below shows the graph of the line.
Step 1. <em>Calculate the slope</em>.
Slope = m = Δy/Δx = (y₂-y₁)/(x₂-x₁)
x₁ = 0; y₁ = -2
x₂ = -2; y₂ = 3 Calculate m
m = [3-(-2)]/(-2-0)
m = (3+2)/(-2)
m = 5/(-2)
m = -5/2
Step 2. <em>Calculate the y-intercept
</em>
When x = 0, y = 2.
The y-intercept (b) is at y = -2
Step 3. <em>Write the equation </em>for the graph
y = mx + b
y = -(5/2)x - 2
to solve for the dimensions (x+7)(x+2)=66,
we can first use the foiling method to simplify the left side.
x^2 + 2x + 7x + 14 = 66
x^2 + 9x + 14 = 66
now, subtract 66 from both sides.
x^2 + 9x - 52 = 0
now, split this into two parentheses.
(x + 13)(x - 4)
since the root of -13 would give you negative values, x=4. This means that the dimensions of the rectangle are 11 and 6.
Scalene I believe. Hope this helps!
2x2-5x-18=0
Two solutions were found :
x = -2
x = 9/2 = 4.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2x2 - 5x) - 18 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 2x2-5x-18
The first term is, 2x2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -18
Step-1 : Multiply the coefficient of the first term by the constant 2 • -18 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
2x2 - 9x + 4x - 18
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x-9)
Add up the last 2 terms, pulling out common factors :
2 • (2x-9)
Step-5 : Add up the four terms of step 4 :
(x+2) • (2x-9)
Which is the desired factorization
Equation at the end of step 2 :
(2x - 9) • (x + 2) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
