Factorise X'2+9X +14

x^2-3x-6x+18

x^2-9x+8
(x-6)(x-3)

hint. which two factors of 14 add up to 9?

and we usually use ^ for powers. x^2+9x+14

To factorize the quadratic expression x^2 + 9x + 14, we need to find two binomials that, when multiplied, give us the given quadratic expression.

We are looking for two binomials of the form (x + a)(x + b), where a and b are constants. To find these constants, we need to find two numbers that satisfy the following conditions:
1. The product of a and b should be equal to the constant term, 14.
2. The sum of a and b should be equal to the coefficient of the linear term, 9.

Let's list down all possible combinations of two numbers whose product is 14:
1 * 14 = 14
2 * 7 = 14

Now let's check which of these combinations satisfies the sum condition:
1 + 14 = 15 (does not satisfy the sum condition)
2 + 7 = 9 (satisfies the sum condition)

Therefore, we have found our two constants, a = 2 and b = 7.

Now we can rewrite the quadratic expression as the product of the two binomials:
x^2 + 9x + 14 = (x + 2)(x + 7)

So, the factored form of the quadratic expression is (x + 2)(x + 7).

X2+9x+14