Rachel C.
asked • 02/27/1320x+11x3=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
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2 Answers By Expert Tutors
Nataliya D. answered • 02/27/13
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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.
ax2 + bx + c = a(x - x1)(x - x2) ; were x1,2 = (-b ± √D)/2a
are roots of the equation
ax2 + bx + c = 0 and D = b2 - 4ac
~~~~~~~~~~
1. x2 - 5x - 54 = 0 does not have rational roots.
2. x2 - 3x - 4 = 6 ----> x2 - 3x - 10 = 0 ---> (-10) = (-5) · 2 ; (- 3) = -5+2
(x - 5)(x + 2) = 0 ---> x1 = 5 , x2 = -2
3. 5x2 + 16x +3 = 0 ; D = 162 - 4 · 5 · 3 = 256 - 60 = 196;
x1,2 = (-16 ± √196)/(2 · 5) = (-16 ± 14)/10 ;
x1 = -2/10 = -1/5
x2 = -30/10 = -3
5(x + 1/5)(x + 3) = (5x +1)(x + 3) = 0
4. 7x2 + 37 + 10 = 0 ; D = 372 - 4*7*10 = 1369 - 280 = 1069
x1,2 = (-37 ± √1069)/14 ; x1 = (-37 - 33)/14 = -5
x2 = (-37 + 33)/14 = -2/7
7(x + 2/7)(x + 5) = (7x + 2)(x + 5) = 0
5. 3x2 + 5x - 2 = 0 ; (3x - 1)(x + 2) = 0 ---> x1 = -2 and x2 = 1/3
Jon G. answered • 02/27/13
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Patient knowledgeable STEM educator/former healthcare practitioner
Rachel..does your teacher want you to factor these trinomials into bionomials?
example x2 - 6x + 5 = ( x - 5)(x - 1)
This this Rachel?
Jon G.
Rachel...very good answers to your inquiry...but might I just add...this is how I help my 9th 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) = x2 + 2xy + y2
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... ax2 + bx + c then the signs are ( + )( + )
Rule 2: if the signs are... ax2 + bx - c then the signs are ( + )( - ) or Rule 3: if the signs are... ax2 + bx - c then the signs are ( - )( + ) dependent on if b > c or b < c
Rule 4: if the signs are... ax2 - bx + c then the signs are ( - )( - )
Step 1: Look at the first value x2 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 cf? Factors will go on the ends of the binomials (x cf )(x cf ) the difference or sum of the factors should equal the bx value in the trinomial. Hope this helps...good luck!
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02/28/13
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Bob V.
what exactly is your question Rachel? Do you need help factoring those functions?
02/27/13