. Factor 0*t + 0 + c*t**3 + 2/9*t**2.
2*t**2*(t + 1)/9
Let v = 35189 + -175938/5. Factor -v*i**2 + 2/5 + i.
-(i - 1)*(7*i + 2)/5
Let p(u) be the third derivative of u**6/2 + 2*u**5/15 - 5*u**4/2 - 4*u**3/3 + u**2 + 6*u. Factor p(a).
4*(a - 1)*(a + 1)*(15*a + 2)
Suppose -3*r - 2*r + 45 = -2*d, d = -3*r - 6. Let a be 5/d - 10/(-3). Factor 4*t + 8*t**a + 2*t**5 + t**3 + 9*t**3 - 14*t**2 - 10*t**4.
2*t*(t - 2)*(t - 1)**3
Let c(r) be the third derivative of r**8/882 - 23*r**7/2205 + 43*r**6/1260 - 11*r**5/210 + r**4/28 - 15*r**2. Let c(s) = 0. What is s?
0, 3/4, 1, 3
Suppose z**4 + 132*z**3 + 3*z**2 + 0*z**4 - 128*z**3 = 0. What is z?
-3, -1, 0
Let m(a) be the second derivative of 7*a**5/15 + 2*a**4/3 + 224*a - 2. Factor m(u).
4*u**2*(7*u + 6)/3
Factor -1/6*i**3 + 25/6*i - 3 - i**2.
-(i - 2)*(i - 1)*(i + 9)/6
Factor -2226*f**2 - 75*f**3 + 74*f**3 + 2235*f**2 - 8*f.
-f*(f - 8)*(f - 1)
Suppose 23*l + 13*l - 11359 + 11251 = 0. Let -4/7*t**l - 4/7*t**4 + 4/7*t**2 + 0 + 4/7*t = 0. Calculate t.
-1, 0, 1
Let q(i) be the second derivative of i**7/7 + 13*i**6/5 + 687*i**5/40 + 49*i**4 + 245*i**3/4 + 75*i**2/2 + 88*i. Find x such that q(x) = 0.
-5, -2, -1/2
Suppose -26*m = -6*m + 10*m. Suppose m = 2*w - 4*n - 0*n + 4, 2*n = 5*w - 14. Suppose 9/7*c**3 + 3/7*c**w + 9/7*c**2 + 3/7*c + 0 = 0. Calculate c.
-1, 0
Let q(r) be the first derivative of -1/2*r**4 - 14 + 0*r**2 + 0*r**3 + 0*r. Determine j, given that q(j) = 0.
0
Let k(c) be the first derivative of c**8/336 + c**7/168 - c**6/72 - c**5/24 - 2*c**3 + 22. Let n(t) be the third derivative of k(t). Factor n(q).
5*q*(q - 1)*(q + 1)**2
Let d(q) = q**2 + 7*q + 12. Suppose -2 = g + 3*x + 13, 5*x + 8 = 4*g. Let t be d(g). Factor 0 + 1/4*w**3 + t*w**2 - 1/4*w.
w*(w - 1)*(w + 1)/4
Let u be (2/3)/((-212)/2067) - -7. Factor 0*b**2 - b**3 + 1/2 - u*b**4 + b.
-(b - 1)*(b + 1)**3/2
Let z(i) be the second derivative of -3/2*i**4 + 18*i + 0 + 11/3*i**3 - 63/5*i**6 - 27/2*i**5 + 2*i**2. Factor z(g).
-2*(3*g + 1)**3*(7*g - 2)
What is l in -27 + 15*l**5 + 725*l**2 - 145*l**2 + 410*l**3 + 130*l**4 + 129*l + 62 + 55 + 246*l = 0?
-3, -1, -2/3
Let p(h) be the third derivative of h**9/80640 - h**7/2240 - h**6/480 - 17*h**5/60 + 24*h**2. Let c(g) be the third derivative of p(g). Factor c(t).
3*(t - 2)*(t + 1)**2/4
Let l(z) be the first derivative of -z**4/42 - 4*z**3/7 - 36*z**2/7 + 31*z + 2. Let h(x) be the first derivative of l(x). Factor h(y).
-2*(y + 6)**2/7
Let w(f) be the second derivative of -1/10*f**4 + 0 + 0*f**2 + 1/10*f**3 + 1/25*f**6 - 3/100*f**5 - 4*f. Solve w(i) = 0 for i.
-1, 0, 1/2, 1
Let y(g) be the second derivative of -1/25*g**5 + 5*g + 1/30*g**4 + 0*g**3 + 0*g**2 + 1/75*g**6 + 0. Factor y(f).
2*f**2*(f - 1)**2/5
Let h(y) be the second derivative of y**4/54 - 11*y**3/27 - 4*y**2/3 - 6*y. Determine t, given that h(t) = 0.
