2
Suppose k - 5*p = -22, -2*k = -3*p + 14 - 5. Factor -4*n**k + 52*n**2 + n**5 + 0*n**4 + n**4 - 52*n**2 + 2*n**4.
n**3*(n - 1)*(n + 4)
Find c such that 5084/7*c**3 - 615648*c**2 - 2/7*c**4 + 174227900*c - 173612978 = 0.
1, 847
Let s(m) be the first derivative of -m**5/35 + 4*m**3/7 + 8*m**2/7 - 1978. Find w, given that s(w) = 0.
-2, 0, 4
Let l(c) be the first derivative of 14 + 4/9*c**4 + 0*c**2 + 1/6*c**5 - 3*c + 4/9*c**3 + 1/45*c**6. Let i(h) be the first derivative of l(h). Solve i(g) = 0.
-2, -1, 0
Let f(i) = -2*i**4 - 66*i**3 - 312*i**2 + 765*i - 390. Let k(n) = -2*n**4 - 34*n**3 - 156*n**2 + 383*n - 194. Let s(l) = 3*f(l) - 5*k(l). Factor s(m).
4*(m - 10)*(m - 1)**2*(m + 5)
Let w(h) be the second derivative of 2 + 0*h**2 + 0*h**3 + 4*h + 1/66*h**4. What is b in w(b) = 0?
0
Let q(y) be the second derivative of y**6/39 - 18*y**5/5 + 737*y**4/78 - 30*y**3/13 - 184*y**2/13 + 1495*y + 2. Determine z, given that q(z) = 0.
-2/5, 1, 92
Let v(f) be the third derivative of -13*f**5/300 - 17*f**4/20 - 89*f**3/30 - 1680*f**2. What is n in v(n) = 0?
-89/13, -1
Let n(p) = -1832*p**2 + 31140*p + 68. Let q be n(17). Determine z, given that 12/7*z**2 - 20/7*z**4 + 22/7*z**3 + q*z + 0 = 0.
-2/5, 0, 3/2
Let g(a) be the second derivative of -a**4/6 + 39*a**3 - 116*a**2 + 465*a. Factor g(j).
-2*(j - 116)*(j - 1)
Factor -383023*s**2 + 383028*s**2 + 7554 - 12875*s + 5316.
5*(s - 2574)*(s - 1)
Let q be (((-51)/(-34))/(3/2))/((-40)/(-80)). Factor 4*v + 0 - 25/6*v**q + 1/6*v**3.
v*(v - 24)*(v - 1)/6
Suppose c - 7*p + 22 = -11*p, 0 = -2*p - 10. Let g be 4 + 3 - (-4 + 9 + c). Factor -v**g - 1/2*v**3 + v**2 + 0 + 1/2*v**5 + 0*v.
v**2*(v - 2)*(v - 1)*(v + 1)/2
Let r(w) be the second derivative of 1/5*w**5 + 2/3*w**4 - 7*w - 3*w**2 + 0 - 2/3*w**3 - 1/15*w**6. Factor r(k).
-2*(k - 3)*(k - 1)*(k + 1)**2
Let a be (-3)/2 - (66/(-4) + -5). Solve -a*h**4 + 2*h**3 + 2*h**3 + 5*h**5 + 10*h**4 + h**3 = 0 for h.
0, 1
Let l(n) = 8*n**5 - 3*n**4 - 43*n**3 + 22*n**2 + 49*n - 5. Let r(c) = -c**5 + 2*c**3 + c**2 + c + 1. Let t(w) = -l(w) - 5*r(w). What is f in t(f) = 0?
-3, -1, 0, 2, 3
Let s(m) = -m**3 - 161*m - 470. Let t be s(-3). Let x(w) be the first derivative of -1715/4*w**4 + t*w + 490*w**3 - 210*w**2 - 2. Let x(u) = 0. Calculate u.
2/7
Let f be 9 + (12860/(-3190) - 3). Let i = f + -36/29. Factor i*g - 8/11 + 2/11*g**2 - 2/11*g**3.
-2*(g - 2)*(g - 1)*(g + 2)/11
Let x(a) be the third derivative of a**6/120 - 9*a**5/4 + 89*a**4/8 - 133*a**3/6 + 2661*a**2. Factor x(w).
(w - 133)*(w - 1)**2
Suppose -43*m = -41*m + 60. Let d be m/(-45)*(6 - 0). Factor -2*q + 4*q + q**4 - 5*q**4 + 0*q + d*q**2 - 2*q**5.
-2*q*(q - 1)*(q + 1)**3
Let q(w) be the second derivative of w**6/120 + 39*w**5/40 + 1969*w**4/48 + 728*w**3 + 6272*w**2 - 295*w - 6. Solve q(y) = 0.
