3 - 1/4*l**4. Factor p(u).
-3*(u - 1)*(u + 2)
Suppose 4*s = u + 7, 2 = -5*s - 3*u - 2. Suppose s = -l + 5. Factor 0*y**2 + 2*y**2 + y - y**3 + 2*y - l*y.
-y*(y - 1)**2
Let y = 63 - 68. Let l(b) = b**2 + 6*b + 7. Let u be l(y). Factor 3/2 + u*p + 1/2*p**2.
(p + 1)*(p + 3)/2
Let c(u) be the third derivative of 9*u**2 - 1/150*u**5 + 0*u + 0*u**3 + 1/60*u**4 + 0. Factor c(x).
-2*x*(x - 1)/5
Suppose 268 - 52 = -8*g. Let x = g + 29. Factor 0*h**x + 0*h - 1/5*h**4 + 0*h**3 + 0.
-h**4/5
Let -z**3 - 23078 + 7*z**3 + 23074 + 3*z + 25*z**2 = 0. Calculate z.
-4, -1/2, 1/3
Let c(t) be the third derivative of -34*t**5/39 - 31*t**4/52 - 2*t**3/39 - 256*t**2. Factor c(r).
-2*(4*r + 1)*(85*r + 2)/13
Let d(b) = b**2 - 67*b + 63. Let z(n) = -68*n + 64. Let f(r) = -4*d(r) + 3*z(r). Suppose f(t) = 0. What is t?
1, 15
Let f(l) be the third derivative of l**7/7560 - l**6/1080 + 9*l**4/8 - 34*l**2. Let p(y) be the second derivative of f(y). Factor p(t).
t*(t - 2)/3
Let b = 62 - 64. Let t be (-8)/4 - (b - -1)*5. Let -3/5*u**2 + 0 + 0*u + 6/5*u**t - 3/5*u**4 = 0. What is u?
0, 1
Let d(f) = -15*f**4 - 80*f**3 - 445*f**2 - 454*f + 972. Let m(x) = 4*x**4 + 20*x**3 + 111*x**2 + 114*x - 243. Let w(b) = -6*d(b) - 22*m(b). Factor w(k).
2*(k - 1)*(k + 3)*(k + 9)**2
Let s(d) be the third derivative of -d**8/224 - 9*d**7/140 - 23*d**6/80 - 3*d**5/8 + 379*d**2. Determine c so that s(c) = 0.
-5, -3, -1, 0
Let h(a) be the second derivative of a**6/180 + a**5/120 - a**4/72 - a**3/36 + 5*a + 9. Factor h(m).
m*(m - 1)*(m + 1)**2/6
Determine z so that 19*z**2 - 18*z**2 - 12*z + 2*z - 84 + 2*z = 0.
-6, 14
Let p be (-40)/((-170)/17) - (0 - 10/(-4)). Factor 3/2*d - 3/2*d**3 - 3/2*d**2 + p.
-3*(d - 1)*(d + 1)**2/2
Let w(x) be the third derivative of x**6/90 + x**5/15 - x**3/3 + 5*x**2. Let b(r) be the first derivative of w(r). Factor b(u).
4*u*(u + 2)
Let a(q) = -q**3 + 5*q**2 + 8*q - 8. Let o = -9 + 15. Let w be a(o). Suppose -6*j**3 - 5*j**w - 3*j**2 - 11*j**4 + 13*j**4 = 0. What is j?
-1, 0
Let n(p) = 25*p**2 - 10*p - 20. Let l(m) = m**3 - 26*m**2 + 11*m + 20. Suppose 33 = 8*y - 7. Let s(r) = y*l(r) + 6*n(r). Factor s(v).
5*(v - 1)*(v + 1)*(v + 4)
Suppose t + 2*x - 8 = -14, 5*t - 25 = x. Suppose -4 = -0*o - 2*o. Factor -u**t - u**3 + 0*u - 1/3*u**5 + 0 - 1/3*u**o.
-u**2*(u + 1)**3/3
Suppose 0*m - 28/15*m**3 + 2/15*m**4 - 64/15*m**2 + 0 = 0. What is m?
-2, 0, 16
Let u = -86 + 23. Let q = -59 - u. Factor 1/4*s**q - 1/4*s**2 + 1/4*s + 0 - 1/4*s**3.
s*(s - 1)**2*(s + 1)/4
Let p(t) = t**2 - 9*t - 5. Let f be p(10). Suppose f*y = -g + 3*y - 4, -y - 16 = -3*g. Suppose 2/7*n**g - 2/7*n**2 + 0 + 0*n**3 + 0*n = 0. What is n?
-1, 0, 1
Let f(b) = -4*b**4 + 88*b**2 + 100*b + 4. Let r(s) = -4*s**4 + 3*s**3 + 88*s**2 + 101*s + 5. Let t(q) = -5*f(q) + 4*r(q). Let t(a) = 0. Calculate a.
