Answer :

To factor the expression [tex]\( x^3 - 7x^2 + 10x \)[/tex] completely, follow these steps:

1. Look for common factors:

Start by identifying any common factors in the terms of the expression. Here, each term contains a factor of [tex]\( x \)[/tex]. So, factor [tex]\( x \)[/tex] out of the expression:

[tex]\[
x(x^2 - 7x + 10)
\][/tex]

2. Factor the quadratic expression:

Now, focus on factoring the quadratic expression [tex]\( x^2 - 7x + 10 \)[/tex]. We need to find two numbers that multiply to 10 (the constant term) and add up to -7 (the coefficient of the middle term).

The numbers that satisfy these conditions are -5 and -2. Therefore, we can write:

[tex]\[
x^2 - 7x + 10 = (x - 5)(x - 2)
\][/tex]

3. Write the completely factored form:

Substituting the factored form of the quadratic expression back into the original expression, we get:

[tex]\[
x(x - 5)(x - 2)
\][/tex]

So, the expression [tex]\( x^3 - 7x^2 + 10x \)[/tex] is completely factored as [tex]\( x(x - 5)(x - 2) \)[/tex].

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Rewritten by : Barada