1, 0, 2
Let i(p) be the first derivative of -p**9/1512 + p**8/840 + p**7/84 + p**6/60 - 41*p**3/3 + 5. Let k(o) be the third derivative of i(o). Factor k(x).
-2*x**2*(x - 3)*(x + 1)**2
Suppose 5*k + 2*t + 100 = -3*t, -k - 22 = -t. Let i = 23 + k. Factor -4*r - 4*r - r**i + 5*r + 5*r.
-r*(r - 2)
Let c(n) = n**4 - n - 1. Let k(u) = 60*u**3 + 110*u**2 - 415*u + 250. Let h(y) = 5*c(y) + k(y). Suppose h(z) = 0. What is z?
-7, 1
Let f(n) = 7*n - 72. Let j be f(11). Suppose 2*l = -5*m + 3*l + 5, 2*l = j*m. Solve -2/11*o**3 + 2/11 - 2/11*o**m + 2/11*o = 0 for o.
-1, 1
Let g(v) = v**3 + v**2. Let r(m) = -48*m**3 + 212*m**2 - 130*m - 40. Let a(k) = 3*g(k) + r(k). Factor a(p).
-5*(p - 4)*(p - 1)*(9*p + 2)
Suppose 4*v = -v. Find z such that 2*z**2 + 1 + 0 + 2*z**2 - 5*z + v = 0.
1/4, 1
Let g(b) be the third derivative of 1/80*b**5 + 0 + 7/8*b**3 - 1/4*b**4 + 0*b - 52*b**2. Determine x so that g(x) = 0.
1, 7
Let j be (7/(-2))/(2/(-16)). Suppose 5*n = 4*f - j, -5*f - n + 2 = n. Factor 6*b**3 + 4*b**2 - 4*b**f + 41*b**4 - 39*b**4.
2*b**3*(b + 3)
Let t(c) = 3*c + 10. Let r be t(6). Let x = r + -25. Factor 3*z**4 + 11*z**3 + 0*z**5 + x*z**5 - 14*z**3 - 3*z**2.
3*z**2*(z - 1)*(z + 1)**2
Let v(j) be the first derivative of 3*j**2 - 3*j - 1. Let a be v(1). Factor -28 - a*s**2 + 28 - 2*s - 3*s**4 + 4*s**4.
s*(s - 2)*(s + 1)**2
Let g(i) be the third derivative of i**7/2100 + 2*i**6/225 + 4*i**5/75 - 9*i**3/2 + 20*i**2. Let a(s) be the first derivative of g(s). Solve a(q) = 0 for q.
-4, 0
Let j(d) be the second derivative of -d**4/90 - d**3/9 - 4*d**2/15 - 637*d. Determine k so that j(k) = 0.
-4, -1
Let z(n) be the first derivative of -n**6/30 + n**5/15 - n**4/36 + 13*n + 31. Let r(y) be the first derivative of z(y). What is d in r(d) = 0?
0, 1/3, 1
Let r(y) be the first derivative of -y**4/2 + 22*y**3/3 - 32*y**2 + 56*y - 31. Solve r(n) = 0.
2, 7
Let x(d) be the third derivative of 1/20*d**5 - 1/2*d**3 + 0 - 1/120*d**6 - 11*d**2 + 0*d + 1/24*d**4. Factor x(o).
-(o - 3)*(o - 1)*(o + 1)
Let t(r) be the third derivative of 1/24*r**6 + 1/42*r**7 + 0 - 1/6*r**5 + 0*r + 0*r**4 - 9*r**2 + 0*r**3. Factor t(n).
5*n**2*(n - 1)*(n + 2)
Suppose 7 = x - 19. Let i = x + 55. Suppose 2*k**4 + 4*k**2 + 79*k**3 - 12*k**2 - i*k**3 + 8*k = 0. What is k?
-2, 0, 1, 2
Let w(b) = -b**3 - b + 1. Let x(s) be the first derivative of -s**5/5 + s**4/2 + s**3/3 + 4*s**2 - 5*s - 31. Let r(u) = 5*w(u) + x(u). Factor r(c).
-c*(c - 1)*(c + 1)*(c + 3)
Let w(s) = s**2 - 23*s + 20. Let i(j) = 15*j**2 - 369*j + 321. Let u(v) = 2*i(v) - 33*w(v). Find k, given that u(k) = 0.
1, 6
Suppose 5*w = w - 5*g + 245, 0 = -5*g - 15. Let y = 131/2 - w. Factor 0 - 1/2*q**2 + y*q.
-q*(q - 1)/2
Let u be 6/(-2) + 3 + 3. Find h, given that 2*h**3 + 4*h**4 + 2*h**5 - 2*h**u + 2*h**3 = 0.
