Factor
X^2 + 7x + 10
To factor the quadratic expression x^2 + 7x + 10, we will need to find two numbers that multiply to give 10 and add up to 7.
The two numbers are 2 and 5 because 2 * 5 = 10 and 2 + 5 = 7.
Using these numbers, we can rewrite the expression as:
x^2 + 2x + 5x + 10
Now, we can group the terms:
(x^2 + 2x) + (5x + 10)
Next, we factor out the greatest common factor of each pair of terms:
x(x + 2) + 5(x + 2)
Finally, we notice that (x + 2) is a common factor of both terms, so we can factor it out:
(x + 2)(x + 5)
Therefore, the factored form of x^2 + 7x + 10 is (x + 2)(x + 5).
X^2-2x-80
To factor the quadratic expression x^2 - 2x - 80, we need to find two numbers that multiply to give -80 and add up to -2.
The two numbers are -10 and 8 because -10 * 8 = -80 and -10 + 8 = -2.
Using these numbers, we can rewrite the expression as:
x^2 - 10x + 8x - 80
Now, we can group the terms:
(x^2 - 10x) + (8x - 80)
Next, we factor out the greatest common factor of each pair of terms:
x(x - 10) + 8(x - 10)
Finally, we notice that (x - 10) is a common factor of both terms, so we can factor it out:
(x - 10)(x + 8)
Therefore, the factored form of x^2 - 2x - 80 is (x - 10)(x + 8).
X^2-5x-14
To factor the quadratic expression x^2 - 5x - 14, we need to find two numbers that multiply to give -14 and add up to -5.
The two numbers are -7 and 2 because -7 * 2 = -14 and -7 + 2 = -5.
Using these numbers, we can rewrite the expression as:
x^2 - 7x + 2x - 14
Now, we can group the terms:
(x^2 - 7x) + (2x - 14)
Next, we factor out the greatest common factor of each pair of terms:
x(x - 7) + 2(x - 7)
Finally, we notice that (x - 7) is a common factor of both terms, so we can factor it out:
(x - 7)(x + 2)
Therefore, the factored form of x^2 - 5x - 14 is (x - 7)(x + 2).
x^2 + x - 30
To factor the quadratic expression x^2 + x - 30, we need to find two numbers that multiply to give -30 and add up to 1.
The two numbers are 6 and -5 because 6 * -5 = -30 and 6 + (-5) = 1.
Using these numbers, we can rewrite the expression as:
x^2 + 6x - 5x - 30
Now, we can group the terms:
(x^2 + 6x) + (-5x - 30)
Next, we factor out the greatest common factor of each pair of terms:
x(x + 6) - 5(x + 6)
Finally, we notice that (x + 6) is a common factor of both terms, so we can factor it out:
(x + 6)(x - 5)
Therefore, the factored form of x^2 + x - 30 is (x + 6)(x - 5).
x^2 - 10x + 25
The quadratic expression x^2 - 10x + 25 is a perfect square trinomial. It can be factored into a binomial squared.
The binomial is (x - 5), since (-5)^2 = 25 and -5 + -5 = -10.
So, the factored form of x^2 - 10x + 25 is (x - 5)(x - 5), or (x - 5)^2.