If , and , what is the value of ?
(a) 0
(b) 6
(c) 6
(d) 8
(e) –8
Correct Answer is Option (d)
The numerator on the left can be factored so the expression becomes which can be simplified to (x  3) = 5.
Then you can solve for x by adding 3 to both sides of the equation, so x = 8
Correct Answer is Option (d)
You need to find two numbers that multiply to give 72 and add up to give 18
easiest way: write the multiples of 72:
1, 72
2, 36
3, 24
4, 18
6, 12: these add up to 18
(x + 6)(x + 12)
Correct Answer is Option (e)
Nothing common cancels at the beginning. To factor this, we need to find two numbers that multiply to 9 x 4 = 36 and sum to 12. 6 and 6 work.
So 9x^{2} + 12x + 4 = 9x^{2} + 6x + 6x + 4
Let's look at the first two terms and last two terms separately to begin with. 9x^{2} + 6x can be simplified to 3x(3x + 2) and 6x + 4 can be simplified into 2(3x + 2). Putting these together gets us
9x^{2} + 12x + 4
= 9x^{2} + 6x + 6x + 4
= 3x(3x + 2) + 2(3x + 2)
= (3x + 2)(3x + 2)
This is as far as we can factor.
Correct Answer is Option (b)
We can first factor out −3:
−3(4x^{2}  9)
This factors further because there is a difference of squares:
−3(2x + 3)(2x − 3)
Correct Answer is Option (d)
Group all the terms with the x variable.
x^{3} + 2x^{2} + a + bx^{2} + 2 = (x^{3} + 2x^{2} + bx^{2}) + a + 2
Pull out an x^{2} term from parentheses.
(x^{3} + 2x^{2} + bx^{2}) + a + 2 = x^{2}(x + 2 + b) + a + 2
There are no more common factors.
The correct answer is: x^{2}(x + 2 + b) + a + 2
Factor and simplify:
(a) 8y − 12
(b) −4
(c) 8y
(d) 8y − 4
(e) 8y + 4
Correct Answer is Option (d)
64y^{2} − 16 is a difference of squares.
The difference of squares formula is a^{2} − b^{2} = (a − b)(a + b).
Therefore,
= 8y − 4
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