e (11/99)/((-2)/(-12)). Find f, given that 6 + a*f**2 - b*f = 0.
3
Let h(f) be the third derivative of 2*f**2 + 0 + 0*f**5 + 0*f + 0*f**4 + 1/315*f**7 - 1/90*f**6 + 0*f**3. Factor h(i).
2*i**3*(i - 2)/3
Factor 10 - 4*c**2 - 8 + 3 + 8 + 15 + 24*c.
-4*(c - 7)*(c + 1)
Let d(k) be the second derivative of -23*k**6/120 + 5*k**5/16 - k**4/24 - k - 63. Let d(w) = 0. Calculate w.
0, 2/23, 1
Let g(h) be the third derivative of h**8/4032 - h**7/720 + h**6/360 - h**5/10 - 13*h**2. Let r(x) be the third derivative of g(x). Solve r(s) = 0 for s.
2/5, 1
Let i be 5/5*(23 + 0). Let w = i - 21. Factor 3/4 + 3/4*m**w - 3/2*m.
3*(m - 1)**2/4
Let a(n) be the first derivative of -1 + 3*n**2 - 1/2*n**4 - 4*n + 0*n**3. Suppose a(z) = 0. Calculate z.
-2, 1
Let w(l) = -l + 11. Let d be w(7). Factor -9*x**3 + x**d - 11 - 39*x + 8 + 21 + 29*x**2.
(x - 3)**2*(x - 2)*(x - 1)
Let z(k) = 6*k**2 + 3*k**3 - 3*k - 7*k**2 - k + 5*k. Let d be z(1). Factor 4*s**d + 4*s**2 - 6*s**3 - 6*s**2.
-2*s**2*(s + 1)
Let w(n) be the second derivative of 0*n**2 + 0 - n**4 + 5*n - 3/2*n**3 - 3/20*n**5. Factor w(r).
-3*r*(r + 1)*(r + 3)
Let z(d) = d**5 - 8*d**4 + 5*d**3 - 4*d**2 + 3*d + 3. Let y(b) = -b**4 - b**3 + b + 1. Let c(w) = 3*y(w) - z(w). Factor c(n).
-n**2*(n - 2)**2*(n - 1)
Let v(a) be the first derivative of 8/3*a**2 - 2/9*a**3 - 4 - 32/3*a. Factor v(y).
-2*(y - 4)**2/3
Suppose 2*w - 210 = -4*w. Factor 0*l - 8*l - l**2 - 28*l**3 - w*l**2.
-4*l*(l + 1)*(7*l + 2)
Factor -4/5*m**5 - 12/5*m**3 - 4/5*m**2 - 12/5*m**4 + 0*m + 0.
-4*m**2*(m + 1)**3/5
Factor 7*k**5 - 15*k - 15*k**4 + 5 + 4*k**5 + 10*k**3 - 6*k**5 + 10*k**2.
5*(k - 1)**4*(k + 1)
Let n be 4*(-3)/(-102) - (-230)/2380. Let d(i) be the first derivative of 0*i + 5/7*i**3 + n*i**2 - 1. Factor d(z).
3*z*(5*z + 1)/7
Find g such that 0 + 1/6*g**5 + 2*g**4 + 0*g**2 + 0*g + 6*g**3 = 0.
-6, 0
Let j(p) = -12*p**4 - 27*p**3 + 29*p**2 + 5*p + 5. Let a(y) = 10*y**4 + 26*y**3 - 28*y**2 - 4*y - 4. Let h(i) = -5*a(i) - 4*j(i). Factor h(c).
-2*c**2*(c - 1)*(c + 12)
Let z = 1 + 1. Let a be 4/26 - -6*27/3510. What is y in a*y**z + 1/5*y + 0 = 0?
-1, 0
Let h be 72/9 + (-572)/77. Determine l, given that 0 + 2/7*l**2 + h*l - 6/7*l**3 = 0.
-2/3, 0, 1
Suppose 1010*x + 120 = 1070*x. Factor -1/3*t - 3*t**3 + 0 + 4/3*t**4 + x*t**2.
t*(t - 1)**2*(4*t - 1)/3
Let p = 13 + -10. Suppose -f - 2*o + 14 = 2*f, p = f - o. Factor -21*t**3 - 22*t**2 - 11*t**3 - 13*t**4 - t**f - 4*t.
-2*t*(t + 1)**2*(7*t + 2)
Let a(s) be the second derivative of -s**7/15120 + s**6/1440 - s**5/360 + s**4/12 + 8*s. Let y(d) be the third derivative of a(d). Let y(i) = 0. Calculate i.
1, 2
Let l(q) be the first derivative of -5*q**4/6 + 56*q**3/27 - 11*q**2/9 - 4*q/9 - 260. Factor l(g).
