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Explain how to factor the following trinomials forms: x2 +

Resolved Question:

Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Explain how to factor the following trinomials forms: x^2 + bx + c and ax^2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

Solution: --------- There are different methods for factoring x^2 + bx + c and ax^2 + bx + c.

Factoring x^2 + bx + c: ----------------------

To factor x^2 + bx + c, find integers m, and n such that Then we can write it as

x^2 + bx + c = (x+m)(x+n) x^2 + bx + c = x^2 + (m+n)x + mn

So the sum of m and n should be equal to b and product of m and n should be equal to c.

Factoring ax^2 + bx + c: -----------------------

To factor ax^2 + bx + c, a ≠ 1, find integers k, l, m, and n such that

ax^2 + bx + c = (kx+m)(lx+n) ax^2 + bx + c = klx^2 + (kn + lm)x + mn

Therefore, k and l must be factors of a and m and n must be factors of c.

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