factor the polynomial 3x^2+3x-6
The answer should be 3(x - 2)(x + 1).
GCF is 3
Factor out 3.
3(x^2 - x - 2)
Numbers that add up to -1 and -2 are -2 and 1.
3(x - 2)(x + 1)
I hope this helps! :)
3x^2 + 3x - 6 = 0
A*C = 3*(-6) = -18 = -3*6
Choose the pair of factors whose sum = B = +3: -3, and 6.
3x^2 + (-3x+6x) - 6 = 0
Form two factorable binomials:
(3x^2-3x) + (6x-6) = 0
3x(x-1) + 6(x-1) = 0
(x-1)(3x+6) = 0
(x-1)*3(x+2) = 0
x-1 = 0
X = 1
3(x+2) = 0
Divide by 3:
x+2 = 0
X = -2
Solution set: X = -2, and 1.
9
To factor the polynomial 3x^2 + 3x - 6, we need to find two binomials that, when multiplied, give us this polynomial.
Step 1: Look at the coefficient of x^2. In this case, it is 3.
Step 2: We need to find two numbers that multiply to give us the product of the coefficient of x^2 (3) multiplied by the constant term (-6). The constant term in this case is -6.
Step 3: The possible pairs of numbers that multiply to -18 (3 * (-6)) are:
-1, 18
-2, 9
-3, 6
-6, 3
1, -18
2, -9
3, -6
6, -3
Step 4: We need to determine which pair will add up to give us the coefficient of x (3). In this case, we can see that the pair is 3 and -2.
Step 5: Now, we rewrite the polynomial by splitting the x-term using the pair we found: 3x^2 + 3x - 6 becomes 3x^2 + 3x - 2x - 6.
Step 6: Next, we factor by grouping. Group the terms as follows: (3x^2 + 3x) + (-2x - 6).
Step 7: Now, take out the common terms from each group: 3x(x + 1) - 2(x + 3).
Step 8: Finally, we can factor out the common binomial (x + 1) from both terms: (3x - 2)(x + 3).
Therefore, the factored form of the polynomial 3x^2 + 3x - 6 is (3x - 2)(x + 3).