Exploring Adding and Subtracting Rational Expressions

What is the first step in the slide and divide method for factoring trinomials?

• Multiply the leading coefficient by the constant term

• Factor out the greatest common factor

• Divide the middle term by the leading coefficient

• Rewrite the trinomial in standard form

Which pair of numbers multiply to -30 and add to 10?

• 6 and -5

• 5 and -6

• 15 and -2

• 10 and -3

What is the factored form of r^2 - 11r - 42?

• (r - 14)(r + 3)

• (r + 14)(r - 3)

• (r - 7)(r + 6)

• (r + 7)(r - 6)

When factoring 2a^3 + 19a^2 + 34a, what is the first step?

• Factor out the greatest common factor

• Divide the middle term by the leading coefficient

• Multiply the leading coefficient by the constant term

• Rewrite the trinomial in standard form

What is the factored form of x^5 - 24x^3 - 25x?

• x(x^2 - 24)(x^2 + 1)

• x(x^2 - 25)(x^2 + 1)

• x(x^4 - 24x^2 - 25)

• x(x^2 - 5)(x^2 + 5)

What is the factored form of 8x^2 - 6x - 5?

• (4x + 5)(2x - 1)

• (2x - 5)(4x + 1)

• (4x - 5)(2x + 1)

• (2x + 5)(4x - 1)

What is the factored form of m^4 - 11m^2 + 24?

• (m^2 - 8)(m^2 - 3)

• (m^2 - 3)(m^2 - 8)

• (m^2 - 4)(m^2 - 6)

• (m^2 - 6)(m^2 - 4)

What is the first step in factoring by grouping?

• Rewrite the polynomial in standard form

• Group the first two and last two terms

• Factor out the greatest common factor

• Multiply the leading coefficient by the constant term

What is the factored form of k^3 + 5k^2 - k - 5?

• (k - 5)(k^2 + 1)

• (k + 5)(k^2 - 1)

• (k + 1)(k^2 - 5)

• (k + 5)(k - 1)

What is the factored form of 2g^4 - 3g^3 + 16g - 24?

• (2g - 3)(g + 2)(g^2 + 2g + 4)

• (2g - 3)(g + 2)(g^2 - 2g + 4)

• (2g - 3)(g^2 + 4)

• (2g - 3)(g^3 + 8)