Factor as the product of two binomials. x^(2)+14 x+49=

Identify Structure: Identify the structure of the quadratic expression. The given expression is a quadratic in the form of x^2 + bx + c. We need to find two numbers that multiply to c (49) and add up to b (14).Find Numbers: Find two numbers that multiply to 49 and add up to 14. The numbers 7 and 7 satisfy both conditions: 7 * 7 = 49 and 7 + 7 = 14.Write Expression: Write the quadratic expression as the product of two binomials using the numbers found in Step 2. The expression can be factored as (x + 7)(x + 7) or (x + 7)^2.Verify Factored Form: Verify the factored form by expanding the binomials to ensure it equals the original expression. (x + 7)(x + 7) = x^2 + 7x + 7x + 49 = x^2 + 14x + 49 This matches the original expression, so the factoring is correct.

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Algebra 1

Factor quadratics: special cases

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Q. Factor as the product of two binomials.

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x^{2}+14x+49=

Identify Structure: Identify the structure of the quadratic expression. $\newline$ The given expression is a quadratic in the form of $x^2 + bx + c$ . We need to find two numbers that multiply to $c$ ( $49$ ) and add up to $b$ ( $14$ ).
Find Numbers: Find two numbers that multiply to $49$ and add up to $14$ . $\newline$ The numbers $7$ and $7$ satisfy both conditions: $7 \times 7 = 49$ and $7 + 7 = 14$ .
Write Expression: Write the quadratic expression as the product of two binomials using the numbers found in Step $2$ . $\newline$ The expression can be factored as $(x + 7)(x + 7)$ or $(x + 7)^2$ .
Verify Factored Form: Verify the factored form by expanding the binomials to ensure it equals the original expression. $\newline$ $(x + 7)(x + 7) = x^2 + 7x + 7x + 49 = x^2 + 14x + 49$ $\newline$ This matches the original expression, so the factoring is correct.