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If s(x) = x – 7 and t(x) = 4x2 – x + 3, which expression is equivalent to (t*s)(x)?

4(x – 7)2 – x – 7 + 3

4(x – 7)2 – (x – 7) + 3

(4x2 – x + 3) – 7

(4x2 – x + 3)(x – 7)

Respuesta :

The correct answer is 4(x-7)²-(x-7)+3.

Explanation:
When we find (t*s)(x), that is the same as t(s(x)). To evaluate this, we take the value of s(x), x-7, and substitute it in for every x in t(x). Instead of 4x², we have 4(x-7)²; instead of -x, we have -(x-7). This gives us 4(x-7)²-(x-7)+3.
SociometricStar

Answer:

[tex](4x^2-x+3)(x-7)[/tex]

D is the correct option.

Step-by-step explanation:

We have been given that

[tex]s(x)=x-7\text{ and }t(x)=4x^2-x+3[/tex]

We have to find [tex](t\cdot x)[/tex]

which means we have to find the product of these two expressions.

We can rewrite [tex](t\cdot x)[/tex] as [tex]t(x)s(x)[/tex]

Therefore, we have

[tex](t\cdot x)\\\\=t(x)s(x)=(4x^2-x+3)(x-7)[/tex]

Hence, the equivalent expression is

[tex](4x^2-x+3)(x-7)[/tex]

D is the correct option.

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