Factoring expression into a product of binomials

Question

Assignment:

Q1. Factor out the greatest common factor from the expression

-3xyz² + 6xz² - 15xyz²

• -3xz²(y + 2 + 5y)
•   3xz(-yz + 2z - 5yz)
•   3xz²(-y + 2 - 5y)
• -3xz(yz + 2z + 5yz)

Q2. Factor out the greatest common factor from the expression

9x⁴y⁴ + 7x⁶y³ - 12x⁴y³

Q3. Megan factored the expression 12x²+13x -14 as (3x +2)(4x -7).  But when Jacob applied the FOIL principle and multiplied out (3x +2)(4x -7), he got

12x² - 13x -14; thus, Megan's solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state.

Q4. Use the "difference of squares" rule to factor the following expression:

16x⁴ -121y⁴

Q5. Factor the following expression into a product of two binomials:

64x² - 64x +16

• (8x - 4)(8x + 4)
• (8x - 16)(8x - 1)
• (8x - 4)(8x - 4)
• x(64x - 16)

Q6. Factor the following expression into a product of binomials:
16a² - 40ab + 25b²

Q7. Factor the following expression into a product of binomials:

16y² - 25z²

Q8. The length of a rectangle is 5 meters more than its width. If the area is 66 square meters, what are the length and width?

Q9. A 200-ft diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 40 ft longer that the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by this brace.

Q10. Completely factor the expression

216x² - 384y²

Q11. Completely factor the expression
245x³ - 840x²y + 180xy²

Provide complete and step by step solution for the question and show calculations and use formulas.