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2.6 Factor x2 + bx + c

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Facts Use the following information to factor trinomials of the form x2 + bx + c: x2 + bx + c = (x + p)(x + q) p + q = b pq = c You can FOIL your answer to check your work!

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Example 1: Factor x2 + 10x + 24 Find two positive factors of 24 whose sum is 10.

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Example 2: Factor w2 – 10w + 9 Because b is negative and c is positive, p and q must be negative.

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Example 3: Factor k2 + 6k – 7 Because c is negative, p and q must have different signs.

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**You Try: Factor the trinomial: y2 + 6y + 5 Answer: (y + 5)(y + 1)**

z2 – 7z + 12 Answer: (z – 3)(z – 4) y2 + 2y – 63 Answer: (y – 7)(y + 9)

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**Example 4: Solve the equation h2 – 4h = 21 Solution:**

Write the original equation: h2 – 4h = 21 Subtract 21 from each side: h2 – 4h – 21 = 0 Factor the left side: (h + 3)(h – 7) = 0 Zero-Product Property: h + 3 = 0 OR h – 7 = 0 Solve for h: h = -3 OR h = 7

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You Try: Solve the equation x = 11x

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Homework: P. 83 # 1 – 27odd

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