 - 1. Let p(l) be the second derivative of 1/18*l**3 + 5*l - 1/36*l**4 + 1/3*l**2 + k. Determine v so that p(v) = 0.
-1, 2
Let v(w) be the third derivative of w**6/160 - w**5/20 + 5*w**4/32 - w**3/4 + 871*w**2 + 2*w. Solve v(r) = 0 for r.
1, 2
Let z(s) = -s**5 - s**4 + s**2 + s + 1. Let m(x) = 6*x**5 + 7*x**4 - 8*x**3 - 9*x**2 + 2*x - 1. Let o(w) = -2*m(w) - 6*z(w). Solve o(k) = 0 for k.
-2, -1, -1/3, 1
Suppose 4 = -5*y + 19. Let o be (y - 2) + 0 + (-1)/1. Find c such that 0*c + 0*c**3 - 2/7*c**4 + o*c**2 - 2/7*c**5 + 0 = 0.
-1, 0
Suppose 0*h + 0 + 1/4*h**3 - 13/2*h**2 = 0. What is h?
0, 26
Let k(l) be the third derivative of -1/540*l**6 + 0 + 0*l + 1/108*l**4 + 2*l**2 - 2/27*l**3 + 1/135*l**5. Factor k(y).
-2*(y - 2)*(y - 1)*(y + 1)/9
Let p be (-2)/(-3)*(-19 + (-196)/(-10)). Suppose 0*s**2 + 2/5*s**3 + 0 - 4/5*s**5 + p*s**4 + 0*s = 0. What is s?
-1/2, 0, 1
Let g = 129 + -125. Let z be ((-6)/(-9))/(g/12). Determine u so that -4/3*u**z + 0 - 2*u = 0.
-3/2, 0
Suppose -4*y - 3*o - 2 = 2, 3*y - 10 = o. Factor -1 - 2*x**2 - 3694*x + 3694*x + 3*x**y.
(x - 1)*(x + 1)
Let z(f) be the third derivative of f**6/30 + 7*f**5 + 1225*f**4/2 + 85750*f**3/3 + 550*f**2. Suppose z(k) = 0. What is k?
-35
Let h be ((-98)/140)/(35/(-60)). Let x = 5 + -5. Solve 0 + 3/5*d**4 - 3/5*d**3 - h*d**2 + x*d = 0.
-1, 0, 2
Let z(c) be the second derivative of -7*c**4/102 + 8*c**3/51 - c**2/17 - 427*c. Let z(t) = 0. Calculate t.
1/7, 1
Let f(m) = -3*m**2 + 2*m - 1. Let l be f(3). Let z be (-62)/l + 18/99. Find i, given that i**2 - i**3 + 3*i**z - 7*i**2 + 8 = 0.
-1, 2
Let h be (-4 - -8) + 510/(-135). Factor 0 + 4/9*a - 2/9*a**2 - h*a**3.
-2*a*(a - 1)*(a + 2)/9
Let g(w) be the first derivative of w**6/240 + w**5/10 + w**4 - 11*w**3/3 - 21. Let r(v) be the third derivative of g(v). Let r(z) = 0. Calculate z.
-4
Let n(g) = -91*g - 996. Let s be n(-11). Factor -8/3*v**3 - 56/3*v**s + 0*v + 0*v**2 - 44/3*v**4 + 0.
-4*v**3*(2*v + 1)*(7*v + 2)/3
Let f(v) = v**4 - v**2 + 1. Let j(p) = 4*p**5 + 2*p**4 - 4*p**3 - 2*p**2 + 6. Let i(k) = 6*f(k) - j(k). Solve i(w) = 0 for w.
-1, 0, 1
Let k(q) be the first derivative of 6*q**5/25 - 39*q**4/10 + 102*q**3/5 - 189*q**2/5 - 9. Factor k(j).
6*j*(j - 7)*(j - 3)**2/5
Factor -132*h**2 - 93*h - 67 - 34*h**3 - 27*h + 27 + 20 + 36.
-2*(h + 2)**2*(17*h - 2)
Factor -22/7*u - 1/7*u**2 - 40/7.
-(u + 2)*(u + 20)/7
Let j(u) = 10*u**2 + 137*u + 248. Let r(a) = -3*a**2 - 46*a - 84. Let y(p) = -4*j(p) - 14*r(p). Factor y(d).
2*(d + 2)*(d + 46)
Let u be -1*(20/(-6) + (-14)/252*-6). What is s in 0 + 3/5*s**u + 1/5*s - 1/5*s**4 - 3/5*s**2 = 0?
0, 1
Let d(t) be the third derivative of -t**7/6300 + 11*t**6/900 - 121*t**5/300 + 13*t**4/8 + 49*t**2. Let m(u) be the second derivative of d(u). Factor m(y).
