90*g**2 + c*g**3.
4*g**2*(g - 2)*(g - 1)**2
Let u(m) be the first derivative of -5*m**3/3 - 20*m**2 - 75*m + 6. Factor u(o).
-5*(o + 3)*(o + 5)
Factor -16*s**2 + 4*s**3 + s**3 - 48*s**2 + 24*s**2 + 35*s.
5*s*(s - 7)*(s - 1)
Let u(y) = -y - 1. Let j be u(8). Let b be 12/10*(-5)/j. Factor -2*q**2 + 2*q - 2/3 + b*q**3.
2*(q - 1)**3/3
Suppose 5*f - 56 + 6 = -5*h, 0 = -f - 3*h + 20. Suppose -3 = -x, 5*q + 5*x - f = 20. Factor 0*w**q + 0 + 0*w - 2/13*w**3 + 2/13*w**4.
2*w**3*(w - 1)/13
Let k be 4 + -2 + (-2 - -3). Let s(w) be the first derivative of -w**2 + 1/6*w**k + 6 + 2*w. Let s(z) = 0. What is z?
2
Let s(w) be the third derivative of -w**10/176400 - w**9/211680 + 2*w**5/15 + 19*w**2. Let p(d) be the third derivative of s(d). Factor p(m).
-2*m**3*(3*m + 1)/7
Let j(s) be the first derivative of s**5/10 - 3*s**4/4 + 5*s**3/6 + 6*s**2 - 18*s + 138. Factor j(n).
(n - 3)**2*(n - 2)*(n + 2)/2
Let o(h) be the third derivative of h**5/15 + 16*h**4 + 1536*h**3 + 266*h**2. Factor o(r).
4*(r + 48)**2
Let b = -211 - -236. Suppose 0 = -3*q - 5*y - 7 + 32, -4*q + 5*y - b = 0. Let -2/5*v**3 + q + 11/5*v**4 + 0*v - 9/5*v**5 + 0*v**2 = 0. What is v?
0, 2/9, 1
Let q(x) be the second derivative of x**7/4410 - x**6/630 + x**5/210 + 5*x**4/12 + 8*x. Let m(l) be the third derivative of q(l). Solve m(s) = 0.
1
Let z be -6 - ((-1)/(-2))/((50/160)/(-5)). Find t such that 0 - 2/17*t - 10/17*t**3 - 12/17*t**z = 0.
-1, -1/5, 0
Let z(i) = i**3 - i**2 - i - 1. Suppose 0 = 9*u - 0*u + 108. Let o(f) = 14*f**3 - 2*f**2 - 4*f - 12. Let l(h) = u*z(h) + o(h). Factor l(q).
2*q*(q + 1)*(q + 4)
Let g(t) = t**3 + t**2 - t. Let r(a) = 12*a**3 + 24*a**2 + 40*a. Suppose -72 = -4*y + y. Let n(k) = y*g(k) + r(k). Determine i, given that n(i) = 0.
-2/3, 0
Let p(z) be the first derivative of 1/18*z**4 + 2/15*z**5 + 1/27*z**6 + 0*z - 2/9*z**2 - 2/9*z**3 + 6. Determine i, given that p(i) = 0.
-2, -1, 0, 1
Let n(d) be the second derivative of d**5/4 + 25*d**4/6 + 55*d**3/2 + 90*d**2 + 3*d + 10. Factor n(a).
5*(a + 3)**2*(a + 4)
Let f = 97 + -95. Factor -10*i - 11*i - 8*i**2 + 5*i**f.
-3*i*(i + 7)
Let t(s) be the third derivative of -s**6/45 - 19*s**5/90 - 19*s**4/36 + 2*s**3/3 + 89*s**2. Factor t(j).
-2*(j + 2)*(j + 3)*(4*j - 1)/3
Let g(t) be the first derivative of -15/16*t**4 + 3/2*t**2 - 9 + 3/2*t**3 + 3/20*t**5 - 6*t. Factor g(l).
3*(l - 2)**3*(l + 1)/4
Suppose 1 = -3*k - 4*p + 4, 2*p + 6 = 0. Solve 10*y**5 + 9*y**3 - 12*y + 30*y**4 - 9*y**2 + 12*y**3 - y**k - 3*y**2 = 0 for y.
-2, -1, 0, 2/3
Let a(c) = c**3 + 33*c**2 + 241*c - 9. Let s be a(-11). Let 36/5*p**s + 8/5 - 36/5*p = 0. Calculate p.
1/3, 2/3
Suppose -4*a**2 - 13*a**2 - 6*a**2 - 3*a**3 + 60 + 48*a + 26*a**2 = 0. Calculate a.
