4*p**3 + 1/2*p**2 = 0.
-1, 1, 2
Determine b so that 2/19*b**3 + 1702/19*b - 134/19*b**2 + 19166/19 = 0.
-7, 37
Suppose 345 = 906*n - 791*n. Factor -3/2*j**n - 11/4*j**2 - 1/4*j**4 - 3/2*j + 0.
-j*(j + 1)*(j + 2)*(j + 3)/4
Let d(t) be the second derivative of t**7/189 - 22*t**6/135 + 19*t**5/10 - 283*t**4/27 + 800*t**3/27 - 128*t**2/3 + 5175*t + 1. Solve d(b) = 0.
1, 2, 3, 8
Suppose 3*h + 0*h = -s + 15, -4*h + s + 13 = 0. Suppose 0 = h*b + 3*g - 15, -13 = -4*b - 3*g + 2*g. Factor -4*l**2 - 35*l**2 - 8 - 1 + b*l**4 + 24*l + 21*l**2.
3*(l - 1)**3*(l + 3)
Let a be 12/81*(-4266)/(-316). Let h(p) be the first derivative of 0*p + 1/4*p**a + 9 + 1/12*p**3. Factor h(w).
w*(w + 2)/4
Let r(z) be the third derivative of -z**5/20 - 87*z**4/8 + 135*z**3 - 2963*z**2. Factor r(a).
-3*(a - 3)*(a + 90)
Let g(o) = -4*o**5 + 90*o**4 + 648*o**3 - 7922*o**2 + 19368*o - 12174. Let b(m) = m**5 + m**3 - 4*m + 1. Let s(i) = 6*b(i) + g(i). Let s(q) = 0. Calculate q.
-26, 1, 3
Let u(b) be the second derivative of -b + 1/9*b**4 + 0*b**3 + 33 - 1/18*b**5 + 0*b**2 + 1/135*b**6. Find c such that u(c) = 0.
0, 2, 3
Let l be 10 + -11 + 5 - -6. Factor -9*g**4 - 16*g + l*g**4 + 8*g**2 + 7*g**3 + 0*g**2.
g*(g - 1)*(g + 4)**2
Let v = -862 + 734. Let c = 131 + v. Factor 0 - 5/2*o**2 + 7/2*o**c - o.
o*(o - 1)*(7*o + 2)/2
Find h such that -4*h + 2/9*h**4 + 0 + 58/9*h**2 - 8/3*h**3 = 0.
0, 1, 2, 9
Let y(i) = -7*i - 26. Let r be y(-4). Let c be -1 + 4 + -2 - -35. Factor c*h - 8 + 7*h**r + 4*h**5 - 44*h**2 + 56*h**3 - 27*h**2 - 24*h**4.
4*(h - 2)*(h - 1)**4
Suppose -53*h**2 + 3*h**3 + 668 - 94*h**2 + 763 + 1725*h + 444 = 0. What is h?
-1, 25
Let r(w) be the third derivative of 32/15*w**3 - 2 - 88/75*w**5 + 0*w - 20*w**2 + 26/15*w**4 + 6/175*w**7 + 11/150*w**6. Find k such that r(k) = 0.
-4, -2/9, 1, 2
Let b be ((-18632)/(-179996))/(10/116). Let d = b + -2/2647. Factor -d + 3/5*j + 6/5*j**2 - 3/5*j**3.
-3*(j - 2)*(j - 1)*(j + 1)/5
Suppose -4*y - 14 = -5*p + 16, 0 = -4*p + 3*y + 23. Determine m, given that 51 - 3*m**2 + 41*m + p*m + 5*m = 0.
-1, 17
Let o(r) = 143*r**3 - 2114*r**2 + 724*r + 1156. Let h(q) = q**4 - 14*q**3 + q**2 - q. Let a(s) = 14*h(s) - 2*o(s). Suppose a(n) = 0. What is n?
-4/7, 1, 17
Determine r, given that 0*r + 1878/13*r**5 + 0*r**2 + 4/13*r**3 + 1258/13*r**4 + 0 = 0.
-2/3, -1/313, 0
Suppose 0 + 39/2*h - 73/4*h**4 + 5/4*h**5 + 241/4*h**2 + 85/4*h**3 = 0. What is h?
-1, -2/5, 0, 3, 13
Let i(o) be the second derivative of -o**4/48 - 11*o**3/8 - 29*o**2/2 + 576*o - 2. Factor i(f).
-(f + 4)*(f + 29)/4
Let v(f) be the second derivative of 8*f**2 - 1/60*f**6 + f + 0*f**5 + 0*f**3 + 0 + 1/12*f**4. Let d(h) be the first derivative of v(h). Solve d(u) = 0 for u.