-32, -7
Find x such that -36 + 145/2*x**2 - 23/2*x**4 + 15*x**3 + x**5 - 41*x = 0.
-2, -1/2, 1, 4, 9
Let g(t) be the third derivative of -t**8/252 - 71*t**7/630 - 29*t**6/60 - 34*t**5/45 - 7*t**4/36 + 5*t**3/6 - 43*t**2 + 8*t. Solve g(c) = 0 for c.
-15, -1, 1/4
Let t be ((-2 + 2)/2)/(-37 + 39). Suppose t = 3*m - 548 + 542. Find q, given that 23/2*q**2 - m*q**3 - 15*q - 9/2 = 0.
-1/4, 3
Let d be (-9)/6*5020/(-10). Let h = d - 751. Factor -3*t**3 - 36/5*t**h - 12/5*t + 0.
-3*t*(t + 2)*(5*t + 2)/5
Let j(n) be the first derivative of 1/7*n**4 - 5/21*n**3 + 0*n + 1/7*n**2 - 1/35*n**5 + 34. Factor j(w).
-w*(w - 2)*(w - 1)**2/7
Let t(m) be the first derivative of -m**4/42 + 11*m**3/21 + 12*m**2/7 - 78*m - 87. Let d(n) be the first derivative of t(n). Let d(q) = 0. Calculate q.
-1, 12
Let w(s) = 115*s**4 - 6*s**3 - 2*s. Let n(l) = l**4 + l. Suppose a + 3*g = -5, -4*g = -1 + 5. Let b(p) = a*n(p) - w(p). Find q such that b(q) = 0.
0, 2/39
Let q(r) be the third derivative of -245*r**8/216 - 4144*r**7/45 + 27776*r**6/135 - 26104*r**5/135 + 100*r**4 - 832*r**3/27 - 3953*r**2. What is c in q(c) = 0?
-52, 2/7, 2/5
Let j(g) be the second derivative of g**5/12 + g**4/24 - 5*g**3/18 - g**2/4 - 2952*g. Let j(u) = 0. What is u?
-1, -3/10, 1
Let l(b) be the third derivative of -b**5/15 + 92*b**4/3 - 16928*b**3/3 + 482*b**2. Find k such that l(k) = 0.
92
Let t(r) be the first derivative of r**6/900 + r**5/150 - 2*r**4/15 - 26*r**3 + 98. Let p(o) be the third derivative of t(o). Factor p(s).
2*(s - 2)*(s + 4)/5
Let q(h) be the second derivative of -h**5/16 + 515*h**4/16 - 53045*h**3/8 + 5463635*h**2/8 + 3*h + 306. Suppose q(x) = 0. Calculate x.
103
Let p(m) = -11*m**2 - m + 41. Let a(w) be the first derivative of 17*w**3/3 + w**2/2 - 62*w + 41. Let q(g) = -5*a(g) - 8*p(g). Factor q(j).
3*(j - 2)*(j + 3)
Let o = -224 + 297. Factor -o + 523 - 132*i + 6*i**2 - 4*i**2 + 72*i.
2*(i - 15)**2
Let b = -193016 - -193018. What is c in -18/7*c + 2/7*c**b + 0 = 0?
0, 9
Let q be (-11 + (16 - 52/13))*4/12. Let c(f) = -f**3 - 2*f**2 - f. Let g be c(-1). Determine k so that 1/3*k**4 + 0*k**3 + 0 + g*k**2 + 0*k + q*k**5 = 0.
-1, 0
Let 723 + 491 - 806*o - 986*o + 574 + 4*o**2 = 0. What is o?
1, 447
Suppose 281 = 5*r - 8*d + 11*d, 0 = -2*r + 4*d + 102. Suppose 9 + r = 16*z. Determine l so that -1/4*l**z + 0*l + 0 + 0*l**2 + 0*l**3 = 0.
0
Let d(a) be the first derivative of a**3/5 - 2839*a**2/10 - 1894*a/5 + 5147. Factor d(c).
(c - 947)*(3*c + 2)/5
Suppose 312*h**5 - 39*h + 27*h**4 - 96*h**3 + h**4 - 310*h**5 + 100*h**2 + 5*h = 0. Calculate h.
-17, 0, 1
Let v(b) = -b**5 - 9*b**4 + 23*b**3 - 3*b**2 - 24*b + 14. Let r(l) = l**5 - l**4 - l**3 + l**2 - 2*l + 2. Let w(g) = 2*r(g) - 2*v(g). Factor w(s).
4*(s - 1)**3*(s + 1)*(s + 6)
Suppose -1/6*y**2 + 21/2 - 1/3*y = 0. Calculate y.
