Factorise to quadratics
X^2+5x-14
X^2-x-90
X^2-13x+40
(x-2)(x+7)
(x-10)(x+9)
(x-5)(x-8)
To factorize a quadratic expression, we need to find two binomial expressions that, when multiplied together, give us the original quadratic expression.
Let's factorize each quadratic expression one by one:
1. x^2 + 5x - 14:
To factorize this quadratic expression, we need to find two numbers that multiply to give -14 and add up to 5. The numbers that fulfill these criteria are 7 and -2. So, we can rewrite the quadratic expression as follows:
x^2 + 7x - 2x - 14
Now, we group the terms:
(x^2 + 7x) + (-2x - 14)
We can factor out the common factors separately from each group:
x(x + 7) - 2(x + 7)
Notice that (x + 7) is a common factor, which we can factor out:
(x + 7)(x - 2)
So, the factors of x^2 + 5x - 14 are (x + 7)(x - 2).
2. x^2 - x - 90:
To factorize this quadratic expression, we need to find two numbers that multiply to give -90 and add up to -1. The numbers that fulfill these criteria are -10 and 9.
So, the quadratic expression can be rewritten as:
x^2 - 10x + 9x - 90
Now, we group the terms:
(x^2 - 10x) + (9x - 90)
We can factor out the common factors separately from each group:
x(x - 10) + 9(x - 10)
Notice that (x - 10) is a common factor, which we can factor out:
(x - 10)(x + 9)
So, the factors of x^2 - x - 90 are (x - 10)(x + 9).
3. x^2 - 13x + 40:
To factorize this quadratic expression, we need to find two numbers that multiply to give 40 and add up to -13. The numbers that fulfill these criteria are -5 and -8.
So, the quadratic expression can be rewritten as:
x^2 - 5x - 8x + 40
Now, we group the terms:
(x^2 - 5x) + (-8x + 40)
We can factor out the common factors separately from each group:
x(x - 5) - 8(x - 5)
Notice that (x - 5) is a common factor, which we can factor out:
(x - 5)(x - 8)
So, the factors of x^2 - 13x + 40 are (x - 5)(x - 8).
By following these steps, you can factorize the given quadratic expressions into two binomial expressions.