ctor a(b).
-3*(b - 96)*(b - 1)*(b + 1)/4
Suppose 0*j + 60 = 6*j. Factor 8*i**2 + 5 - 1 + j*i - 475*i**3 + 477*i**3.
2*(i + 1)**2*(i + 2)
Let s = 35681/7 - 5097. Factor 0*n**3 + 4/7*n**4 + 0 + 2/7*n - 4/7*n**2 - s*n**5.
-2*n*(n - 1)**3*(n + 1)/7
Factor -3*v**2 + 5*v**2 - 905*v + 923*v.
2*v*(v + 9)
Suppose -338 = 10*c - 368. Determine u so that 3/2 + 3/2*u - 9/8*u**4 + 21/4*u**c - 57/8*u**2 = 0.
-1/3, 1, 2
Let s(r) be the second derivative of -3*r**5/20 - r**4/4 + 2*r**3 + 6*r**2 + 3*r + 13. Factor s(f).
-3*(f - 2)*(f + 1)*(f + 2)
Let g(r) be the third derivative of r**5/60 + r**4/2 - 13*r**3/6 - r**2. Let h be g(-13). What is k in -1/4*k**3 - 1/2*k**2 - 1/4*k + h = 0?
-1, 0
Let f(l) = 6*l**2 - 3*l - 4. Let m be f(-1). Determine t, given that t**4 - 3*t**2 + t**2 - 23*t**3 + 1 - t - t**m + 25*t**3 = 0.
-1, 1
Let j be 3/(-18) - (-44)/(43296/287). Factor -169/8 - j*z**2 - 13/4*z.
-(z + 13)**2/8
Let f(h) be the third derivative of h**8/5040 - h**7/2520 - h**6/540 + 11*h**3/6 - 26*h**2. Let v(u) be the first derivative of f(u). Factor v(s).
s**2*(s - 2)*(s + 1)/3
Let w be 17 - (0 + -2) - (-4 - -2). Suppose w*r = 26*r - 20. Factor -1/3*l**5 + 0*l**r + 2/3*l**3 + 0*l**2 - 1/3*l + 0.
-l*(l - 1)**2*(l + 1)**2/3
Let p be 552/28 + (-4)/(-14). Let -20*c**4 + 36*c**3 - 9*c**2 + 8*c**3 + 45*c**2 - 12*c**5 + p - 4 - 64*c = 0. Calculate c.
-2, 1/3, 1
Let b(p) = -9*p**2 + 8*p - 1. Let r(d) = 36*d**2 - 33*d + 4. Suppose -2*m + 0*m + 8 = 0. Suppose -m*l - 20 - 16 = 0. Let o(c) = l*b(c) - 2*r(c). Factor o(t).
(3*t - 1)**2
Let d be (-2)/(28/9256*4)*5. Let k = d + 829. What is w in 0*w + 0 + 57/7*w**3 - 3*w**4 + k*w**2 = 0?
-2/7, 0, 3
Let h be ((-7)/(-3) - 3) + (-42)/(-9). Suppose -4*k = -2*k - h. Factor q - 1/2 - 1/2*q**k.
-(q - 1)**2/2
Determine l so that 5*l**3 - 5*l**4 - 3 + 32*l - 5*l + 3 + 13*l + 50*l**2 = 0.
-2, -1, 0, 4
Factor 5*q**2 + 0*q**2 - 35*q - 41 - 37 - 12.
5*(q - 9)*(q + 2)
Let b = 8013/38 + -3978/19. Let -1/2*m**2 - 3/2*m**3 + b*m + 1 - 1/2*m**4 = 0. Calculate m.
-2, -1, 1
Let i(v) be the first derivative of v**4/20 - 2*v**3/3 - 11*v**2/10 + 184. Factor i(r).
r*(r - 11)*(r + 1)/5
Let i = -155/2 - -4189/54. Let r(o) be the third derivative of 3*o**2 + i*o**3 + 1/36*o**4 + 0*o + 0 + 1/270*o**5. Factor r(m).
2*(m + 1)*(m + 2)/9
Let t = 1301959/916734 + 1/13286. Let j = t - 2/23. What is n in 0 + 0*n + 2/3*n**3 - j*n**2 = 0?
0, 2
Suppose 3*r - 2*g - 1 = 0, 2*g - 11 = -r - 0*g. Factor -4*z**4 + 8*z**2 + 4*z - 4 + r*z**5 - 74*z**3 + z**5 + 66*z**3.
4*(z - 1)**3*(z + 1)**2
Let o(v) be the first derivative of -v**4/4 - 4*v**3/3 - 5*v**2/2 - 2*v + 126. Solve o(q) = 0 for q.
-2, -1
Determine p so that -10 - 21*p**3 + 32*p**3 - 9*p**3 + 10*p**2 - 2*p = 0.
