Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, or factors, that when multiplied together give the original expression.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, typically expressed as a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression.

Front

What are the factors of 5m^2 - 45m + 90?

Back

5(m - 3)(m - 6) is the factorization of the polynomial.

Front

How do you factor a polynomial of the form ax^2 + bx + c?

Back

To factor a polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

Front

What is the factored form of 12x - 20?

Back

4(3x - 5) is the factored form of the polynomial.

Front

What is the factored form of 3x^2 - 17x + 10?

Back

(x - 5)(3x - 2) is the factored form of the polynomial.

Front

What are the factors of x^2 - 8x - 48?

Back

(x - 12)(x + 4) are the factors of the polynomial.

Front

What is the factored form of 6x^2 - 11x + 3?

Back

(3x - 1)(2x - 3) is the factored form of the polynomial.