QuestionFactor the given polynomial. $x^{2}-13 x+40$
Select the correct choice below and, if necessary, fill in the answer box within your choice. A. $x^{2}-13 x+40=$ $\square$

Studdy Solution

STEP 1

1. We are given a quadratic polynomial $x^2 - 13x + 40$ .
2. We need to factor this polynomial into the product of two binomials.
3. The polynomial is in the standard form $ax^2 + bx + c$ , where $a = 1$ , $b = -13$ , and $c = 40$ .

STEP 2

1. Identify two numbers that multiply to $c$ (the constant term) and add up to $b$ (the coefficient of $x$ ).
2. Write the polynomial as a product of two binomials using the identified numbers.

STEP 3

Identify two numbers that multiply to $40$ and add up to $-13$ .
- The numbers are $-5$ and $-8$ because: (-5) \times (-8) = 40 \] (-5) + (-8) = -13 \]

STEP 4

Write the polynomial as a product of two binomials using the numbers $-5$ and $-8$ .
- The factored form is: $ x^2 - 13x + 40 = (x - 5)(x - 8) \]
The correct choice is: A. $x^2 - 13x + 40 = (x - 5)(x - 8)$

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