-1, 12
Let t = 97 - 95. Let a(j) be the second derivative of 2/3*j**3 + 0*j**t + 0 + 5/6*j**4 + 1/15*j**6 + 2/5*j**5 - j. Factor a(v).
2*v*(v + 1)**2*(v + 2)
Let b(n) be the first derivative of 3/4*n**3 - 3/20*n**5 + 3/16*n**4 - 14 + 3/2*n - 15/8*n**2. Factor b(c).
-3*(c - 1)**3*(c + 2)/4
Let f(i) be the second derivative of 0*i**2 - 7/3*i**3 - 1/18*i**4 - 2*i + 0 + 0*i**5 + 1/1080*i**6. Let a(o) be the second derivative of f(o). Factor a(g).
(g - 2)*(g + 2)/3
Let a = 2/27083 - -27071/162498. Factor 0 + a*q**3 - 2/3*q**2 + 2/3*q.
q*(q - 2)**2/6
Let j(m) = m**3 + 3*m**2 - 4*m + 5. Let c be j(-4). Let y be -2 + -1 + c/10*6. Factor y - 2/5*o**3 - 4/5*o - 6/5*o**2.
-2*o*(o + 1)*(o + 2)/5
Let l(u) be the first derivative of -7*u**5/15 + 3*u**4/4 + 4*u**3/3 - 2*u**2/3 + 31. Let l(k) = 0. Calculate k.
-1, 0, 2/7, 2
Let t(m) be the third derivative of m**8/2520 + m**7/630 - m**6/180 - m**5/45 + m**4/9 - 3*m**3 - 8*m**2. Let q(k) be the first derivative of t(k). Factor q(i).
2*(i - 1)**2*(i + 2)**2/3
Let c = -81 - -89. Suppose c*a - 10 = 6. Find u, given that -4/3*u**a + 0*u + 4/3 = 0.
-1, 1
Factor -51/2*k - 3/4*k**4 - 207/4*k**2 - 27*k**3 + 0.
-3*k*(k + 1)**2*(k + 34)/4
Let q(m) be the third derivative of -1/2*m**4 + 1/14*m**7 + 0 - 3/40*m**6 + 0*m**3 + 0*m - 2*m**2 - 3/5*m**5. Factor q(p).
3*p*(p - 2)*(p + 1)*(5*p + 2)
Suppose -6*r - 23 = -c - 3*r, 0 = 3*r + 3. Factor 0*x**2 + 21*x**3 - c*x**3 + 4*x**2.
x**2*(x + 4)
Let p(w) = w**2 - 13*w + 20. Let u be p(15). Factor -28*z**2 + 17 + 108 + u*z + 33*z**2.
5*(z + 5)**2
Let o = 195811/37655 - 1/7531. Factor 4/5 - o*k**2 - 22/5*k.
-2*(k + 1)*(13*k - 2)/5
Let v(f) be the second derivative of 2*f**7/21 - 8*f**6/15 + 4*f**5/5 - 319*f. Factor v(m).
4*m**3*(m - 2)**2
Let y(k) be the second derivative of -k**7/105 - k**6/30 + k**4/6 + k**3/3 + 19*k**2 + 2*k. Let l(d) be the first derivative of y(d). Factor l(n).
-2*(n - 1)*(n + 1)**3
Factor -108/7 - 30/7*s + 2/7*s**2.
2*(s - 18)*(s + 3)/7
Let h(g) be the third derivative of g**6/2160 - g**5/240 + g**4/72 - 5*g**3/6 + 7*g**2. Let u(q) be the first derivative of h(q). Factor u(s).
(s - 2)*(s - 1)/6
Let l = 251/5 - 1737/35. Solve 8/7*f**3 + l - 2/7*f - 12/7*f**2 + 8/7*f**4 - 6/7*f**5 = 0 for f.
-1, -2/3, 1
Let p = 8207/2 + -4099. Determine j, given that -3/4*j**2 - 27/4 + p*j = 0.
3
Let x(f) be the second derivative of 1/3*f**2 + 1/15*f**5 + 1/45*f**6 - 3*f - 1/63*f**7 - 1/9*f**3 - 1/9*f**4 + 0. Determine u, given that x(u) = 0.
-1, 1
Factor 4*m**2 - 37*m**3 - 2*m**4 + 35*m**3 + 0*m**4.
-2*m**2*(m - 1)*(m + 2)
Suppose -2*c = -5*c - 4*p + 13, -4*p - 2 = -2*c. Suppose -z + 16 = c*z. Factor -z + 14*t**3 + 4*t**2 + 4*t - 10*t**3 - 8*t**3.
