c) \( 3 x^{2}-10 x+8 \) d) \( 2 a^{2}(3 a+2)-8 a^{4}(3 a+2) \) e) \( 27 x^{3}+8 y^{6} \)

Here’s how to factor each expression: c) Factor 3x² – 10x + 8 1. Multiply the coefficient of x² (3) by the constant (8): 3 × 8 = 24. 2. Find two numbers that multiply to 24 and add to –10. These numbers are –4 and –6. 3. Rewrite the middle term using –4x and –6x:   3x² – 4x – 6x + 8 4. Group terms:   (3x² – 4x) + (–6x + 8) 5. Factor each group:   x(3x – 4) – 2(3x – 4) 6. Factor out the common factor (3x – 4):   (3x – 4)(x – 2) So, c) factors as (3x – 4)(x – 2). d) Factor 2a²(3a + 2) – 8a⁴(3a + 2) 1. Notice that both terms share the common factor 2a²(3a + 2). 2. Factor it out:   2a²(3a + 2)[1 – 4a²] 3. Recognize that 1 – 4a² is a difference of squares:   1 – 4a² = (1 – 2a)(1 + 2a) Thus, d) factors completely as 2a²(3a + 2)(1 – 2a)(1 + 2a). e) Factor 27x³ + 8y⁶ 1. Write each term as a cube:   27x³ = (3x)³ and 8y⁶ = (2y²)³ 2. Use the sum of cubes formula:   a³ + b³ = (a + b)(a² – ab + b²)  with a = 3x and b = 2y². 3. Substitute into the formula:   (3x + 2y²)[(3x)² – (3x)(2y²) + (2y²)²] 4. Simplify inside the brackets:   (3x + 2y²)(9x² – 6xy² + 4y⁴) Thus, e) factors as (3x + 2y²)(9x² – 6xy² + 4y⁴). To summarize: c) (3x – 4)(x – 2) d) 2a²(3a + 2)(1 – 2a)(1 + 2a) e) (3x + 2y²)(9x² – 6xy² + 4y⁴)