Algebra 2 Questions?

1.
4a³ + 4a² - 48a
= 4a(a² + a - 12)
= 4a(a + 4)(a - 3)

The answer: C. 4a(a + 4)(a - 3)


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2.
(3p + 2)(5p - 7)
= 3p(5p - 7) + 2(5p - 7)
= 15p² - 21p + 10p - 14
= 15p² - 11p - 14

The answer: D. 15p² - 11p - 14


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3.
[(w² - 11w - 12) / (w² - 1)] ÷ [(w² + 13w + 12) / (w² - 13w + 12)]
= [(w - 12)(w + 1) / (w + 1)(w - 1)] ÷ [(w + 12)(w + 1) / (w - 12)(w - 1)]
= [(w - 12) / (w - 1)] ÷ [(w + 12)(w + 1) / (w - 12)(w - 1)]
= [(w - 12) / (w - 1)] × [(w - 12)(w - 1) / (w + 12)(w + 1)]
= (w - 12)²(w - 1) / (w + 12)(w + 1)(w - 1)
= (w - 12)² / (w + 1)(w + 12)

The answer: C. (w - 12)² / (w + 1)(w + 12)


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4.
f(x) = (x + 5) / (2x + 3)

The denominator should not be zero. Otherwise, the expression is undefined (meaningless).
2x + 3 ≠ 0
2x ≠ -3
x ≠ -3/2

The answer: D. all real numbers except -3/2


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5.
5 / √2
= (5√2) / (√2)(√2)
= (5√2) / 2

The answer: B. (5√2) / 2


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6.
(⁵√m)^11
= [m^(1/5)]^11
= m^(11/5)

The answer: A. m^(11/5)

1) Factor out 4a first.

4a^3 + 4a^2 - 48

4a(a^2 + a - 12)

4a(a - 3)(a + 4). C).
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2) Use the FOIL method: first, outermost, innermost, last.

(3p + 2)(5p - 7) = (3p * 5p) + (3p * -7) + (2 * 5p) + (2 * -7) = 15p^2 - 21p + 10p - 14...

= 15p^2 - 11p - 14. D).
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3) I suggest using parentheses to avoid anything getting misconstrued. Factor each numerator and denominator.

(w^2 - 11w - 12) / (w^2 - 1) = [(w + 1)(w - 12)] / [(w + 1)(w - 1)]. You can cancel out (w + 1) here; you're left with (w - 12) / (w - 1).

(w^2 + 13w + 12) / (w^2 - 13w + 12) = [(w + 1)(w + 12)] / [(w - 1)(w - 12)]. Since this fraction is a divisor, flip this and multiply.

[(w - 12) / (w - 1)] * [(w - 1)(w - 12) / (w + 1)(w + 12)]

Now, (w - 1) can be canceled out, and:

(w - 12) * [(w - 12) / (w + 1)(w + 12)]

= (w - 12)^2 / (w + 1)(w + 12). C).
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4) I'd assume that is (x + 5) / (2x + 3). Just set the numerator to 0 and solve for x. Whatever x value you get is excluded from the domain. The x-value that would be excluded here is -3/2, so the answer is D).
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5) Rationalize the denominator by multiplying each part by sqrt(2) / sqrt(2).

5 / sqrt(2)

5(sqrt(2)) * (sqrt(2))^2

5 sqrt(2) / 2. B).
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6) I assume by ^5 sqrt(m) you actually mean 5th root(m).

The 5th root of a number is the same thing as raising that number to the 1/5 power. With that known, use the rule of power of a power and multiply the exponents.

(m^(1/5))^11 = m^(1/5 * 11) = m^(11/5). A).

All done. Good luck! ????

1.
Which factored form is equivalent to 4a³ + 4a² - 48a?
A. 4a(a + 4)(a + 3)
B. 4a(a - 4)(a - 3)
C. 4a(a + 4)(a - 3)
D. 4a(a - 4)(a + 3)
2.
Which simplified form is equivalent to (3p + 2)(5p - 7)?
A. 15p² + 31p - 14
B. 15p² + 11p - 14
C. 15p² - 31p - 14
D. 15p² - 11p - 14
3.
What is the quotient of w² - 11w - 12/w² - 1 ÷ w² + 13w + 12/w² - 13w + 12 in lowest terms?
A. (w + 1)(w + 12)/(w - 1)²
B. w - 12/w - 1
C. (w - 12)²/(w + 1)(w + 12)
D. w - 12/w + 1
4.
What is the domain of the function f(x) = x + 5/2x + 3?
A. all real numbers except -5
B. all real numbers except 3/2
C. all real numbers except 5
D. all real numbers except -3/2
5.
Which expression is the simplest form of 5/√2?
B. 5√2/2
6.
Which expression is equivalent to (^5√m)¹¹ in exponential form?
A. m^11/5

You need only determine the constant. If more than one is zero check the coefficient of a³

4a³ + 4a² - 48a = 4a(a² + a - 12)
= 4a(a-3)(a+4)