-6, -1, 0, 4
Let m(n) = 9*n**2 - 19*n + 18. Let c(w) = -2*w - w**2 + 3*w - 2 + 2. Suppose 0*g + j = 4*g - 61, g - 29 = 3*j. Let b(a) = g*c(a) + 2*m(a). Factor b(p).
4*(p - 3)**2
Suppose -8*n - 109 - 27 = 0. Let h = n - -17. Factor -2/3*v**4 + 0*v**3 + 4/3*v**2 + h*v - 2/3.
-2*(v - 1)**2*(v + 1)**2/3
Let v be (50 - 51)/((-1)/4). Factor 16/17*h**3 - 2/17*h**2 - 10/17*h**v + 0 - 4/17*h.
-2*h*(h - 1)**2*(5*h + 2)/17
Suppose -4*y = 5*l - 39, 22 = -7*l + 3*y + 25. Suppose -3/8*f**4 - 9/8*f**l + 3/2*f + 0*f**2 + 0 = 0. What is f?
-2, 0, 1
Let m be ((-38)/8)/(6/(-24)). Suppose 3*i + 6 = 4*l - 0*l, 5*l + 2*i - m = 0. Factor 2*g**2 - l*g**2 - 6*g - 9 + 3*g**2 - 3*g**2.
-(g + 3)**2
Suppose 7 + 7 = 7*p. What is n in 4 + p*n**2 - 8 - 5*n**2 - 20 - 18*n = 0?
-4, -2
Suppose 42 - 20 = 11*x. Determine p, given that 11/2*p**3 - 7/2*p - 5/2*p**4 - 1 - x*p**5 + 7/2*p**2 = 0.
-2, -1, -1/4, 1
Let b(u) be the third derivative of -u**8/43680 - u**7/3276 - u**6/2340 + 2*u**5/195 - u**4/6 + 20*u**2. Let a(r) be the second derivative of b(r). Factor a(m).
-2*(m - 1)*(m + 2)*(m + 4)/13
Let w(d) = -6*d - 1 - 7*d**3 + 2 - 8*d**2 + 0 + d. Let y(f) = -8*f**3 - 8*f**2 - 4*f + 2. Let m = -24 + 18. Let u(x) = m*w(x) + 5*y(x). Factor u(i).
2*(i + 1)**2*(i + 2)
Factor 3/4*g**5 + 0*g - 3/2*g**3 + 0*g**2 + 0 - 3/4*g**4.
3*g**3*(g - 2)*(g + 1)/4
Let l(f) be the third derivative of -f**7/2520 + f**6/540 - 53*f**3/6 - f**2 + 25*f. Let w(m) be the first derivative of l(m). Factor w(o).
-o**2*(o - 2)/3
Let u(p) = -4*p**2 - p - 3. Let o be u(3). Let v be 3 - (-366)/o - -6. Determine k so that -2/7*k**3 - 4/7*k**2 + v*k + 4/7 = 0.
-2, -1, 1
Let p(d) = -3*d**3 + 108*d**2 - 408*d + 420. Let i(v) = 3*v**3 - 109*v**2 + 410*v - 418. Let z(c) = 6*i(c) + 5*p(c). Find y such that z(y) = 0.
2, 34
Let x(w) be the third derivative of -7*w**6/3420 + 3*w**5/380 - w**4/114 - 5*w**3/6 + 14*w**2. Let m(p) be the first derivative of x(p). Factor m(q).
-2*(q - 1)*(7*q - 2)/19
Let g be ((-20)/(-6))/((-1)/21). Let d = g - -72. Factor 2/3*w - 2/3*w**3 - 2/3*w**d + 2/3.
-2*(w - 1)*(w + 1)**2/3
Suppose 0 = -4*p - 3*k - 78, -5*p - 6*k = -7*k + 88. Let q be (16/(-66))/(-1 - 6/p). Factor q*h - 2/11 - 2/11*h**2.
-2*(h - 1)**2/11
Let q be 1 - ((-70)/45)/(-4 + 2). Let h(t) be the first derivative of 3 + 0*t**2 - 2/3*t + q*t**3. Solve h(j) = 0 for j.
-1, 1
Let p = 163 + -162. Suppose 13*n - 1 = -p. Suppose 0 - 1/4*d**2 + 1/4*d**3 + n*d = 0. Calculate d.
0, 1
Let y be (-81)/45 - 531/(-270). Factor -y*t**2 + 0 + 0*t.
-t**2/6
Suppose -i - 2*i - 6 = 4*b, -3*i = 2*b. Let a be i*((-52)/(-16) - 3). Factor 0 + 1/2*n**2 - a*n.
n*(n - 1)/2
Let x = 21179 - 42357/2. Factor -x*y**2 + y + 3/2.