-2*(y - 11)**2/5
Let n(f) be the third derivative of 0*f + 1/1848*f**8 + 0*f**3 - 8*f**2 - 7/330*f**5 + 0 - 1/231*f**7 + 1/66*f**4 + 3/220*f**6. What is j in n(j) = 0?
0, 1, 2
Factor 91/10*f - 9 - 1/10*f**2.
-(f - 90)*(f - 1)/10
Let p(b) be the second derivative of -b**6/45 + 4*b**5/5 - 83*b**4/9 + 88*b**3/3 - 121*b**2/3 - 12*b - 2. Find z, given that p(z) = 0.
1, 11
Let j(a) be the second derivative of 5*a**4/46 + 193*a**3/69 - 26*a**2/23 + 73*a. Determine c, given that j(c) = 0.
-13, 2/15
Let j be 8*4/5*5/(-2). Let a be (-6)/27*6*4/j. What is r in a*r**2 + 0 + 1/3*r = 0?
-1, 0
Let h(o) be the first derivative of o**6/8 + 109*o**5/20 + 193*o**4/4 - 327*o**3 + 580*o**2 - 400*o + 65. Solve h(g) = 0.
-20, 2/3, 1, 2
Factor 2/9*p**3 - 10/3*p + 8/9*p**2 - 4.
2*(p - 3)*(p + 1)*(p + 6)/9
Let z = 151 + -130. Suppose 0*l**3 - 36*l**5 - 51*l**3 - z*l**2 - 84*l**4 - 13*l**3 + 5*l**2 = 0. What is l?
-1, -2/3, 0
Suppose 4 - 14 = -2*l. Let -125*u**3 + 0*u**4 + 6*u**2 + 12*u**4 - 3*u**l + 110*u**3 = 0. Calculate u.
0, 1, 2
Let v be -15 + 2 - 2/((-8)/12). Let m be 2 + v/4 - (-45)/18. Factor 2/11*z**m - 20/11*z + 50/11.
2*(z - 5)**2/11
Let a(i) = -55*i**3 + 365*i**2 - 5*i - 365. Let h(x) = 8*x**3 - 52*x**2 + x + 52. Let g(z) = -3*a(z) - 20*h(z). Factor g(k).
5*(k - 11)*(k - 1)*(k + 1)
Let i = 85 - 85. Let k = -5/21 + 8/21. Factor 0*f**3 + i - k*f - 2/7*f**4 + 2/7*f**2 + 1/7*f**5.
f*(f - 1)**3*(f + 1)/7
Let r(g) = g + 1. Let f(a) = 2*a**3 + 5*a**2 - 5*a - 8. Let s = -2 - -20. Let u(q) = s*r(q) + 2*f(q). Factor u(b).
2*(b + 1)**2*(2*b + 1)
Let b(c) be the first derivative of -c**5/20 + c**4/12 + c**3/3 + 21*c + 1. Let l(x) be the first derivative of b(x). Factor l(g).
-g*(g - 2)*(g + 1)
Let y(n) be the first derivative of -30/7*n**2 - 9/28*n**4 + 30 + 24/7*n + 2*n**3. Factor y(z).
-3*(z - 2)**2*(3*z - 2)/7
Factor 1920*g + 25600 + 48*g**2 + 2/5*g**3.
2*(g + 40)**3/5
Let x(r) = 32 + 206*r**2 + 28 - 79*r**3 - 256*r + 4*r**4 + 76*r. Let b(j) = -j**4 + 16*j**3 - 41*j**2 + 36*j - 12. Let g(a) = 11*b(a) + 2*x(a). Factor g(z).
-3*(z - 2)**2*(z - 1)**2
Let r(c) = 43*c**2 - 1. Let q be r(-1). Factor -8 - 231*a**5 - q*a + 392*a**4 - 112*a**5 + 161*a**3 - 134*a**2 - 26*a.
-(a - 1)**2*(7*a + 2)**3
Let k be (-4)/(4*(-1)/2). Factor 6 + 10*b - k*b + b + 3*b**2.
3*(b + 1)*(b + 2)
Solve 4*p**2 + 28*p**3 + 161*p**2 - 789*p**2 + 118*p + 122*p - 64*p = 0 for p.
0, 2/7, 22
Let g(p) = -2*p + 11. Let l be g(4). Let z be 3 - 0 - (1 + -1 + l). Factor -1/3*r**4 + 2/3*r**3 - 1/3*r**2 + 0*r + z.
-r**2*(r - 1)**2/3
Let j(o) be the first derivative of -2*o**3/15 - o**2/5 + 24*o/5 - 36. Determine i so that j(i) = 0.
-4, 3
Factor 0*b + 0 - 1/5*b**2.
