We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4
6 + 4 = 10
6*4 = 24
So we can break up the 10ab into 6ab+4ab and then use factor by grouping
a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)
Therefore, the original expression factors completely to (a+4b)(a+6b)
Answer:
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Step-by-step explanation:
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Answer:
4 hours
Step-by-step explanation:
120 ÷ 30 = 4
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Answer:

Step-by-step explanation:
<u>Common Factors</u>
An algebraic expression that is formed by sums or subtractions of terms can be factored provided there are numeric or variable common factors in all the terms.
The following expression

Can be factored in the constants and in the variable x.
1. To find the common factor of the variable, we must locate if the variable is present in all terms. If so, we take the common factor as the variable with an exponent which is the lowest of all the exponents found throughout the different terms. In this case, the lowest exponent is x (exponent 1).
2. To find the common factors of the constants, we take all the coefficients:
12 - 20 - 32
and find the greatest common divisor of them, i.e. the greatest number all the given numbers can be divided by. This number is 4, since 12/4=3, 20/4=5 and 32/4=8
3. The factored expression is


Step-by-step explanation:
the slope of a line function is always the factor of x.
in our case : -1/4
it is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.
in our case y decreases by 1 for every x increase by 4.
now, the perpendicular slope simply changes x and y upside-down and flips the sign.
in our case it is : 4/1 = 4
so, the line function in point slope form is then (using the new slope and the point coordinates)
y - 3 = 4(x - 1)