-1, 0
Factor -12*b**2 + 1101*b**4 - 1097*b**4 + b**3 + 3*b**3 + 4*b**2.
4*b**2*(b - 1)*(b + 2)
Let t(b) be the first derivative of b**4/16 + 7*b**3/12 - b**2 - 48. Factor t(o).
o*(o - 1)*(o + 8)/4
Factor 520*r**2 + 5*r**5 + 161 + 240*r**3 + 560*r + 153 - 74 + 55*r**4.
5*(r + 2)**4*(r + 3)
Let f(g) be the first derivative of g**5/5 + g**4/2 + g**3/3 + 77. Factor f(o).
o**2*(o + 1)**2
Let k(r) be the first derivative of -r**4/36 + 5*r**3/27 + 13*r**2/18 + 7*r/9 - 51. Factor k(t).
-(t - 7)*(t + 1)**2/9
Suppose 14 = 6*r - 4. Let k be (-4 + 3)*(1 - (-2 - -3)). Factor 0*c - 1/2*c**r + 0*c**2 + k.
-c**3/2
Suppose 56 = 7*o - 63. Suppose 5 = -4*c + 5*c + n, 4*c + 3*n - o = 0. Determine l so that -4/3*l + 2/9*l**c + 2 = 0.
3
Let g(l) be the first derivative of -l**6/2 + 9*l**5/5 - 9*l**4/4 + l**3 - 110. Suppose g(w) = 0. What is w?
0, 1
Let v = 4053/5 - 810. Find o, given that 3/5*o - 3/5*o**2 - v*o**3 + 3/5 = 0.
-1, 1
Find c such that 1/2*c**3 - 2*c**2 - 11/2*c - 3 = 0.
-1, 6
Let f(v) be the third derivative of 7*v**5/12 - 15*v**4/8 + 5*v**3/3 + 2*v**2 + 17. Factor f(q).
5*(q - 1)*(7*q - 2)
Let d(h) be the second derivative of h**7/14 + 4*h**6/5 - 27*h**5/20 - 76*h. Factor d(k).
3*k**3*(k - 1)*(k + 9)
Let t(g) be the second derivative of -g**4/4 + 6*g**2 + 44*g. Factor t(l).
-3*(l - 2)*(l + 2)
Let k = -16 + 19. Factor -k + 2 + 3*u**2 + 6*u + 1.
3*u*(u + 2)
Let q(x) be the second derivative of -x**8/1120 - 3*x**7/1120 - x**6/480 - 5*x**3/6 + 5*x. Let v(l) be the second derivative of q(l). Factor v(f).
-3*f**2*(f + 1)*(2*f + 1)/4
What is t in -32000 - 7*t**4 + 88*t**3 + 3*t**4 + 36800*t - 5040*t**2 + 156*t**3 = 0?
1, 20
Let q(j) be the first derivative of j**6/15 - j**5/15 - 5*j**4/6 - 4*j**3/3 - 9*j**2 - 22. Let h(d) be the second derivative of q(d). Find v such that h(v) = 0.
-1, -1/2, 2
Suppose -3*z = -2*o - 8, 4*z - 4 = -z + o. Suppose -4*f**5 + 2*f - 4*f**2 + 25*f**4 + 2*f**5 - 21*f**4 + z*f = 0. Calculate f.
-1, 0, 1
Suppose -o - 42 = -42. Let g(v) be the second derivative of -1/120*v**6 + 0*v**5 + 0 + o*v**2 + v + 1/12*v**3 + 1/16*v**4. Find m, given that g(m) = 0.
-1, 0, 2
Let u(h) be the second derivative of -9/20*h**5 - 2/3*h**4 + 4/15*h**6 + 5/42*h**7 + 0*h**2 + 2/3*h**3 - 5*h + 0. Let u(o) = 0. What is o?
-2, -1, 0, 2/5, 1
Let i(m) be the third derivative of 1/3*m**3 - 1/120*m**6 + 16*m**2 + 1/24*m**4 + 1/210*m**7 - 1/20*m**5 + 0*m + 0. Factor i(q).
(q - 2)*(q - 1)*(q + 1)**2
Let g(q) be the first derivative of 2*q + 20 - 4/3*q**2 + 2/9*q**3. Find n, given that g(n) = 0.
1, 3
Let q(m) be the first derivative of m**7/168 + m**6/24 + 3*m**5/80 - 3*m**4/16 + 2*m - 2. Let d(k) be the first derivative of q(k). Factor d(f).
f**2*(f - 1)*(f + 3)**2/4
Let h = 911 + -6371/7. Suppose 0 + 3/7*t**3 - h*t**2 + 0*t = 0. What is t?
