Hello. Can someone check my answers to the following
Factor each of the following
1. a^2 - 9
My answer
a^2 - 9 = 0
(a - 3)a + 3)
2. 4a^2 - 4a+1
My Answer
4a^2 - 4a + 1
= 4a^2 - 2a - 2a + 1
= 2a(2a - 1) - 1(2a - 1)
= (2a - 1)(2a - 1)
3. 72 - 22x + x^2
My answer
72 - 22x + x^2
= x^2 - 22x + 72
= x^2 - 18x - 4x + 72
= x (x - 18) - 4 (x - 18)
= (x - 4) (x - 18)
4. Solve by factoring 3x^2 + 5x - 2 =0
My Answer
3x^2+5x-2=0
=3x^2+6x-x-2
=3x(x-2)-(x+2)
=(3x-1)(x+2)
Oh, the x^2 is squared.
Thanks in advance.
1. correct
2. correct
3. correct but could go from 2nd line to last
4. correct
You know you can check these by foiling, right? (when you multiply out your answers and then see if you got what you started with)
Let's check your answers.
1. To factor a^2 - 9, we can use the difference of squares formula. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, a^2 - 9 is in the form of a difference of squares because 9 is a perfect square (3^2). So we can write it as (a + 3)(a - 3). Therefore, the correct factoring of a^2 - 9 is (a + 3)(a - 3). Your answer is correct.
2. To factor 4a^2 - 4a + 1, we can try factoring it by grouping. Your attempt is almost correct, but there is a small mistake. When you applied the distributive property in the step 4a^2 - 2a - 2a + 1, you actually distributed -1 to both terms, not +1. So the correct factoring of 4a^2 - 4a + 1 should be (2a - 1)(2a - 1) or simply (2a - 1)^2. Your final answer is correct.
3. To factor 72 - 22x + x^2, we need to find two numbers that multiply to 72 and add up to -22x. Your attempt is almost correct, but there is a small mistake. Instead of rewriting the equation as x^2 - 18x - 4x + 72 in the third step, it should be x^2 - 18x - 4(x - 18). The correct factoring of 72 - 22x + x^2 should be (x - 4)(x - 18). Therefore, your final answer is incorrect.
4. To solve the equation 3x^2 + 5x - 2 = 0 by factoring, we need to factor the quadratic expression on the left side. Your attempt is correct. You correctly factor the expression as (3x - 1)(x + 2). This means that either (3x - 1) = 0 or (x + 2) = 0. Solving these equations gives us two solutions: x = 1/3 and x = -2. Therefore, your final answer is correct.
Overall, your answers are mostly correct. Just double-check the factorization in question 3.