-2*(g - 1)**2*(15*g + 2)/9
Let x = 31862/27 - 925153/783. Let n = -17/29 - x. Factor -n*p - 2/9*p**3 + 8/9*p**2 + 0.
-2*p*(p - 2)**2/9
Let q(l) = 2*l**3 + 2*l**2 - 12*l + 12. Let w(c) = 4*c**3 + 3*c**2 - 23*c + 23. Let x(h) = 7*q(h) - 4*w(h). Factor x(b).
-2*(b - 2)*(b - 1)*(b + 2)
Let v(u) be the third derivative of -25*u**8/84 + 152*u**7/21 - 214*u**6/5 - 1216*u**5/15 - 128*u**4/3 + 6*u**2 - 16. Factor v(i).
-4*i*(i - 8)**2*(5*i + 2)**2
Let l(c) = 7*c**3 + 8*c**2 + 11*c + 4. Let u(t) = -20*t**3 - 23*t**2 - 31*t - 11. Let x(q) = -17*l(q) - 6*u(q). Let x(w) = 0. What is w?
-2, -1, 1
Let v(c) = -c**2 - 6*c + 11. Let a be v(-7). Factor -12*i + 6 + 6 + a*i**2 - 2 - 2.
4*(i - 2)*(i - 1)
Let o(p) be the second derivative of 5*p**2 + 35/6*p**3 + 15/4*p**4 + 31*p + 5/4*p**5 + 1/6*p**6 + 0. Factor o(c).
5*(c + 1)**3*(c + 2)
Factor 207/4*i**2 + 1/4*i**3 + 328509/4 + 14283/4*i.
(i + 69)**3/4
Let o(m) be the first derivative of 16/3*m**3 + 10*m**2 + 8*m + m**4 + 8. Let o(u) = 0. What is u?
-2, -1
Suppose 17*o = 63*o + 2*o + 28*o. Let o - 44/3*h**2 - 16/3*h**4 - 52/3*h**3 - 8/3*h = 0. Calculate h.
-2, -1, -1/4, 0
Let z be (-19)/(570/(-96)) + 12/15. Let p(g) be the first derivative of 5*g**3 - 5/4*g**z + 11 + 0*g - 5*g**2. Factor p(i).
-5*i*(i - 2)*(i - 1)
Suppose -23*i = -19*i - 16. What is r in -51*r**3 + 8*r + i*r**5 - 20*r + 27*r**3 + 0*r**5 + 32*r**2 = 0?
-3, 0, 1
Let c be (60/(-16))/((360/32)/(-15)). Let m(h) be the third derivative of 0*h - 2/21*h**3 + 0 - 1/28*h**4 + 9*h**2 - 1/210*h**c. Factor m(l).
-2*(l + 1)*(l + 2)/7
Let i(j) = j**3 - 2*j**2 - 10*j - 27. Let d be i(5). Let f be -3 - (d - 0) - (-1 + -2). Find h, given that 1/2*h**5 + h**f - h**4 - 1/2*h + 0 + 0*h**3 = 0.
-1, 0, 1
Let j be 5 + 3/(-7 + 4). Let d be 1 - (-3 - (-3 + 2)). Solve j*l + 12 - 4*l**d + 2*l - 2*l - 12*l**2 = 0 for l.
-3, -1, 1
Let z be ((-6)/(-8))/((-2)/(-8)). Suppose 0 = 6*a - z*a - 12. Find g such that 31*g**3 + a*g**3 - 7*g**3 + 49*g**4 + 4*g**2 = 0.
-2/7, 0
Factor 9/4*r**3 + 1/2*r - 5/4*r**4 - 7/4*r**2 + 1/4*r**5 + 0.
r*(r - 2)*(r - 1)**3/4
Let t be -4 + (-4 + 6 - 3). Let y be (2 - -3) + t + 4. Factor -2*u**y + 6*u**5 - 3*u**3 - 7*u**4 + 6*u**4.
3*u**3*(u - 1)*(2*u + 1)
Suppose -h = -3*h - z + 15, 5*z = 5*h. Suppose 1 - 11 = -h*a. Factor -4 - 2*c**2 + 2 + 9*c - 6*c**2 + c**a.
-(c - 1)*(7*c - 2)
Let f = 231 - 123. Let h be f/26 - 6/39. Factor 0 - 3*r**2 - 12*r - 4 + h.
-3*r*(r + 4)
Let -51*h**2 - 7*h**5 + 815*h**3 - 444*h**3 - 428*h**3 + 51*h**4 + 54*h + 10*h**5 = 0. Calculate h.
-18, -1, 0, 1
Let j(c) be the first derivative of 2/7*c**6 + 1/21*c**2 + 10 - 2/7*c**3 + 29/42*c**4 - 26/35*c**5 + 0*c. Solve j(m) = 0 for m.
