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# Factorization of Polynomials.

I sent my problems via attachment word document. Please read the instructions and fill out all problems that show any extension of work. please.

1.Factor completely. If the polynomial is prime, state this.
75x2 - 3

2. Factor completely. If the polynomial is prime, state this.
48x2 + 40xy - 48y2
3. Solve using the principle of zero products.
(2x + ½)(4x - 1/7) = 0
4. Multiply. Assume that all variables represent nonnegative real numbers.

( - )2
5. Divide and, if possible, simplify. Assume all variables represent positive real numbers.

6 Divide and, if possible, simplify. Assume all variables represent positive real numbers.

7. Multiply.

8. Divide.

9. solve the problem.

A rancher in Calgary decides to build a silo inside his corral. The rectangular corral measures 22 m by 11 m and the silo's base is circular with a diameter of x meters. Find a polynomial for the remaining area of the corral (in square meters) after the silo is built.
10. Factor completely. If the polynomial is prime, state this.

4a3 + 12a2 - 72a
11. Factor completely. If the polynomial is prime, state this.

y2 - y +
12. Factor completely. If the polynomial is prime, state this.

5n + 5w - n2 - nw
13. Solve by factoring and using the principle of zero products.

b2 + 11b = 0
14. Solve the problem.

The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.

#### Solution Preview

Please see the attachment.

1.Factor completely. If the polynomial is prime, state this.
75x2 - 3
75x2 - 3 = 3(25x2 - 1) = 3(5x + 1)(5x - 1) (Since a2 - b2 = (a + b)(a - b)
2. Factor completely. If the polynomial is prime, state this.
48x2 + 40xy - 48y2
48x2 + 40xy - 48y2 = 8(6x2 + 5xy - 6y2) and the given polynomial is prime.
3. Solve using the principle of zero products.
(2x + ½)(4x - 1/7) = 0