Factoring Polynomials when a > 1

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

Front

What does it mean when a polynomial is in the form ax^2 + bx + c?

Back

This is the standard form of a quadratic polynomial, where 'a', 'b', and 'c' are constants, and 'a' is not equal to zero.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree. It affects the direction of the parabola when graphed.

Front

How do you factor a polynomial when a > 1?

Back

To factor a polynomial where the leading coefficient 'a' is greater than 1, look for two numbers that multiply to 'a*c' and add to 'b', then use these to split the middle term.

Front

What is the first step in factoring the polynomial 5k^2 - 18k + 9?

Back

Identify the leading coefficient (5), the middle coefficient (-18), and the constant term (9). Then find two numbers that multiply to 5*9=45 and add to -18.

Front

What are the factors of the polynomial 3v^2 - 4v - 7?

Back

The factors are (3v - 7)(v + 1).

Front

How do you check if your factors are correct?

Back

Multiply the factors back together to see if you obtain the original polynomial.

Front

What is the role of the quadratic formula in factoring?

Back

The quadratic formula can be used to find the roots of a polynomial, which can help in factoring it.

Front

What is the difference between factoring and expanding?

Back

Factoring is breaking down an expression into products, while expanding is multiplying out the factors to get the original expression.