-9, 7
Let s(x) be the second derivative of -x**6/120 + x**4/24 - 19*x**2 + 53*x. Let i(z) be the first derivative of s(z). Factor i(o).
-o*(o - 1)*(o + 1)
Let k(g) be the second derivative of -g**6/6 - 14*g**5 - 2095*g**4/6 - 1260*g**3 - 3645*g**2/2 + 1512*g + 2. Factor k(a).
-5*(a + 1)**2*(a + 27)**2
Let 1035/8*a**2 + 93/4*a**3 + 84 + 381/2*a + 3/8*a**4 = 0. What is a?
-56, -4, -1
Let f be (-7)/((-7)/(-2))*10/12. Let z = 13/6 + f. Factor 0*d - z*d**2 + 0.
-d**2/2
Factor 41 - w**5 + 142*w**3 - 1004*w**4 - 3*w**5 - 41 - 1142*w**3.
-4*w**3*(w + 1)*(w + 250)
Let q(b) be the second derivative of -1/24*b**4 + 0*b**3 - b - 6 + 1/8*b**5 - 1/15*b**6 + 0*b**2. Factor q(y).
-y**2*(y - 1)*(4*y - 1)/2
Let t = 9730637/15 - 648709. Solve 0*b - t*b**2 + 6/5 = 0 for b.
-3, 3
Let n(g) = -g**2 + 58*g - 629. Let d(o) = 2*o - 1. Let s = -90 + 94. Let t(m) = s*d(m) - n(m). Factor t(u).
(u - 25)**2
Let f be (6 + -2 - 8)/((-2)/7). Let i be (-12)/f*(-721)/309. Factor -12/5*l**i - 4/5*l**4 + 0*l - 16/5*l**3 + 0.
-4*l**2*(l + 1)*(l + 3)/5
Let j be -20*(4 - -10)/(1 - 3). Let k = -137 + j. Factor 0*u - 3/7*u**k - 3/7*u**2 + 0.
-3*u**2*(u + 1)/7
Let r(m) be the second derivative of m**7/63 - 11*m**5/10 - 22*m**4/9 + 44*m**3/3 + 48*m**2 - 4785*m. Suppose r(w) = 0. Calculate w.
-4, -3, -1, 2, 6
Suppose -2*w - f + 4 = 0, -5*f = -2*w - 16 + 8. Suppose 9*v - 28 = -w. Let 3/4*n - 3/8*n**v + 0 + 9/8*n**4 - 3/8*n**5 - 9/8*n**2 = 0. What is n?
-1, 0, 1, 2
Find b, given that 1/4*b**3 - 165/4 - 3/4*b**2 - 73/4*b = 0.
-5, -3, 11
Let s(g) = 7*g**2 - 4*g + 1. Let b be s(1). Factor 16*n**3 - 64*n - 61*n**2 + b*n**4 + 157*n**2 - 61*n**2 - 51*n**2.
4*n*(n - 2)*(n + 2)*(n + 4)
Let h(v) = -2*v + 1. Let o(m) = 27*m**2 + 240*m + 4092. Let f(i) = 8*i**2 + 80*i + 1364. Let g(t) = 14*f(t) - 4*o(t). Let n(d) = -g(d) + 24*h(d). Factor n(k).
-4*(k + 26)**2
Let o be ((-9088)/(-24850))/(3*2/745). Let s = -604/15 + o. Factor s*n**2 + 2*n**3 + 40/7*n + 16/7 + 2/7*n**4.
2*(n + 1)*(n + 2)**3/7
Let h(v) be the second derivative of v**6/120 - 187*v**5/80 + 23*v**4/2 + v**3/6 - 92*v**2 - 10641*v. Let h(l) = 0. What is l?
-1, 2, 184
Find j such that 6 + 1 - 170*j**2 + 166*j**2 + 404*j - 7 = 0.
0, 101
Let p = 1213264 - 8492846/7. Factor -86/7 + 88/7*m - p*m**2.
-2*(m - 43)*(m - 1)/7
Factor -126*z**3 - 7*z**2 + 20*z + 49*z**4 + 67*z**2 - 28*z.
z*(z - 2)*(7*z - 2)**2
Let j(s) be the third derivative of s**8/3360 + s**7/1680 - 71*s**3/2 + s**2 - 58. Let z(a) be the first derivative of j(a). Factor z(u).
u**3*(u + 1)/2
Let a(z) be the third derivative of z**7/840 + 19*z**6/480 + 127*z**5/240 + 119*z**4/32 + 15*z**3 + 1328*z**2. Let a(v) = 0. Calculate v.
-8, -5, -3
Let 