Factor completely. 7x^(2)+35 x+42=

Identify Form: Identify the form of the quadratic trinomial. The given expression 7x^2 + 35x + 42 is a quadratic trinomial in the form ax^2 + bx + c.Find Common Factors: Look for common factors in all three terms. The coefficients 7, 35, and 42 all have a common factor of 7.Factor Out GCF: Factor out the greatest common factor (GCF) from the expression. The GCF of 7x^2, 35x, and 42 is 7. Factoring out 7 gives us 7(x^2 + 5x + 6).Factor Quadratic Expression: Factor the quadratic expression inside the parentheses. The quadratic x^2 + 5x + 6 can be factored into (x + 2)(x + 3), since 2 and 3 are the numbers that multiply to 6 and add up to 5.Write Final Factored Form: Write the final factored form of the original expression. Combining the GCF with the factored quadratic, we get 7(x + 2)(x + 3).

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Q. Factor completely.

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7x^{2}+35x+42=

Identify Form: Identify the form of the quadratic trinomial. $\newline$ The given expression $7x^2 + 35x + 42$ is a quadratic trinomial in the form $ax^2 + bx + c$ .
Find Common Factors: Look for common factors in all three terms. $\newline$ The coefficients $7$ , $35$ , and $42$ all have a common factor of $7$ .
Factor Out GCF: Factor out the greatest common factor (GCF) from the expression. $\newline$ The GCF of $7x^2$ , $35x$ , and $42$ is $7$ . Factoring out $7$ gives us $7(x^2 + 5x + 6)$ .
Factor Quadratic Expression: Factor the quadratic expression inside the parentheses. $\newline$ The quadratic $x^2 + 5x + 6$ can be factored into $(x + 2)(x + 3)$ , since $2$ and $3$ are the numbers that multiply to $6$ and add up to $5$ .
Write Final Factored Form: Write the final factored form of the original expression. $\newline$ Combining the GCF with the factored quadratic, we get $7(x + 2)(x + 3)$ .