Can someone give me step by step instructions on how to solve this problem?

Question

Can someone give me step by step instructions on how to solve this problem? Please do not just give the answer. I need to know the method of solving a problem like this. Thanks!

Factor: y^2 - 9y + 14

Answer 1

Ax^2 + Bx + C = 0

to solve this equation, set it equal to 0

y^2 - 9y + 14 = 0

to factor, look for two numbers that multiply to AC and add up to B.

AC means A x C.

in this case:
A = 1
B = -9
C = 14

1 x 14 = 14

so look for two numbers that multiply to 14 and add t0 -9

the two numbers are -2 and - 7

since the leading coefficient is 1, plug the two numbers in factor form

(y - 2) (y - 7) = 0

y = 2 or 7

hope this helps

Answer 2

The only possible factors of y² are y and y so these are placed in position:-
(y-------).(y------)
Then require factors of 14 that can be arranged to add/subtract to give - 9
These factors are 7 and 2 with appropriate signs:-
(y------7).(y-------2)
Signs are then inserted:-
(y - 7).(y - 2)
Check
y.(y - 2) - 7.(y - 2)
= y² - 2y - 7y + 14
= y² - 9y + 14 (as required)

Answer 3

The trick here is to figure out which factors of +14 when added together get to -9 when considering the cross-multiplied term.

In this case, -7 and -2 do the trick.

So, you get:

(y-7)(y-2)

Answer 4

Consider (y - a)(y -b) as your factorizaion. That expands out to y^2 - (a + b)y + ab

ab =14. Since it is a positive number, a and b have the same sign, both positive or both negative.

a + b = 9. Since their sum is positive, we know a and b are both positive and not both negative.

Look then for a pair of factors of 14 that sum to 9 and you have your answer.

Good luck!

Answer 5

First, multiply the -6 and you're able to do away with the parentheses -12b + -6 + 13b -7 = 0 Regroup and upload what you are able to (-12b + 13b) + (-6-7)=0 b-13=0 to do away with the 13 b-6+13=0+13 b=13

Answer 6

=y^2 - 7y - 2y + 14
=y(y - 7) - 2(y - 7)
=(y - 7)(y-2)

Answer 7

y^2-9y+14
=y^2-2y-7y+14
=y(y-2)-7(y-2)
=(y-2)(y-7)