0, 2
Let b be (2/(-16) + 65/2600)*-18. Determine i so that -12/5*i**3 + 6/5*i**5 - 9/5*i**4 + 6/5*i + b*i**2 + 0 = 0.
-1, -1/2, 0, 1, 2
Let r be 1 - 4 - (-2 + -1). What is b in -2/3*b**4 + 0*b + r - 10/3*b**2 + 4*b**3 = 0?
0, 1, 5
Find d such that -2/9*d**2 - 10082/9 + 284/9*d = 0.
71
Let j(f) be the second derivative of -f**4/54 + f**3/9 - 2*f**2/9 - 39*f. Suppose j(g) = 0. What is g?
1, 2
Suppose 0 = -o - 4 + 19. Suppose 2*c - 7*c = -o. What is n in -4*n**2 + 4*n**c + 84 - 84 = 0?
0, 1
Factor -142/9 - 2/9*f**2 + 16*f.
-2*(f - 71)*(f - 1)/9
Let m(o) be the third derivative of -1/660*o**6 - 8/33*o**3 + 0 - 1/11*o**4 + 6*o**2 - 1/55*o**5 + 0*o. Factor m(j).
-2*(j + 2)**3/11
What is t in -32460*t**2 + 130*t + 32455*t**2 - 1125 - 40*t + 60*t = 0?
15
Suppose 0 = k + 4*x - 19, -3*x - 2 + 5 = -3*k. Suppose k*o = -0 + 6. Factor 1/2*j**5 - 1/2*j**3 + 0*j + 0 - 1/2*j**o + 1/2*j**4.
j**2*(j - 1)*(j + 1)**2/2
Let s(t) = -t**3 - 23*t + 15*t**2 + 7*t**2 + 40 + 4. Let y be s(21). Factor 1/9*c**y - 2/9*c + 0.
c*(c - 2)/9
Let y(r) be the first derivative of -r**7/1680 + r**6/288 - r**5/480 - r**4/48 + 7*r**3/3 + 3. Let j(u) be the third derivative of y(u). Factor j(b).
-(b - 2)*(b - 1)*(2*b + 1)/4
Let v be (12 - 14)/6*0. Let x(q) be the third derivative of -2/3*q**5 + 0*q**3 + v + 5/6*q**4 + 5*q**2 - 7/24*q**6 + 0*q + 5/42*q**7. What is a in x(a) = 0?
-1, 0, 2/5, 2
Factor -80*i - 200/3 - 14*i**2 - 2/3*i**3.
-2*(i + 1)*(i + 10)**2/3
Suppose -304*m**3 + 308*m**3 + 11*m**2 + 7*m**2 + 8*m = 0. Calculate m.
-4, -1/2, 0
Find k, given that 2*k**2 + 0*k + 1/3*k**3 + 0 = 0.
-6, 0
Let l be (-352)/154 + (34 - 30). Solve -10/7 - 2/7*b**2 - l*b = 0 for b.
-5, -1
Let y(a) be the second derivative of a**4/36 - 2*a**3/9 - 6*a - 1. Factor y(n).
n*(n - 4)/3
Let u(w) be the first derivative of -w**5/20 + w**4/4 - w**3/3 - 27*w - 14. Let p(i) be the first derivative of u(i). Factor p(z).
-z*(z - 2)*(z - 1)
Let n(x) be the first derivative of -x**8/2240 + 3*x**3 - 6. Let l(r) be the third derivative of n(r). Factor l(b).
-3*b**4/4
Let a be 7 + (-6 + 35/(-42) - (4 - 4)). Suppose 11/6*h + 1/2 + h**3 - a*h**4 + 7/3*h**2 - 1/6*h**5 = 0. Calculate h.
-1, 3
Let z(n) be the first derivative of -3*n**5/5 + 27*n**4/4 + 33*n**3 + 105*n**2/2 + 36*n - 143. Let z(m) = 0. What is m?
-1, 12
Let i(s) = -10*s**2 - 215*s + 460. Let v(b) = -b**2 - 24*b + 51. Let y(a) = -6*i(a) + 55*v(a). Solve y(o) = 0.
3
Let f(d) = 3*d**2 + 21*d + 24. Let n(a) = a**2 + 2. Let m(q) = f(q) - 2*n(q). Factor m(o).
(o + 1)*(o + 20)
Let w be 290/96 - 12/(-20)*-5. Let f(g) be the third derivative of 0*g**3 + 0 - 8*g**2 - w*g**5 - 1/48*g**4 - 1/120*g**6 - 1/840*g**7 + 0*g. Factor f(j).
-j*(j + 1)*