i need some homework help with factoring having with to do algebra they include
x^2-5x-54=0
x^2-3x-4=6
5x^2+16x+3=0
7x^2+37x+10-0
3x^2+5x-2=0
i need some homework help with factoring having with to do algebra they include
x^2-5x-54=0
x^2-3x-4=6
5x^2+16x+3=0
7x^2+37x+10-0
3x^2+5x-2=0
It's hard, some times, to see the rational roots of the quadratic polynomial, especially if roots are irrational or complex numbers. There are formulas which can help to factorize trinomials.
ax^{2} + bx + c = a(x - x_{1})(x - x_{2}) ; were x_{1,2} = (-b ± √D)/2a
are roots of the equation
ax^{2} + bx + c = 0 and D = b^{2} - 4ac
~~~~~~~~~~
1. x^{2} - 5x - 54 = 0 does not have rational roots.
2. x^{2} - 3x - 4 = 6 ----> x^{2} - 3x
- 10 = 0 ---> (-10) = (-5) · 2 ; (- 3) = -5+2
(x - 5)(x + 2) = 0 ---> x_{1} = 5 , x_{2} = -2
3. 5x^{2} + 16x +3 = 0 ; D = 16^{2} - 4 · 5 · 3 = 256 - 60 = 196;
x_{1,2} = (-16 ± √196)/(2 · 5) = (-16 ± 14)/10 ;
x_{1} = -2/10 = -1/5
x_{2} = -30/10 = -3
5(x + 1/5)(x + 3) = (5x +1)(x + 3) = 0
4. 7x^{2} + 37 + 10 = 0 ; D = 37^{2} - 4*7*10 = 1369 - 280 = 1069
x_{1,2} = (-37 ± √1069)/14 ; x_{1} = (-37 - 33)/14 = -5
x_{2} = (-37 + 33)/14 = -2/7
7(x + 2/7)(x + 5) = (7x + 2)(x + 5) = 0
5. 3x^{2} + 5x - 2 = 0 ; (3x - 1)(x + 2) = 0 ---> x_{1} = -2 and x_{2} = 1/3
Rachel..does your teacher want you to factor these trinomials into bionomials?
example x^{2} - 6x + 5 = ( x - 5)(x - 1)
This this Rachel?
Rachel...very good answers to your inquiry...but might I just add...this is how I help my 9^{th} graders being to answer these kinds of problems. (In words, these kinds of problems are 'factoring a trinomial', which means finding factors, which when multiplied together will equal the trinomial, which usually is a 'binomial'...basically (x + y) (x + y) = x^{2} + 2xy + y^{2}
With that said, assume the answer will most likely be something like the one above, so begin with writing ( )( ) now, we just have to find out what belong inbetween the parenthesis. Next, look at the signs inside the parenthesis, here are the rules(you know these from 6th grade:
Rule 1: if the signs are... ax^{2} + bx + c then the signs are ( + )( + )
Rule 2: if the signs are... ax^{2} + bx - c then the signs are ( + )( - ) or Rule 3: if the signs are... ax^{2} + bx - c then the signs are ( - )( + ) dependent on if b > c or b < c
Rule 4: if the signs are... ax^{2} - bx + c then the signs are ( - )( - )
Step 1: Look at the first value x^{2} you know that it will be x times x, right? So you know the first values in the binomials will be 'x' (x )(x ) Step 2: Look at the last value in the trinomial 'c' What are some of the factors of c_{f}? Factors will go on the ends of the binomials (x c_{f} )(x c_{f }) the difference or sum of the factors should equal the bx value in the trinomial. Hope this helps...good luck!
Comments
what exactly is your question Rachel? Do you need help factoring those functions?