Factoring Polynomials: Key Concepts and Techniques

What is the product of the lead coefficient and the constant term in the trinomial?

• -7

• 7

• 18

• -18

Which two numbers multiply to -18 and add up to 7?

• -9 and -2

• -9 and 2

• 9 and 2

• 9 and -2

What is the result of factoring by grouping the terms 9x and -2x?

• (3x-2)(x-3)

• (3x+2)(x+3)

• (3x-2)(x+3)

• (3x+2)(x-3)

What common factor is pulled out from the first group in the factor by grouping method?

• x

• -2

• 2x

• 3x

What should you always factor out first when the lead coefficient is negative?

• The constant term

• The lead coefficient

• -1

• 1

After factoring out -1, what is the new form of the trinomial 9x^2 - 15x + 5?

• 9x^2 + 15x - 5

• 9x^2 - 15x + 5

• -9x^2 + 15x - 5

• -9x^2 - 15x + 5

Which two numbers multiply to 36 and add up to -15?

• 6 and 6

• 12 and 3

• -6 and -6

• -12 and -3

What is the final factored form of the trinomial with a negative lead coefficient?

• -(3x-4)(3x-1)

• -1(3x-4)(3x-1)

• -1(3x+4)(3x+1)

• -(3x+4)(3x+1)

What common factor is pulled from the groups in the final example?

• 3x

• x

• -1

• 3

Why is it crucial to factor out the negative in a trinomial with a negative lead coefficient?

• To make it a positive trinomial

• To change the signs of the terms

• To avoid calculation errors

• To simplify the trinomial