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Sagot :
To determine which number is a zero of the function [tex]\( h(x) = (x^2 - 49)(x + 4) \)[/tex], we need to find the values of [tex]\( x \)[/tex] for which [tex]\( h(x) = 0 \)[/tex].
1. Factor the polynomial [tex]\( x^2 - 49 \)[/tex]:
[tex]\[ x^2 - 49 \text{ can be written as a difference of squares: } (x - 7)(x + 7) \][/tex]
Thus, the function [tex]\( h(x) \)[/tex] can be rewritten as:
[tex]\[ h(x) = (x - 7)(x + 7)(x + 4) \][/tex]
2. Set each factor equal to zero to find the zeros:
[tex]\[ (x - 7) = 0 \][/tex]
Solving this equation:
[tex]\[ x = 7 \][/tex]
[tex]\[ (x + 7) = 0 \][/tex]
Solving this equation:
[tex]\[ x = -7 \][/tex]
[tex]\[ (x + 4) = 0 \][/tex]
Solving this equation:
[tex]\[ x = -4 \][/tex]
3. Identify the zeros:
The zeros of [tex]\( h(x) = (x - 7)(x + 7)(x + 4) \)[/tex] are [tex]\( x = 7 \)[/tex], [tex]\( x = -7 \)[/tex], and [tex]\( x = -4 \)[/tex].
4. Choose the correct answer from the provided options:
Among the options given:
- A. [tex]\( 0 \)[/tex] is not a zero
- B. [tex]\( 4 \)[/tex] is not a zero
- C. [tex]\( 7 \)[/tex] is a zero
- D. [tex]\( 49 \)[/tex] is not a zero
Therefore, the correct answer is:
[tex]\[ \boxed{7} \][/tex]
1. Factor the polynomial [tex]\( x^2 - 49 \)[/tex]:
[tex]\[ x^2 - 49 \text{ can be written as a difference of squares: } (x - 7)(x + 7) \][/tex]
Thus, the function [tex]\( h(x) \)[/tex] can be rewritten as:
[tex]\[ h(x) = (x - 7)(x + 7)(x + 4) \][/tex]
2. Set each factor equal to zero to find the zeros:
[tex]\[ (x - 7) = 0 \][/tex]
Solving this equation:
[tex]\[ x = 7 \][/tex]
[tex]\[ (x + 7) = 0 \][/tex]
Solving this equation:
[tex]\[ x = -7 \][/tex]
[tex]\[ (x + 4) = 0 \][/tex]
Solving this equation:
[tex]\[ x = -4 \][/tex]
3. Identify the zeros:
The zeros of [tex]\( h(x) = (x - 7)(x + 7)(x + 4) \)[/tex] are [tex]\( x = 7 \)[/tex], [tex]\( x = -7 \)[/tex], and [tex]\( x = -4 \)[/tex].
4. Choose the correct answer from the provided options:
Among the options given:
- A. [tex]\( 0 \)[/tex] is not a zero
- B. [tex]\( 4 \)[/tex] is not a zero
- C. [tex]\( 7 \)[/tex] is a zero
- D. [tex]\( 49 \)[/tex] is not a zero
Therefore, the correct answer is:
[tex]\[ \boxed{7} \][/tex]
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