-5, -1, 1
Let g(r) be the third derivative of r**7/1080 - r**6/135 + r**5/90 + r**4/12 - r**3/3 + 2*r**2 - 3*r. Let h(z) be the second derivative of g(z). Factor h(a).
(a - 2)*(7*a - 2)/3
Let n = -50 + 53. Factor -n*c**2 - 3*c**3 - 3106 + 3106.
-3*c**2*(c + 1)
Let i(o) be the second derivative of 1/56*o**7 - 3/8*o**3 + 0 - 3/8*o**2 + 3/40*o**6 + 3/40*o**5 - 1/8*o**4 + 3*o. Factor i(s).
3*(s - 1)*(s + 1)**4/4
Suppose 127*b = -79*b + 618. Determine f, given that 1/9*f**2 + 0*f + 1/9*f**b + 0 = 0.
-1, 0
Let v(j) be the first derivative of -2*j**5/15 - 13*j**4/6 - 14*j**3/3 + 13*j**2/3 + 44*j/3 - 337. Let v(i) = 0. What is i?
-11, -2, -1, 1
Let n(d) be the third derivative of -d**8/3360 + d**7/336 - d**6/120 - 17*d**3/3 - 9*d**2. Let m(r) be the first derivative of n(r). Factor m(p).
-p**2*(p - 3)*(p - 2)/2
Let g be 2/7 - (1 - (-8588)/560). Let y = -61/4 - g. Factor 4/5 - y*z + 1/5*z**2.
(z - 2)**2/5
Let d(p) be the first derivative of p**6/1620 + p**5/180 + p**4/54 - 17*p**3/3 + 57. Let v(m) be the third derivative of d(m). Factor v(x).
2*(x + 1)*(x + 2)/9
Let i = 139/402 + -12/67. Let v(f) be the first derivative of 0*f + i*f**3 + 1/8*f**4 - 3 - 1/2*f**2. Determine d, given that v(d) = 0.
-2, 0, 1
Suppose 0 = -18*o - 25*o + 172. Factor 4/5*c**2 + o*c + 16/5.
4*(c + 1)*(c + 4)/5
Let h be -4*10/(-4) + 7616/(-784). Factor 6/7*j**3 - 10/7*j**2 + h + 2/7*j.
2*(j - 1)**2*(3*j + 1)/7
Factor 21675/4 + 3/4*a**2 - 255/2*a.
3*(a - 85)**2/4
Determine w, given that 2/7*w**3 + 1320/7*w - 7200/7 + 16*w**2 = 0.
-30, 4
Factor 2*b**2 - 5*b + 20*b**5 + 8*b**2 - 15*b**5 - 10*b**4.
5*b*(b - 1)**3*(b + 1)
Let s(p) be the second derivative of p**5/70 - 61*p**4/14 + 3721*p**3/7 - 226981*p**2/7 - 224*p. Factor s(x).
2*(x - 61)**3/7
Let p(i) be the first derivative of -108*i**5/55 + 129*i**4/22 - 52*i**3/33 - 36*i**2/11 + 16*i/11 + 100. Determine u, given that p(u) = 0.
-1/2, 2/9, 2/3, 2
Let b be (-12)/57*(-15 + 13). What is k in 4/19*k - b*k**2 - 4/19*k**3 + 6/19*k**4 + 2/19 = 0?
-1, -1/3, 1
Factor -3/4 + 1/4*s + 3/4*s**2 - 1/4*s**3.
-(s - 3)*(s - 1)*(s + 1)/4
Factor -134 + 6*p**3 - 411*p - 3*p**3 - 181 - 93*p**2.
3*(p - 35)*(p + 1)*(p + 3)
Let d = 731/21 - 243/7. Factor -d*o**5 - 8/21*o**2 + 0*o + 2/7*o**4 + 0*o**3 + 0.
-2*o**2*(o - 2)**2*(o + 1)/21
Let 0 - 8/7*o**2 - 9/7*o + 1/7*o**3 = 0. Calculate o.
-1, 0, 9
Let x(f) be the third derivative of -f**6/540 + f**5/90 - f**4/54 + 2*f**2 - 67*f. Factor x(h).
-2*h*(h - 2)*(h - 1)/9
Let q(n) = 13*n**2 + 115*n - 28. Let h(o) = 19*o**2 + 172*o - 42. Let m(g) = -5*h(g) + 7*q(g). Suppose m(w) = 0. Calculate w.
-14, 1/4
Let l(w) be the third derivative of 0*w**4 + 1/80*w**6 + 0*w**3 + 0*w - 1/80*w**5 + 0 - 1/280*w**7 - 17*w**2. Determine h, given that l(h) = 0.