-4*(t - 1)**2*(t + 1)
Let m = -683/312 + 215/24. Let -48/13 + 100/13*x**2 + 46/13*x**3 - 10/13*x**4 - m*x = 0. What is x?
-2, -2/5, 1, 6
Let o(i) = 11*i**4 - 18*i**3 + 17*i**2 - 3*i + 7. Let w(n) = -n**4 + n**3 - n**2 - 1. Let a(j) = -3*o(j) - 21*w(j). Suppose a(u) = 0. What is u?
0, 3/4, 1
Let a(b) be the first derivative of -b**5 + 85*b**4/4 - 305*b**3/3 - 585*b**2/2 + 810*b + 184. Determine f so that a(f) = 0.
-2, 1, 9
Let y be (-52)/(-39) + (-1)/12. Factor -5*f**3 - 25/4*f**2 + 0 - 5/2*f - y*f**4.
-5*f*(f + 1)**2*(f + 2)/4
Factor -52/5*q**2 + 24/5*q + 0 - 4*q**3.
-4*q*(q + 3)*(5*q - 2)/5
Let s(p) be the second derivative of 13*p**4/12 + 2*p**3 - 97*p + 1. Let s(d) = 0. What is d?
-12/13, 0
Find d, given that 121*d**2 + 13*d + 83*d**3 + d**4 - 141876 + 141846 + 4*d**4 = 0.
-15, -1, 2/5
Let s = 13 - 11. Determine v so that 3*v**3 + 3 - 11*v + 9*v**s - 3*v**4 + 3 - 4*v = 0.
-2, 1
Suppose 58*t**2 + 4*t + 207/2*t**4 + 147*t**3 + 0 = 0. Calculate t.
-2/3, -2/23, 0
Suppose -2*g = 2*g + 72. Let n(s) = -3*s**3 + 21*s**2 + 3*s - 3. Let d(q) = q**3 - 6*q**2 - q + 1. Let k(p) = g*d(p) - 5*n(p). Find v, given that k(v) = 0.
-1, 1
Let i(r) be the second derivative of -9*r**5/20 - 5*r**4/4 - r**3 + 2*r - 1. Find k such that i(k) = 0.
-1, -2/3, 0
Suppose 2*b = 5*v, 4*b - 21*v = -20*v. Let i(u) be the first derivative of u**3 - 3/2*u**2 + b*u + 3. Solve i(x) = 0.
0, 1
Let m(c) = -c**2 - 7*c - 4. Let g be m(-6). Let t be (9/6)/(g/4). Determine x so that 5*x**3 - 3*x + 6*x**3 - 6*x**3 - 2*x**t = 0.
-1, 0, 1
Factor -555*x**2 - 690*x + 39675 + 279*x**2 + 279*x**2.
3*(x - 115)**2
Factor -2/5*n**2 - 72/5 + 24/5*n.
-2*(n - 6)**2/5
Let i = 1208/369 - 116/41. Solve -2/9*v**4 + 2/9*v - 4/9*v**3 - 2/9 + 2/9*v**5 + i*v**2 = 0.
-1, 1
Suppose -2*m + 0 = -4. Determine b so that 1 - 5*b**3 - 6*b**2 - 1 + 11*b**m = 0.
0, 1
Let c(w) = -w**2 - 69*w - 485. Let i be c(-8). Let k = 199/171 + -1/19. Find o such that -k*o + 10/9*o**i + 2*o**2 - 4/9 - 14/9*o**4 = 0.
-1, -2/7, 1
Let r = 684 + -4103/6. Let c(f) be the second derivative of 0*f**2 - r*f**3 + 7*f - 1/4*f**4 - 1/10*f**5 + 0. Solve c(m) = 0 for m.
-1, -1/2, 0
Factor 320/7*h + 2/7*h**3 - 52/7*h**2 - 576/7.
2*(h - 18)*(h - 4)**2/7
Let w(d) be the second derivative of d**7/7 - d**6/10 - 3*d**5/4 - d**4/2 - 32*d + 2. Solve w(a) = 0.
-1, -1/2, 0, 2
Let f = -252 - -252. Find k, given that -3/4*k**2 + f - 9/2*k = 0.
-6, 0
Determine q so that 16/9*q + 76/3*q**3 - 190/9*q**4 + 50/9*q**5 - 104/9*q**2 + 0 = 0.
0, 2/5, 1, 2
Let y(g) be the second derivative of -g**4/9 - 212*g**3/9 - 5618*g**2/3 + 103*g. Determine p so that y(p) = 0.
-53
Suppose 2*s - 19 = -3. Factor -s*w + w**3 - 11*w**3 + 2*w**4 + 3*w**2 + 0*w**3 + 13*w**2.
2*w*(w - 2)**2*(w - 1)
Let p = -3 + 5. Factor 