Factoring Trinomials

Front

What does GCF stand for in factoring trinomials?

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GCF stands for Greatest Common Factor, which is the largest factor that divides all terms in a polynomial.

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How do you find the GCF of the terms in a trinomial?

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To find the GCF, identify the highest common factor of the coefficients and the common variable factors in each term.

Front

What is the first step in factoring a trinomial?

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The first step is to look for the GCF of all the terms and factor it out.

Front

What is a trinomial?

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A trinomial is a polynomial with three terms, typically in the form ax² + bx + c.

Front

How do you factor a trinomial in the form ax² + bx + c?

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To factor a trinomial, find two numbers that multiply to ac (the product of a and c) and add to b.

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What is the factored form of a trinomial?

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The factored form of a trinomial is expressed as (px + q)(rx + s), where p, q, r, and s are constants.

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What is the significance of the leading coefficient in factoring trinomials?

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The leading coefficient (a) affects the method used to factor the trinomial, especially when a is not equal to 1.

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What is the difference between factoring by grouping and factoring trinomials?

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Factoring by grouping involves rearranging terms and grouping them to find common factors, while factoring trinomials focuses on finding two binomials that multiply to the trinomial.

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What is the role of the discriminant in factoring quadratics?

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The discriminant (b² - 4ac) determines the nature of the roots of the quadratic equation; if it's positive, there are two distinct real roots.

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How can you check if your factored form is correct?

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You can check by multiplying the factors back together to see if you obtain the original trinomial.