So what does this have to do with factoring? 8. For what value of the variable q

Question

So what does this have to do with factoring? 8. For what value of the variable quantity x does the expression x4 have output zero? What about the expression x+5? (Don't over-think these. They're really easy.) 9. Now look at the product (x-4Xx+5), which is a polynomial in factored form. Find the value of the product when... d. x=-1 Conclusion: 10. The only way a product of algebraic expressions can have value zero is if And THAT'S why factoring is a big deal in algebra. It provides an important technique of solving equations that have zero on one side. I1. Write the number 37 as a product 12. Write the polynomial expression 3x+5 as a product In Questions 11 and 12, there's only one way to write the given number or expression as a product (unless you're willing to use fractions, which we are not at the moment): one times the product or expression itself. In the case of 37, we call it a prime number. For the polynomial 3x + 5, we say that it is a prime polynomial. The point: Not every expression can be factored if we restrict our attention to integer coefficients

Explanation / Answer

8. x - 4 = 0

=> x = 4.

x + 5 = 0

=> x = -5.

9. a. x = 2

(x - 4) (x + 5)

= (2 - 4) * (2 + 5)

= -2 * 7

= -14.

b. x = 4

(x - 4) (x + 5)

= (4 - 4) * (4 + 5)

= 0 * 9

= 0.

c. x = 0

(x - 4) (x + 5)

= (0 - 4) * (0 + 5)

= -4 * 5

= -20.

d. x = -1

(x - 4) (x + 5)

= (-1 - 4) * (-1 + 5)

= -5 * 4

= -20.

d. x = -5

(x - 4) (x + 5)

= (-5 - 4) * (-5 + 5)

= -9 * 0

= 0.

10. The only way a product of algebraic expressions can have a value zero is if atleast one of the expressions evaluate to zero.

11. 37 = 37 * 1.

12. 3x + 5 = (3x + 5) * 1

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