-1, 0, 1
Let o(a) = 3 - 15 + 26*a - 27*a. Let c be o(-14). Find l such that -25*l**2 + 7*l**c + l**3 + 8*l - 4 + 13*l**2 = 0.
1, 2
Let p(f) = -3*f**3 + 42*f**2 - 12*f - 42. Let u(l) = -13*l**3 + 189*l**2 - 53*l - 189. Let a(g) = -22*p(g) + 5*u(g). What is x in a(x) = 0?
-21, -1, 1
Factor 1542*k - 264*k**4 - 241*k**4 + 746*k**4 - 102*k**3 - 3528 - 239*k**4 + 166*k**2.
2*(k - 49)*(k - 3)**2*(k + 4)
Let x(y) be the second derivative of -y**5/5 - 2502*y**4 - 12520008*y**3 - 31325060016*y**2 + 920*y - 2. Suppose x(w) = 0. Calculate w.
-2502
Let v(i) = 32*i**2 + 39*i - 715. Let m(s) = -6*s**2 - 8*s + 142. Let y(t) = 11*m(t) + 2*v(t). Factor y(w).
-2*(w - 6)*(w + 11)
Let i = -212 - -218. Factor j**4 - 2*j**2 + 0*j**4 + 6*j + 5*j**2 - i*j**3 - 4*j**2.
j*(j - 6)*(j - 1)*(j + 1)
Let t(v) = 10*v**2 + 69*v + 215. Let l(a) = -12*a**2 - 68*a - 184. Let o(f) = -3*l(f) - 4*t(f). Factor o(k).
-4*(k + 7)*(k + 11)
Let h(d) = -3*d**4 - 21*d**3 + 31*d**2 - 21*d - 7. Let z(u) = 6*u**4 + 42*u**3 - 63*u**2 + 45*u + 15. Let x(k) = -15*h(k) - 7*z(k). Factor x(m).
3*m**2*(m - 1)*(m + 8)
Let j(x) be the second derivative of -x**4/6 + 5858*x**3/3 - 8579041*x**2 - 13145*x. Factor j(y).
-2*(y - 2929)**2
Factor -64/5*n + 512/5 + 2/5*n**2.
2*(n - 16)**2/5
Let i(j) be the second derivative of -5*j**4/72 - 545*j**3/36 + 140*j**2 + j - 149. Factor i(m).
-5*(m - 3)*(m + 112)/6
Determine u, given that 0*u + 0*u + 512*u**4 + 80*u**3 - 800*u**2 - 514*u**4 = 0.
0, 20
Suppose 80*v - 70*v = 50. Find w such that 6 + w**5 - 3*w**4 - 2045*w**2 + 2048*w**2 - v*w**3 + 4*w - 6 = 0.
-1, 0, 1, 4
Suppose 0 = 8*w - 13*w - 190. Let n = -35 - w. Let 6*k - n*k**3 + 754*k**2 + 0*k**3 - 757*k**2 = 0. What is k?
-2, 0, 1
Let q = -3055 + 3083. Let g = 68 - 39. What is s in -69*s**3 - 4*s**4 + 24*s**2 + g*s**3 + 32*s + q*s**3 = 0?
-4, -1, 0, 2
Let a(u) be the first derivative of -u**7/1680 - u**6/144 - u**5/60 + u**3 - u - 40. Let k(l) be the third derivative of a(l). Determine h so that k(h) = 0.
-4, -1, 0
Let q be ((-26)/715)/(((-1)/4)/((-1)/(188/(-517)))). Factor 18 - 36/5*i + q*i**2.
2*(i - 15)*(i - 3)/5
Let c(n) = 2*n**2 + 15*n - 27. Let j be c(-9). Let z be j/(-6 - 3/3). Factor z + 2/3*u**2 - 4/3*u.
2*u*(u - 2)/3
Let l(v) be the first derivative of -84 - 40/9*v**2 - 2/27*v**3 - 26/3*v. Factor l(h).
-2*(h + 1)*(h + 39)/9
Suppose 0 = 872064*j - 872101*j + 1110. Determine o, given that 0 - 52/5*o + 46/5*o**4 - j*o**3 + 154/5*o**2 + 2/5*o**5 = 0.
-26, 0, 1
Let z(r) be the third derivative of 0 + 1/2*r**4 - 22*r**2 + 0*r - 1/180*r**5 - 35/18*r**3. Factor z(b).
-(b - 35)*(b - 1)/3
Let u = 40 - 38. Suppose u*f - 15 = -f. Let 5*p**2 - 11 - 15*p - 4 + f*p = 0. What is p?
-1, 3
Suppose 0 = 9*m - 72 - 36. Suppose 4*u = u + m. Factor -20 - q**2 - 7*q + 27*q - u*q**2.