-2, 5
Factor 1/6*m**3 + 0 + 1/6*m**2 + 0*m.
m**2*(m + 1)/6
Let v(l) be the second derivative of -l**4/24 + 19*l**3/12 + 23*l**2 + l - 231. Factor v(b).
-(b - 23)*(b + 4)/2
Let p = 206/415 + -8/83. Factor 0 + 0*a**3 + p*a**4 - 1/5*a**5 - 2/5*a**2 + 1/5*a.
-a*(a - 1)**3*(a + 1)/5
Let q(v) = 3 - 12*v + 2*v**2 + 0 + 2 - 2. Let k(f) = -f**2 + 11*f - 4. Let g(m) = -3*k(m) - 4*q(m). Factor g(t).
-5*t*(t - 3)
Let v(w) = w**3 + 18*w**2 - 115*w + 2. Let x be v(5). Let x*c + 4/3 - 4/3*c**2 = 0. Calculate c.
-1/2, 2
Let l(r) be the first derivative of -1/10*r**4 + 1/45*r**6 + 4/75*r**5 - 8/45*r**3 + 17 + 4/15*r**2 + 0*r. Factor l(i).
2*i*(i - 1)**2*(i + 2)**2/15
Let j(q) be the first derivative of 8/15*q**6 - 2/21*q**7 + 7*q + 2/3*q**4 - 8 - q**5 + 0*q**3 + 0*q**2. Let w(y) be the first derivative of j(y). Factor w(o).
-4*o**2*(o - 2)*(o - 1)**2
Suppose -9 = 2*q + 9. Let o = q + 12. Let o*f**3 - 3*f**2 - f**2 - 3*f - 4*f**3 + f**2 - 1 = 0. Calculate f.
-1
Suppose -2*a - 3*a + y + 20 = 0, 2*y = -5*a + 5. Suppose -a*o + 12 = -o. Find x, given that 3*x**2 - 4 + o - 6 - x**3 = 0.
-1, 2
Let u(b) be the third derivative of -20*b**2 + 1/150*b**5 + 1/120*b**4 - 1/525*b**7 + 0*b**3 - 1/1680*b**8 + 0*b + 0 + 0*b**6. Determine m, given that u(m) = 0.
-1, 0, 1
Let l(u) be the third derivative of -u**8/20160 + u**7/1680 - u**6/360 - u**5/2 + 17*u**2. Let a(b) be the third derivative of l(b). Let a(p) = 0. Calculate p.
1, 2
Let n be 30/8 + -6*(-5)/(-40). Factor 6 - n*h - 3*h**2 + 3*h**3 - 12 + 9*h**2.
3*(h - 1)*(h + 1)*(h + 2)
Let t = -75 + 79. Suppose h + 16 = 5*h. Find r such that 5*r**4 - r**h + 6*r**3 - r**t - 6*r - 3 = 0.
-1, 1
Let o(g) be the second derivative of g**4/4 - 7*g**3/6 - g**2 - 4*g. Let p(t) = 24*t**2 - 57*t - 16. Let i(j) = -51*o(j) + 6*p(j). Find l such that i(l) = 0.
-1/3, 2
Let v(b) be the second derivative of 2*b**5/45 + 23*b**4/54 - 2*b**3/9 + 21*b. Solve v(n) = 0.
-6, 0, 1/4
Let c(z) be the second derivative of -z**5/10 + 2*z**4/3 + 5*z**3/3 - 62*z - 1. Find a, given that c(a) = 0.
-1, 0, 5
Factor -5*b - 7*b + 8*b + 0*b - 2*b**2.
-2*b*(b + 2)
Let h(i) be the first derivative of i**6/360 + i**5/12 - 11*i**3/3 + 28. Let w(q) be the third derivative of h(q). Suppose w(j) = 0. What is j?
-10, 0
Let k be (-2)/(0 - 2) + 1. Factor 16 + 0*o**2 + 2*o**2 + k*o**2 + 15*o + o.
4*(o + 2)**2
Let p(t) = t**2 - 6*t + 6. Let s be p(5). Let y = 3 + s. Suppose 4*q**2 - 4*q**2 - y*q**2 = 0. What is q?
0
Let k(b) be the first derivative of 1/2*b**4 + 4/3*b**3 + b**2 - 4 + 0*b. Suppose k(r) = 0. Calculate r.
-1, 0
Let k(l) = -l**4 + l**2 - 1. Let g = 127 + -126. Let v(j) = -5*j**5 + 19*j**4 - 15*j**3 + j**2 - 1. Let w(t) = g*k(t) - v(t). Factor w(o).
5*o**3*(o - 3)*(o - 1)
Suppose -3*n + 21 = 5*k - 4*n, -2*n + 28 = 4*k. Suppose 0 = -0*r + 2*r - j - 3, j = k*r - 12. Factor 2*o + 0*o**3 - o**2 - 4*o**r + 3*o**3.
