Asked by Bobby Gallimore on May 15, 2024
Verified
Factor the trinomial, if possible. 12x2−8x−1512 x ^ { 2 } - 8 x - 1512x2−8x−15
A) (2x−3) (6x−5) ( 2 x - 3 ) ( 6 x - 5 ) (2x−3) (6x−5)
B) (2x+3) (6x+5) ( 2 x + 3 ) ( 6 x + 5 ) (2x+3) (6x+5)
C) (2x−3) (6x+5) ( 2 x - 3 ) ( 6 x + 5 ) (2x−3) (6x+5)
D) (3x+2) (5x−6) ( 3 x + 2 ) ( 5 x - 6 ) (3x+2) (5x−6)
E) The trinomial is prime.
Factor
A number or expression that divides another number or expression evenly, with no remainder.
- Determine whether a polynomial can be factored and identify prime polynomials.
Verified Answer
MS
Muhammad SaeedMay 16, 2024
Final Answer :
C
Explanation :
To find the factors, first multiply the coefficient of the leading term (12) by the constant term (-15) to get -180. Next, find two factors of -180 that add up to the coefficient of the middle term (-8). It turns out that these factors are -15 and 12. Then, split the middle term -8x into -15x + 12x, so the trinomial becomes: 12x2−15x+12x−15=3x(4x−5)+3(4x−5)=(4x−5)(3x+3)=(2x−3)(6x+5)12x^2 - 15x + 12x - 15 = 3x(4x-5) + 3(4x-5) = (4x-5)(3x+3)=(2x-3)(6x+5)12x2−15x+12x−15=3x(4x−5)+3(4x−5)=(4x−5)(3x+3)=(2x−3)(6x+5) Therefore, the correct answer is C.
Learning Objectives
- Determine whether a polynomial can be factored and identify prime polynomials.