factor each trinomial (explain simple)
x^2 + 12x + 11
To factor the trinomial x^2 + 12x + 11, we need to find two numbers that multiply to 11 and add up to 12. The two numbers are 1 and 11 because 1 * 11 = 11 and 1 + 11 = 12.
Now we can rewrite the trinomial as:
x^2 + 1x + 11x + 11
Next, we factor by grouping:
x(x + 1) + 11(x + 1)
Now, we can see that both terms have a common factor of (x + 1), so we can factor out the (x + 1):
(x + 1)(x + 11)
Therefore, the factored form of the trinomial x^2 + 12x + 11 is (x + 1)(x + 11).
factor each trinomial (explain simple)
x^2 + 6x + 5
To factor the trinomial x^2 + 6x + 5, we need to find two numbers that multiply to 5 and add up to 6. The two numbers are 1 and 5 because 1 * 5 = 5 and 1 + 5 = 6.
Now we can rewrite the trinomial as:
x^2 + 1x + 5x + 5
Next, we factor by grouping:
x(x + 1) + 5(x + 1)
Now, we can see that both terms have a common factor of (x + 1), so we can factor out the (x + 1):
(x + 1)(x + 5)
Therefore, the factored form of the trinomial x^2 + 6x + 5 is (x + 1)(x + 5).
factor each trinomial (explain simple)
x^2 + x - 12
To factor the trinomial x^2 + x - 12, we need to find two numbers that multiply to -12 and add up to 1. The two numbers are 4 and -3 because 4 * -3 = -12 and 4 + (-3) = 1.
Now we can rewrite the trinomial as:
x^2 + 4x - 3x - 12
Next, we factor by grouping:
x(x + 4) - 3(x + 4)
Now, we can see that both terms have a common factor of (x + 4), so we can factor out the (x + 4):
(x + 4)(x - 3)
Therefore, the factored form of the trinomial x^2 + x - 12 is (x + 4)(x - 3).
factor each trinomial (explain simple)
x^2 + x - 20
x^2 - 11x + 18
To factor the trinomial x^2 + x - 20, we need to find two numbers that multiply to -20 and add up to 1. The two numbers are 5 and -4 because 5 * (-4) = -20 and 5 + (-4) = 1.
Now we can rewrite the trinomial as:
x^2 + 5x - 4x - 20
Next, we factor by grouping:
x(x + 5) - 4(x + 5)
Now, we can see that both terms have a common factor of (x + 5), so we can factor out the (x + 5):
(x + 5)(x - 4)
Therefore, the factored form of the trinomial x^2 + x - 20 is (x + 5)(x - 4).
For the trinomial x^2 - 11x + 18, we need to find two numbers that multiply to 18 and add up to -11. The two numbers are -2 and -9 because -2 * -9 = 18 and -2 + (-9) = -11.
Now we can rewrite the trinomial as:
x^2 - 2x - 9x + 18
Next, we factor by grouping:
x(x - 2) - 9(x - 2)
Now, we can see that both terms have a common factor of (x - 2), so we can factor out the (x - 2):
(x - 2)(x - 9)
Therefore, the factored form of the trinomial x^2 - 11x + 18 is (x - 2)(x - 9).
x^2 - 4x - 21
x^2 + 10x + 9
To factor the trinomial x^2 - 4x - 21, we need to find two numbers that multiply to -21 and add up to -4. The two numbers are -7 and 3 because -7 * 3 = -21 and -7 + 3 = -4.
Now we can rewrite the trinomial as:
x^2 - 7x + 3x - 21
Next, we factor by grouping:
x(x - 7) + 3(x - 7)
Now, we can see that both terms have a common factor of (x - 7), so we can factor out the (x - 7):
(x - 7)(x + 3)
Therefore, the factored form of the trinomial x^2 - 4x - 21 is (x - 7)(x + 3).
For the trinomial x^2 + 10x + 9, we need to find two numbers that multiply to 9 and add up to 10. The two numbers are 1 and 9 because 1 * 9 = 9 and 1 + 9 = 10.
Now we can rewrite the trinomial as:
x^2 + x + 9x + 9
Next, we factor by grouping:
x(x + 1) + 9(x + 1)
Now, we can see that both terms have a common factor of (x + 1), so we can factor out the (x + 1):
(x + 1)(x + 9)
Therefore, the factored form of the trinomial x^2 + 10x + 9 is (x + 1)(x + 9).
x^2 - 12x + 32
x^2 +13x +42