0, 1/3, 1/2, 1
Let y(j) be the third derivative of 1/1008*j**8 - 1/60*j**5 + 42*j**2 - 1/36*j**4 + 1/360*j**6 + 1/210*j**7 + 0 + 0*j**3 + 0*j. Factor y(r).
r*(r - 1)*(r + 1)**2*(r + 2)/3
Let i = 33 + -29. Let u(d) be the second derivative of 25/12*d**i + 5/6*d**3 + 0*d**2 - 9*d + 0. Factor u(m).
5*m*(5*m + 1)
Let s(j) be the second derivative of 8*j + 7/100*j**5 - 1/50*j**6 + 0 + 0*j**2 + 0*j**4 - 2/15*j**3. Factor s(w).
-w*(w - 2)*(w - 1)*(3*w + 2)/5
Let u(q) = 16*q**5 - 7*q**4 + 38*q**3 - 20*q**2 - 18*q + 18. Let n(a) = -7*a**5 + 4*a**4 - 19*a**3 + 10*a**2 + 8*a - 8. Let s(h) = 9*n(h) + 4*u(h). Factor s(x).
x**2*(x - 1)**2*(x + 10)
Let y(j) be the first derivative of -5*j**4/12 - 125*j**3/9 + 5. Solve y(u) = 0.
-25, 0
Let a(r) be the second derivative of -4*r - 1/75*r**6 - 1/30*r**4 + 0 - 1/25*r**5 + 0*r**2 + 0*r**3. Determine c so that a(c) = 0.
-1, 0
Determine i, given that 11/9*i - 1/9*i**3 + 10/9*i**2 + 0 = 0.
-1, 0, 11
Let q(p) = -17*p**3 - 35*p**2 - 30*p - 12. Let r = 14 - 25. Let i(c) = 9*c**3 + 18*c**2 + 15*c + 6. Let j(b) = r*i(b) - 6*q(b). Suppose j(g) = 0. What is g?
-2, -1
Let f(k) be the second derivative of k**7/315 - k**5/90 + 6*k**2 - 2*k. Let p(r) be the first derivative of f(r). Factor p(a).
2*a**2*(a - 1)*(a + 1)/3
Let u(g) be the third derivative of g**6/24 + g**5/3 + 5*g**4/24 - 5*g**3 - 2*g**2 + 66*g. Factor u(s).
5*(s - 1)*(s + 2)*(s + 3)
Suppose 0 = -p + 18*n - 17*n, -5*p + 12 = n. Factor 10/3 + 7/3*z**p + 37/3*z.
(z + 5)*(7*z + 2)/3
Let d(s) = -2*s**2 - 14*s - 16. Let k be d(-5). Solve 160*x**2 - 28*x**5 + 121 - 113 - 200*x**3 + 120*x**k - 42*x - 18*x = 0.
2/7, 1
Let s = 3891/5156 + -6/1289. Suppose s*u**5 + 4*u**2 + 0 + 23/4*u**3 + 7/2*u**4 + u = 0. Calculate u.
-2, -1, -2/3, 0
Let n be ((-16)/(-10) + -1)*(-35)/(-7). Suppose -2*s + 6 = -0. Factor -14*z + 14*z + n*z**2 + 3*z**s.
3*z**2*(z + 1)
Suppose -2*s + j = -124 + 18, -53 = -s + 2*j. Suppose -23*a - 35 + s*a - 5*a**2 - 10 = 0. What is a?
3
Let m(t) = 4*t**3 + 2. Let n(h) = h**3 - h**2 + 1. Let d(s) = -m(s) + 5*n(s). Let u be d(5). Factor 16/11 + 120/11*p + 98/11*p**u + 252/11*p**2.
2*(p + 2)*(7*p + 2)**2/11
Let u(n) be the third derivative of -n**9/30240 - n**8/3360 + 29*n**5/60 + 26*n**2. Let w(k) be the third derivative of u(k). Factor w(f).
-2*f**2*(f + 3)
Factor -361 - 3*w**2 - 371 + w + 2*w + 750.
-3*(w - 3)*(w + 2)
Let l = 2716 - 86903/32. Let b(q) be the second derivative of -6*q - l*q**4 + 0*q**2 - 9/40*q**5 - 1/16*q**6 + 0 - 1/8*q**3. Factor b(c).
-3*c*(c + 1)**2*(5*c + 2)/8
Suppose 0 = 2*k - 2*i + 359 - 361, 0 = -4*k + 5*i. Factor 6/7*x**3 - 2/7*x**2 + 0 + 0*x - 6/7*x**4 + 2/7*x**k.
2*x**2*(x - 1)**3/7
Let r(v) = -59*v**3 + 410*v**2 - 714*v - 185. Let a(p) = -30*p**3 + 204*p**2 - 357*p - 93. Let g(t) = 5*a(t) - 3*r(t). Factor g(i).
3*(i - 5)*(i - 3)*(9*i + 2)
Let h(u) be the first derivative of u**5/5 - 3*u**4/2 - 7*u*