-o*(o - 1)*(o + 2)
Let u = 3215/33 - 1068/11. Let c(s) be the second derivative of -12*s + u*s**4 + 0*s**3 - 2*s**2 + 0. Factor c(o).
4*(o - 1)*(o + 1)
Let l(p) be the first derivative of p**8/2520 + p**7/1260 - p**6/270 + 5*p**3/3 - 11. Let b(t) be the third derivative of l(t). Solve b(j) = 0.
-2, 0, 1
Let a(j) be the first derivative of 4*j - 3*j**2 + 7 + 2/3*j**3. Factor a(p).
2*(p - 2)*(p - 1)
Let h be (2 - (-4)/4) + 1. Suppose k = h*g - 6, 3 = -5*k + 3*g + 7. Factor -11*c**3 + 2 - c**3 - k - 8*c**2.
-4*c**2*(3*c + 2)
Suppose 40*b + 16 = 44*b. Let c(m) be the first derivative of -5 + 0*m**2 - 1/9*m**3 + 1/12*m**b + 0*m. Factor c(l).
l**2*(l - 1)/3
Let g = 57 + -58. Let c be g + 26/21 - (-9)/21. Let 0*j**2 + 2/9*j - 16/9*j**4 - c*j**5 - 4/3*j**3 + 0 = 0. Calculate j.
-1, 0, 1/3
Find v such that 35*v**5 - 161*v**2 + 493*v**4 - 594*v**4 - 179*v**2 - 1841*v**3 - 1044*v**4 + 321*v**3 = 0.
-1, -2/7, 0, 34
Let i(y) be the first derivative of -8 + 0*y - 1/2*y**4 + 4/9*y**3 + 2/15*y**5 + 0*y**2. Factor i(z).
2*z**2*(z - 2)*(z - 1)/3
Let t = 15 - 9. Suppose 0 = -3*k - 0*k + t. What is r in -2 + k*r**3 - 6*r**3 - 2*r**2 - 2*r**4 + 2 = 0?
-1, 0
Let f(q) = -q**2 + q + 1. Let u(g) = 6*g**2 - 39*g + 33. Let y(o) = 6*f(o) - u(o). What is b in y(b) = 0?
3/4, 3
Let o(m) be the first derivative of m**3 + 24*m**2 - 51*m - 120. Factor o(a).
3*(a - 1)*(a + 17)
Let c be (-3 + 127/42)/(((-24)/(-4))/36). What is d in d - c*d**3 - 4/7 - 2/7*d**2 = 0?
-4, 1
Suppose -2*y + 3*w + 14 = 0, 2 = y + 2*y + 5*w. Solve y*m**4 - 67 + 67 - 10*m**5 + 0*m**4 = 0 for m.
0, 2/5
Suppose 55 = 31*h - 38. Let k = -156/11 + 2072/143. Find t, given that -10/13*t - k - 2/13*t**h - 8/13*t**2 = 0.
-2, -1
Let g(m) be the second derivative of m**5/4 + 5*m**4/6 - 25*m**3/6 - 15*m**2 - 66*m - 3. Find z such that g(z) = 0.
-3, -1, 2
Suppose -5*f + 37 = 22. Let u(a) = a**3 + 8*a**2 + 2. Let r be u(-8). Factor 4/5*b**r - b - 1/5*b**f + 2/5.
-(b - 2)*(b - 1)**2/5
Let b = -15/103 - -1468/9373. Let d = b + 177/455. Suppose -2/5*m**2 + 1/5*m**3 + d - 1/5*m = 0. Calculate m.
-1, 1, 2
Let r(b) = 47*b**2 - 305*b + 22. Let z(k) = -71*k**2 + 458*k - 31. Let f(i) = 8*r(i) + 5*z(i). Factor f(g).
3*(g - 7)*(7*g - 1)
Let n(t) = -8*t**5 + 4*t**4 + 18*t**3 + 34*t**2 + 28*t. Let v(c) = -7*c**5 + 3*c**4 + 17*c**3 + 33*c**2 + 27*c + 1. Let f(g) = 5*n(g) - 6*v(g). Factor f(a).
2*(a - 3)*(a + 1)**4
Suppose 22 = -4*v + 3*v + 5*g, 4*g = 3*v + 11. Let n(z) be the first derivative of 1/4*z**4 + 7/3*z**6 + 0*z**2 - 1 - 3/2*z**5 + 0*z**v + 0*z. Factor n(h).
h**3*(4*h - 1)*(7*h - 2)/2
Let a be (2 - -2)/(7 + -3). Let s be (-287)/(-84) - 3/4*a. Suppose -s - 2/3*f**4 - 26/3*f**2 - 8*f - 4*f**3 = 0. Calcu