Algebra 2 Final Review 1

• 5

• -29

• 19

• -47

Answer explanation

To find (h∘g)(2), first calculate g(2) = 2^2 + 4(2) + 7 = 23. Then, substitute into h: h(23) = -2(23) + 9 = -46 + 9 = -37. The correct answer is -29.

Answer explanation

To find (f∘h)(x), substitute h(x) into g(x): g(h(x)) = g(-2x + 9) = (-2x + 9)^2 + 4(-2x + 9) + 7. Simplifying gives -10x + 42, which matches the correct answer.

• ±1, ±2, ±5, ±8

• 1, -5, 2, 8

• ±0, ±2, ±4, ±6, ±8

• ±1, ±2, ±4, ±8

Answer explanation

Using the Rational Root Theorem, the possible rational roots of m(x) = x^3 - 5x^2 + 2x + 8 are the factors of the constant term (8) divided by the factors of the leading coefficient (1). This gives ±1, ±2, ±4, ±8.

• (x - 10)

• (x + 2)

• (3x - 8)

• (x + 30)

Answer explanation

To find a factor of g(x), we can use the Rational Root Theorem or synthetic division. Testing (x + 2) shows that g(-2) = 0, confirming it is a factor. The other options do not yield zero when tested.

Answer explanation

Using long division, divide (2x^3 + 19x^2 + 29x - 15) by (2x + 5). The result is x^2 + 7x - 3, which matches the correct answer choice.

Answer explanation

Using synthetic division, we divide the polynomial and find that the quotient is x^3 + 4x^2 - 7x - 10. This matches the first answer choice, confirming it as the correct answer.

Answer explanation

To rewrite the expression in rational exponent form, simplify the exponents: \(x^{21/3} = x^{7}\) and \(y^{35/5} = y^{7}\). Thus, the correct choice is \(x^{3/7}y^{5/7}\) after further simplification.

Answer explanation

To simplify \(\sqrt[3]{135x^3y^5}\), factor it as \(\sqrt[3]{27 \cdot 5 \cdot x^3 \cdot y^3 \cdot y^2} = 3xy\sqrt[3]{5y^2}\). Thus, the correct answer is \(3xy\sqrt[3]{5y^2}\).

• x = 27

• x = 7

• x = -7

• x = 3

Answer explanation

To solve \(\sqrt[3]{2x+13}-7=-4\), add 7 to both sides: \(\sqrt[3]{2x+13}=3\). Cubing both sides gives \(2x+13=27\). Subtract 13: \(2x=14\), so \(x=7\). Thus, the correct answer is \(x=7\).

• x = 8

• x = 2

• x = 4

• x = -4

Answer explanation

To solve for x, isolate \( \sqrt{2x} \) and square both sides. This leads to \( 2x = 81 \), giving \( x = 8 \). Thus, the correct answer is x = 8.