-(y - 3)*(y + 1)/2
Let q(u) be the second derivative of -u**5/130 - 33*u**4/26 - 833*u**3/13 - 2401*u**2/13 - u - 7. Factor q(m).
-2*(m + 1)*(m + 49)**2/13
Let z = 63/68 + 367/136. Let g = z + -27/8. Factor -3/4 + g*x**2 + 1/2*x.
(x - 1)*(x + 3)/4
Let i be 261/(-27) - (1 - 11). Factor -i - 1/3*f**2 - 2/3*f.
-(f + 1)**2/3
Let o be 12/(-72) - (-290)/1308. Let s = 272/981 - o. Determine p, given that 0*p**2 + s*p - 2/9*p**3 + 0 = 0.
-1, 0, 1
Suppose 11*c - 26 = -4. Let t(q) be the first derivative of 5 + 1/3*q**c + 1/3*q + 1/9*q**3. Factor t(f).
(f + 1)**2/3
Suppose 6*t - 22 - 8 = 0. Let n(a) be the second derivative of 0*a**3 + 0 + 0*a**2 + 1/6*a**4 - t*a + 1/15*a**6 + 1/5*a**5. Suppose n(d) = 0. What is d?
-1, 0
Factor 45*p**2 - 3*p**3 + 6 - 114*p + 68 + 9 - 11.
-3*(p - 12)*(p - 2)*(p - 1)
Suppose -8*p - 18/5*p**2 - 2/5*p**3 - 24/5 = 0. What is p?
-6, -2, -1
Let l(b) be the first derivative of -4*b**5/5 + 8*b**4 - 32*b**3 + 64*b**2 - 64*b - 39. Factor l(p).
-4*(p - 2)**4
Let p be (-242)/(-143) - (-24)/78. Factor 21/4*m + 3/4*m**3 - 15/4*m**p - 9/4.
3*(m - 3)*(m - 1)**2/4
Suppose -18 = 3*d + 3*y, 1007 = d - 2*y + 995. Let 9/2*s**3 - 3/4*s**4 + 0*s + d*s**2 + 0 = 0. Calculate s.
0, 6
Let g be 6/27 + 18/(-81). Let f be g + -4 + 8 - (-10)/(-4). Factor 0 + 3*x**2 - 3*x**4 + f*x**5 - 3/2*x + 0*x**3.
3*x*(x - 1)**3*(x + 1)/2
Suppose 0 = 7*h - 12*h + 15. Let 3*k**4 - 8*k**4 + 7*k**h + 3*k**3 = 0. What is k?
0, 2
Let x(r) = -3*r**3 + r**2 - 9*r - 5. Let t(v) = -4*v**3 + 3*v**2 - 17*v - 10. Let o(l) = -4*t(l) + 7*x(l). Factor o(i).
-5*(i - 1)*(i + 1)**2
Let n(y) = y**3 - 2*y**2 + 35*y - 34. Let j be 1/(((-24)/81)/(-8)). Let i(l) = 6*l**3 - 15*l**2 + 246*l - 237. Let o(v) = j*n(v) - 4*i(v). Factor o(u).
3*(u - 2)*(u - 1)*(u + 5)
Let d(q) be the first derivative of -3*q**4/8 + 225*q**2/4 + 375*q + 88. Determine t so that d(t) = 0.
-5, 10
Suppose 83 = 51*x - 121. Let s(g) be the third derivative of -7*g**2 + 1/30*g**5 + 0 - 1/4*g**x + 2/3*g**3 + 0*g. Solve s(o) = 0 for o.
1, 2
Let v(a) = 3*a**2 + 9*a - 15. Let u be v(5). Let t be 4 - u/14 - -5. Factor 9/2*y**3 + 0 + 3*y**2 + t*y**4 + 0*y.
3*y**2*(y + 1)*(y + 2)/2
Let r(i) be the second derivative of 3*i**8/2240 + i**7/160 + i**6/240 - 2*i**3/3 + 11*i. Let z(b) be the second derivative of r(b). Factor z(w).
3*w**2*(w + 2)*(3*w + 1)/4
Let m(d) be the first derivative of -13*d**3/3 - 103*d**2 + 32*d + 301. Find n, given that m(n) = 0.
-16, 2/13
Let b be 2/3 + -1 + 273/468. Let s(x) be the first derivative of 0*x + 2 + 1/16*x**4 - 1/4*x**3 + b*x**2. Determine q so that s(q) = 0.
0, 1, 2
Let w(n) be the first derivative of -n**4/14 - 244*n**3/21 - 3721*n**2/7 + 42. Determine f so that w(f) = 0.
-61, 0
Let l(k) = 2*k**3 - 2*k**2 - k. Let c(s) = s**4 + 16*s**3 - 17*s**2 - 41*s + 36. Le