Completely factor the polynomial or state that the polynomial is prime.

w squared minus 59 w plus 408w2−59w+408 

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Part 1

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

w squared minus 59 w plus 408w2−59w+408equals=enter your response here

​(Factor completely.)

B.

Let's begin by factoring the given quadratic expression:

\[
w^2 - 59w + 408
\]

We will attempt to factor this by finding two numbers that multiply to give 408 (the constant term) and add up to -59 (the coefficient of the linear term).

1. The product we need is \( 408 \), and the sum we need is \( -59 \).
2. Let's find factors of 408 that could sum to -59.

Factors of 408 include:
\[
1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
\]

We can try different factor pairs to see if any add up to -59.

The correct pair is \( -51 \) and \( -8 \) because:
\[
(-51) \times (-8) = 408
\]
\[
(-51) + (-8) = -59
\]

Thus, the factorization is:
\[
w^2 - 59w + 408 = (w - 51)(w - 8)
\]

So, the polynomial can be factored as:

\[
(w - 51)(w - 8)
\]

### Final Answer:
\[
A. \ (w - 51)(w - 8)
\]

Would you like more details on the factorization process or have any other questions?

Here are 5 related questions for practice:
1. How would you factor \( x^2 - 40x + 375 \)?
2. Can you factor \( z^2 - 25z + 150 \)?
3. What are the factors of \( y^2 - 16y + 63 \)?
4. How do you solve \( x^2 - 12x + 36 = 0 \)?
5. Can you find the solutions of \( m^2 - 7m + 10 = 0 \)?

**Tip:** Always check your factorization by expanding it back to ensure it matches the original polynomial.

Completely factor the polynomial or state that the polynomial is prime.

w^2 - 59w + 408

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Learn how to factor the quadratic polynomial w^2 - 59w + 408 with a step-by-step solution. This guide covers essential algebraic techniques, including factoring quadratics and applying the zero product property. Suitable for students in Grades 8-10.

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