Factoring a>1

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What is the process of factoring a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of two binomials. This is typically done by finding two numbers that multiply to the constant term and add to the coefficient of the linear term.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you factor the expression 5v² − 30v + 40?

Back

To factor 5v² − 30v + 40, first factor out the greatest common factor (GCF), which is 5. This gives 5(v² - 6v + 8). Then, factor the quadratic to get 5(v - 2)(v - 4).

Front

What is the significance of the discriminant in factoring quadratics?

Back

The discriminant, given by b² - 4ac, determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are no real roots.

Front

What is the factored form of the quadratic 6x² + 7x - 3?

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The factored form of 6x² + 7x - 3 is (2x + 3)(3x - 1).

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How do you factor the expression 2x² - 3x - 2?

Back

To factor 2x² - 3x - 2, look for two numbers that multiply to (2 * -2) = -4 and add to -3. The factors are -4 and 1. Rewrite the expression as 2x² - 4x + x - 2, then factor by grouping to get (2x + 1)(x - 2).

Front

What is the method of grouping in factoring?

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The method of grouping involves rearranging and grouping terms in a polynomial to factor it. This is often used when dealing with four-term polynomials.

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What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as x + 5 or 3y - 2.

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What is the difference between factoring and expanding?

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Factoring is the process of breaking down an expression into its component factors, while expanding is the process of multiplying out the factors to obtain the original expression.

Front

How do you factor the expression 2m² + 3m - 9?

Back

To factor 2m² + 3m - 9, find two numbers that multiply to (2 * -9) = -18 and add to 3. The factors are 6 and -3. Rewrite the expression as 2m² + 6m - 3m - 9, then factor by grouping to get (m + 3)(2m - 3).