#1
Which of the following is a quadratic trinomial?
2x^2 - 5x + 3
ExplanationQuadratic trinomials have three terms, with the highest degree term having an exponent of 2.
#2
What is the first step in factoring a quadratic trinomial?
Factor out the greatest common factor
ExplanationFactoring out the greatest common factor is the initial step to simplify and factor quadratic trinomials.
#3
What is the factored form of the quadratic trinomial: 6x^2 - 11x + 4?
(2x - 1)(3x - 4)
ExplanationThe factored form is obtained by finding two binomials whose product equals the original trinomial.
#4
Which method is used to factor a quadratic trinomial with a leading coefficient other than 1?
AC method
ExplanationThe AC method involves splitting the middle term to factor trinomials with a leading coefficient not equal to 1.
#5
Which method can be used to check the correctness of factoring a quadratic trinomial?
Multiplying the factors
ExplanationMultiplying the factored form should result in the original quadratic trinomial, providing a check for correctness.
#6
What is the factored form of the quadratic trinomial: x^2 + 7x + 12?
(x + 3)(x - 4)
ExplanationThe factored form consists of two binomials whose product equals the given quadratic trinomial.
#7
What is the factored form of the quadratic trinomial: 4x^2 - 12x + 9?
(2x - 3)^2
ExplanationThis trinomial is a perfect square trinomial, and its factored form is the square of a binomial.
#8
Which property is used in factoring the quadratic trinomial: x^2 - 6x + 9?
Perfect square trinomial
ExplanationThis trinomial is a perfect square, and factoring involves recognizing it as (a - b)^2.
#9
What is the factored form of the quadratic trinomial: 2x^2 - 9x - 5?
(2x + 1)(x - 5)
ExplanationFactoring involves finding two binomials whose product is equal to the given quadratic trinomial.
#10
Which of the following is a special case of factoring quadratic trinomials?
Perfect square trinomials
ExplanationPerfect square trinomials have a special factored form: (a ± b)^2.
#11
What is the factored form of the quadratic trinomial: 3x^2 + 10x + 8?
(3x + 2)(x + 4)
ExplanationFactoring involves finding two binomials whose product equals the given quadratic trinomial.
#12
Which technique is used to factor a quadratic trinomial with a leading coefficient greater than 1?
AC method
ExplanationThe AC method is employed for factoring trinomials with a leading coefficient greater than 1.
#13
What is the factored form of the quadratic trinomial: 2x^2 - 8x + 6?
2(x - 1)(x - 3)
ExplanationFactoring involves finding two binomials whose product equals the given quadratic trinomial.
#14
Which method is typically used to factor quadratic trinomials with leading coefficients greater than 1 and not easily factorable?
Quadratic formula
ExplanationThe quadratic formula is used for factoring when other methods are impractical.