I have a maths problem. I need to find out how to factorise these:?

Question

a) x[squared]+5x+6
b) x[squared]-4x-12
c) x[squared]-7x+10

Thanks in advance..

Answer 1

a) (x + 2)(x + 3)
b) (x - 6)(x + 2)
c) (x - 2)(x - 5)
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Details:
Factorizing when you have x².

Just think of the factors of the last number and see which add to be the multiplier of the x term.

a) What two numbers multiply to be 6 and add to be 5?

6 has the following factors:
1 x 6 -- > 1 + 6 = 7
2 x 3 --> 2 + 3 = 5 *
3 x 2 --> 3 + 2 = 5 *
6 x 1 --> 6 + 1 = 7
-1 x -6 --> -1 + -6 = -7
-2 x -3 --> -2 + -3 = -5
-3 x -2 --> -3 + -2 = -5
-6 x -1 --> -6 + -1 = -7

So the answer is 2 and 3 --> (x + 2)(x + 3) = x² + 5x + 6
Or equivalently (x + 3)(x + 2) = x² + 5x + 6

b) Multiply to -12, Add to -4
-1 x 12 --> -1 + 12 = 11
-2 x 6 --> -2 + 6 = 4
-3 x 4 --> -3 + 4 = 1
-4 x 3 --> -4 + 3 = -1
-6 x 2 --> -6 + 2 = -4 *
-12 x 1 --> -12 + 1 = -11

(x - 6)(x + 2) = x² - 4x - 12

c) Multiply to 10, add to -7
1 x 10 --> 1 + 10 = 11
2 x 5 --> 2 + 5 = 7
5 x 2 --> 5 + 2 = 7
10 x 1 --> 10 + 1 = 11
-1 x -10 --> -1 + -10 = -11
-2 x -5 --> -2 + -5 = -7 *
-5 x -2 --> -5 + -2 = -7 *
-10 x -1 --> -10 + -1 = -10

(x - 2)(x - 5) = x² - 7x + 10

Answer 2

you need to find the 2 numbers (including signs) that when timesed together form the number on its own and when added together make the X factor (not the X squared).

so in your first example the factors of 6 are 1&6 2&3
to make 5 you would have to use +6 -1 which when timesed gives -6 but our end expression is +6.
so we use +3 +2 which when timesed becomes +6
so (x+3)(x+2)

in the 2nd example the factors of 12 are 1&12 2&6 3&4
to get -4 we need -6 +2 which when timesed gives us -12.
(x-6)(x+2)

in the last one factors of 10 are 1&10 2&5
to get -7 we need -2-5 when we times minus x minus = posative. so that gives us +10
(x-2)(x-5)

Answer 3

x^2 + 5x + 6 = 0
(x + 3) (x +2) = 0 (when you multiply these two back, you will get the original one)
x = -3 and x = -2

x^2 -4x -12 = 0
(x-6) (x + 2) = 0
x = 6 and x = -2

x^2 -7x +10 = 0
(x-5) (x-2) = 0
x = 5 and x = 2

Answer 4

a) (X+2)(x+3)
b)(x-6)(X+2)
C)(x-5)(x-2)

Answer 5

well you write it out

x^2+5x+6

you take the 6 and see what numbers you multiply to get six

2x3 -- because 2+3 =5
1x6

(x+2)(x+3)

Answer 6

(x+3)(x+2)
(x-6)(x+2)
(x-5)(x-2)

Answer 7

1. you want two numbers that multiply to 6 and add to 5:
(x+2)(x+3)
2. you want two numbers that multiply to -12 and add to -4:
(x-6)(x+2)
3. two numbers that multiply to +10 and add to -7:
(x-5)(x-2)

Answer 8

(x+3)(x+2)
(x-6)(x+2)
(x-5)(x-2)

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