-5*(q - 2)**2
Let f(c) = 11*c**2 + 371*c - 94. Suppose -37*n = -36*n + 6. Let p(y) = -54*y**2 - 1856*y + 470. Let t(o) = n*p(o) - 28*f(o). Factor t(u).
4*(u + 47)*(4*u - 1)
Let p(f) be the first derivative of -106 - 8/11*f**3 - 3/22*f**4 + 0*f + 0*f**2. What is z in p(z) = 0?
-4, 0
Let c(y) = y**4 - 2*y**3 + y**2 - y - 1. Let p(f) = 5*f**4 + 26*f**3 + 38*f**2 - 272*f - 569. Let u(k) = 2*c(k) - p(k). Factor u(b).
-3*(b - 3)*(b + 3)**2*(b + 7)
Suppose 11 - 23 = -3*b. Let d be (-12)/30*20/(-32). Factor -2*c**2 + 1/2*c**b + c**3 + 0*c - d*c**5 + 0.
-c**2*(c - 2)**2*(c + 2)/4
Let r be 689/39 + 7/21. Let n be ((-54)/16)/(r/(-12)). Suppose -n*j**2 - 4 - 6*j - 1/4*j**3 = 0. Calculate j.
-4, -1
Let g(n) be the second derivative of 0 - 1/96*n**4 + 1/24*n**3 + 0*n**2 - 11*n. Solve g(y) = 0 for y.
0, 2
Let w = 319 - 2225/7. Let v be (5440/1020)/(16/3 + -4). Find n, given that 0 - 2/7*n**v + 0*n - 8/7*n**3 + 2/7*n**5 + w*n**2 = 0.
-2, 0, 1, 2
Let a be 12 - (-22)/220*15/57*-452. Factor -4/19*x**2 + 40/19*x - 48/19 - a*x**3.
-2*(x - 2)**2*(x + 6)/19
Suppose -3*g + 6 = -6, -q - 28 = -4*g. Let r be ((-30)/q - -4)*1*2. Factor 2*k**2 + 13 + r + 34 - 10 + 20*k.
2*(k + 5)**2
Let i = 5176 + -10351/2. Determine h, given that 0*h**3 + i*h + 0 + 3/4*h**2 - 1/4*h**4 = 0.
-1, 0, 2
Let d be (-55)/(-44) + (-75)/(-20). Factor 27*v - 3986 + 12*v**4 - 36*v**2 - 6*v**3 + 3*v**d + 3986.
3*v*(v - 1)**2*(v + 3)**2
Let c(s) be the third derivative of s**7/40 - 11*s**6/60 + s**5/10 + 3*s**4 - 28*s**3/3 + 2*s**2 + 11*s. Let b(a) be the first derivative of c(a). Factor b(w).
3*(w - 2)**2*(7*w + 6)
Let 18*m**4 - 6*m**4 - 16*m**4 - 2 + 96*m**3 + 2 + 100*m**2 = 0. Calculate m.
-1, 0, 25
Let n = 74 - 65. Factor -3*l**3 - 4*l - l + 39*l**4 + n*l**2 - 40*l**4.
-l*(l - 1)**2*(l + 5)
Let f(q) be the second derivative of 74*q + 2/3*q**2 + 0 - 1/18*q**4 - 1/9*q**3. Factor f(r).
-2*(r - 1)*(r + 2)/3
Let m(a) be the first derivative of 17*a - a**3 + 66*a**2 - 9*a**2 - 1136*a + 36*a - 26. Factor m(h).
-3*(h - 19)**2
Let i be 67 + -77 - -48*395. Let x be 6/33 + i/4675. Determine h, given that -x*h - 2/17*h**3 - 24/17*h**2 + 0 = 0.
-6, 0
Factor 213*y**2 - 120*y + 612 + 221*y**2 - 431*y**2.
3*(y - 34)*(y - 6)
Let j be (2 - (-16 + 8)) + 52 + -60. Determine q so that -56/11*q - 16/11 - 28/11*q**j + 30/11*q**3 = 0.
-2/3, -2/5, 2
Let d be 16131/(-64740) + 320/(-52) + 6. Let b = -1/332 - d. Factor 2/5*i**3 + 0 - b*i + 0*i**2.
2*i*(i - 1)*(i + 1)/5
Let w(x) be the first derivative of x**3/9 + 35*x**2/12 - 33*x - 3970. Factor w(i).
(i + 22)*(2*i - 9)/6
Suppose -l = -4*l - 9. Let d be 7/3 - 2/(3 - l). What is t in 4*t**3 - 82*t - 3*t**3 - 40 + 62*t + 10*t**d + 4*t**3 = 0?
-2, 2
Let b(t) = 3*t**2 + 10*t - 9. Let g(u) = 11*u**2 + 30*u - 27. Let j(v) = v**2 - 5*v + 10. Let z be j(3). 