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Answered

1. If we are told that (x+4)(x+7)=0, then what can we infer?
By zero product property we know: __ = 0 OR __ = 0
And therefore we know that X=__ OR X= ___

2. If we are told that (3x-7)(2x+5)=0 then what can we infer?
By zero product property we know: __ = 0 OR __ = 0
And therefore we know that X=__ OR X= ___

3.We want to solve the equation x^2-3x-40=0
First factor x^2-3x-40: ___
By zero product property we know: __ = 0 OR __ = 0
And therefore we know that X=__ OR X= ___

4.We want to solve the equation 3x^2-11x-42=0
First factor 3x^2-11x-42: ___
By zero product property we know: __ = 0 OR __ = 0
And therefore we know that X=__ OR X= ___

5.We want to solve the equation 10x^2+9x+2=0
First factor 10x^2+9x+2
By zero product property we know: __ = 0 OR __ = 0
And therefore we know that X=__ OR X= ___

Answer :

1. x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2. 3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. (x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

How to determine the values

1. (x+4)(x+7)=0

We have that;

Zero product property;

x + 4 = 0 or x + 7 = 0

x = -4 or x = -7

2.  (3x-7)(2x+5)=0

We have that;

Zero product property ;

3x - 7 = 0 or 2x + 5 = 0

x = 7/ 3 or x = -5/ 2

3. x² -3x - 40=0

x² -8x + 5x - 40 = 0

factorize the common multipliers

x(x - 8) + 5(x - 8) = 0

Zero product property;

x + 5 = 0 or x -8 = 0

x = -5 or x = 8

4. 3x² - 11x - 42=0

3x² +7x - 18x - 42 = 0

Factorize further

x(3x + 7) - 6(3x + 7) = 0

Zero product property;

(x - 6) = 0 or (3x + 7) = 0

x = 6 or x = -7/ 3

5. 10x² + 9x + 2 = 0

10x² + 5x + 4x + 2 = 0

Factorize

5x( 2x + 1) + 2 (2x + 1) = 0

Zero product property;

5x + 2 = 0 or 2x + 1 = 0

x = -2/ 5 or x = -1/ 2

Thus, the zero product property states that the product of two non-zero elements is not zero

Learn more about zero product property here:

https://brainly.com/question/1626209

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