-b**2/5
Determine r, given that 2435*r**2 - 1250*r**2 - 282*r + r**3 + r**3 - 905*r**2 = 0.
-141, 0, 1
Let v(f) be the third derivative of f**5/510 + 22*f**4/51 + 1936*f**3/51 + 2*f**2 + 27. Factor v(t).
2*(t + 44)**2/17
Let s(g) = -10*g**2 + 39*g - 39. Let a(i) = i**2 - 4*i - 1. Let d(k) = 22*a(k) + 2*s(k). Let d(y) = 0. Calculate y.
-5, 10
Let p(a) be the first derivative of 5*a**3/3 - 95*a**2/2 + 90*a + 269. Factor p(u).
5*(u - 18)*(u - 1)
Let l(t) be the first derivative of -3*t**4/28 - t**3 - 9*t**2/7 - 160. Factor l(c).
-3*c*(c + 1)*(c + 6)/7
Factor -968/3 + 352*d - 30*d**2 + 2/3*d**3.
2*(d - 22)**2*(d - 1)/3
Let d be -2 - 0 - -7*(-3)/(-6). Let t(s) be the second derivative of -3/20*s**5 + 0*s**4 + d*s**3 - 2*s - 3*s**2 + 0. Factor t(c).
-3*(c - 1)**2*(c + 2)
Factor 27*g**2 - 126*g**2 - 126*g - 6*g**3 - 2*g**3 + 605*g**2.
-2*g*(g - 63)*(4*g - 1)
Find y such that -98*y - y**2 + 502*y + 20402 + 2*y**2 - 4*y**2 + 5*y**2 = 0.
-101
Determine h so that 1176*h**3 + 1215*h + 9*h**4 - 2778*h**2 + 541*h + 236*h - 399 = 0.
-133, 1/3, 1
Factor 16*o**2 + 5*o**3 + 1061 + 29*o**2 - 405*o - 386.
5*(o - 3)**2*(o + 15)
Let t(f) be the second derivative of -2*f**7/105 - 22*f**6/75 - 24*f**5/25 + 12*f**4/5 - 4*f - 27. Solve t(v) = 0.
-6, 0, 1
Let x be (0/(-2))/((-5 - -4) + 4). Suppose 32*y - 30*y = x. Factor y - 1/3*j**2 - 1/3*j**3 + 2/3*j.
-j*(j - 1)*(j + 2)/3
Suppose 0 = -b + 2. Suppose -16 = -b*n - 2*o, 6*n = n - 4*o + 35. Determine h, given that -3*h**3 + 4*h**2 - n*h**2 - 4*h**2 + 6*h = 0.
-2, 0, 1
Factor 13/2*i - 5/2*i**2 - 1/2*i**3 - 7/2.
-(i - 1)**2*(i + 7)/2
Let d(q) be the second derivative of -q**7/840 + q**6/480 + 12*q**2 + 12*q. Let v(h) be the first derivative of d(h). Solve v(m) = 0.
0, 1
Suppose -2*k = n + 1, -23 + 20 = 3*k. Let u(f) be the first derivative of -f**2 - n + 1/3*f**3 + 0*f. Factor u(i).
i*(i - 2)
Let g(j) be the third derivative of j**5/105 - 67*j**4/21 + 8978*j**3/21 + 11*j**2 + 5*j. Factor g(l).
4*(l - 67)**2/7
Let u(j) be the first derivative of -j**5/12 - 25*j**4/24 + 5*j**3 + 25*j**2/2 - 12. Let i(v) be the second derivative of u(v). Solve i(a) = 0 for a.
-6, 1
Suppose -5 = 4*g - 2*v - 19, -3*g + 24 = 3*v. Let q be (-8)/7*3 + 20/g. Solve -8/7*i - 4/7 - q*i**2 = 0 for i.
-1
Let g(x) be the first derivative of 3 + 3/2*x**4 + 2*x + 13/3*x**3 + 9/2*x**2. Solve g(p) = 0 for p.
-1, -2/3, -1/2
Let p(t) = 4*t**5 + t**4 + t**3 + 1. Let f(h) = -2*h**5 + 29*h**4 - 31*h**3 - 12*h**2 + 38*h - 15. Let x(g) = 2*f(g) - 2*p(g). Let x(n) = 0. What is n?
-1, 1, 8/3
Solve -1191/5*o**2 + 0 - 21/5*o**3 + 342/5*o = 0.
-57, 0, 2/7
Let p(j) be the second derivative of -j**4/54 + 10*j**3/27 - 25*j**2/9 - 102*j + 2. Factor p(z).
-2*(z - 5)**2/9
Let k(l) be the second derivative of 0*l**3 + 0 + 0*l**2 - 11*l + 1/10*l**5 - 1/30*l**6 - 1/12*l**4. Factor k(x).
-x**2*(x - 1)**2