0, 1
Let p(m) be the third derivative of -m**7/525 + m**5/150 + 17*m**2 - 1. Factor p(k).
-2*k**2*(k - 1)*(k + 1)/5
Let l(f) be the third derivative of 5*f**8/168 - f**7/15 - f**6/10 + f**5/3 + f**4/12 - f**3 - f**2 + f. Determine p, given that l(p) = 0.
-1, -3/5, 1
Let d(l) be the second derivative of -l**8/15120 + l**7/7560 - 7*l**3/6 + 8*l. Let r(k) be the second derivative of d(k). Factor r(m).
-m**3*(m - 1)/9
Let c(d) be the second derivative of -d**6/90 + d**5/15 + d**4/6 - 2*d**3/9 - 5*d**2/6 - 27*d - 1. Solve c(n) = 0.
-1, 1, 5
Factor 336/5*f - 36/5*f**3 + 8/5*f**2 + 4/5*f**4 + 288/5.
4*(f - 6)**2*(f + 1)*(f + 2)/5
Let f be 110/(-50) - 355/300*-2. Factor 1/6*g**5 - f*g**3 + 0*g - 1/6*g**4 + 1/6*g**2 + 0.
g**2*(g - 1)**2*(g + 1)/6
Let w(s) be the third derivative of -s**7/70 + 5*s**5/4 + 416*s**2. Solve w(u) = 0.
-5, 0, 5
Let s(v) be the first derivative of -v**6/10 - 3*v**5/25 + 57*v**4/20 + 13*v**3/5 - 117*v**2/5 - 216*v/5 + 466. Find n such that s(n) = 0.
-4, -2, -1, 3
Let f be (12/10)/((-108)/(-180)). Let o(v) be the second derivative of 3*v + 0 + 0*v**f + 1/6*v**4 + 1/10*v**5 - 2/3*v**3. Factor o(k).
2*k*(k - 1)*(k + 2)
What is c in -12*c - 14*c - 6*c**2 - 39*c**4 + 9*c**5 - 3*c**5 + 63*c**3 + 8*c - 6*c = 0?
-1/2, 0, 1, 2, 4
Determine x so that 69/5*x + 3/5*x**2 + 36 = 0.
-20, -3
Factor 0 + 10/13*z**2 + 12/13*z + 2/13*z**3.
2*z*(z + 2)*(z + 3)/13
Factor -2*w + 4 - 46*w**2 - 41*w**2 + 2*w**3 + 83*w**2.
2*(w - 2)*(w - 1)*(w + 1)
Let r be (-1000)/(-400) - (-37)/(-18). Factor r*b - 4/9*b**5 + 0*b**3 + 0 + 8/9*b**4 - 8/9*b**2.
-4*b*(b - 1)**3*(b + 1)/9
Let c(u) = -8*u + 4. Let l be c(2). Let h be (78/20 - 3)/((-9)/l). Determine o so that -4/5 - h*o - 2/5*o**2 = 0.
-2, -1
Let u = 87/194 + 5/97. Let j(i) be the first derivative of -1/3*i**3 - u*i**2 + 9 + 0*i. Factor j(q).
-q*(q + 1)
Let i(c) be the first derivative of -3*c**4/16 - 89*c**3/12 + 4*c**2 + 15*c + 293. Solve i(h) = 0.
-30, -2/3, 1
Let a(h) be the third derivative of -h**7/630 - h**6/90 - h**5/60 + h**4/18 + 2*h**3/9 + 125*h**2. Factor a(n).
-(n - 1)*(n + 1)*(n + 2)**2/3
Let u(q) = 8*q**4 + 128*q**3 - 517*q**2 + 353*q - 7. Let h(v) = -3*v**4 - 43*v**3 + 172*v**2 - 118*v + 2. Let y(t) = -7*h(t) - 2*u(t). Factor y(o).
5*o*(o - 2)*(o - 1)*(o + 12)
Let n = 29 - 27. Factor 10*h**2 - 20*h**2 - 3 - 3*h**3 + 3*h + 13*h**n.
-3*(h - 1)**2*(h + 1)
Let x(z) be the third derivative of -z**8/5040 - z**7/315 + z**5/10 - 12*z**2. Let c(v) be the third derivative of x(v). Factor c(y).
-4*y*(y + 4)
Let f = 5729/7005 + -25/1401. Factor 24/5*p**2 + f*p**3 + 36/5*p + 0.
4*p*(p + 3)**2/5
Let b = 993 + -990. Let h(j) be the first derivative of -1/4*j**4 + 0*j**b + 0*j + 0*j**2 - 11. Find w, given that h(w) = 0.
0
Let l = -443/11 - -3189/77. Find m, given that -l + 4/7*m**2 - 4/7*m = 0.
-