)*(x + 1)**2/3
Let u(y) be the second derivative of -y**6/210 - y**5/70 + y**4/28 - 8*y. Determine b, given that u(b) = 0.
-3, 0, 1
Let w be 4/(-18) + 80/36. Factor -40*t**2 - 41*t**2 + 87*t**2 - 2*t + w*t**4 - 6*t**3.
2*t*(t - 1)**3
Let g(m) = -m**3 + 10*m**2 - 2*m + 20. Let h be g(10). Let z(k) be the first derivative of -1/5*k**5 - k + h*k**2 + 0*k**4 + 2 + 2/3*k**3. Factor z(i).
-(i - 1)**2*(i + 1)**2
Suppose 25*q - 96 = -46. Suppose 2/9*v**q - 4/9*v + 2/3*v**3 + 0 = 0. What is v?
-1, 0, 2/3
Let f(q) be the first derivative of 175*q**4/12 + 40*q**3/3 - 85*q**2/6 - 10*q - 66. Solve f(j) = 0 for j.
-1, -2/7, 3/5
Let m = -151/4 + 2269/60. Let n(h) be the first derivative of -7 - m*h**2 + 4/15*h - 2/45*h**3. What is z in n(z) = 0?
-2, 1
Let f = -596715/11 - -54031. Let v = f + 216. Suppose v + 4/11*d + 2/11*d**2 = 0. What is d?
-1
Let d be (2/4 + -1)*-8. Let h = 28 + -24. Factor d*a**3 - 2*a + 3*a - h*a**2 - 3*a**3 + 3*a.
a*(a - 2)**2
Let k(l) be the second derivative of -l**4/4 + 3*l**3 - 12*l**2 - l + 7. Factor k(p).
-3*(p - 4)*(p - 2)
Let h(r) be the second derivative of r**5/40 + 7*r**4/8 - 4*r - 1. Factor h(w).
w**2*(w + 21)/2
Let j(y) be the third derivative of 55/24*y**4 + 7/24*y**6 + 0*y + 11*y**2 + 4/3*y**5 + 0 + 5/3*y**3. Factor j(q).
5*(q + 1)**2*(7*q + 2)
Let p(l) be the third derivative of l**5/30 + 7*l**4/3 + 9*l**3 + 143*l**2. What is i in p(i) = 0?
-27, -1
Let i(g) be the third derivative of 0 - 1/4*g**4 + 0*g + 0*g**3 - 12*g**2 - 1/20*g**5. Factor i(t).
-3*t*(t + 2)
Let s(c) be the second derivative of -2*c**6/15 - 2*c**5/5 + 8*c**4/3 + 13*c + 1. Factor s(v).
-4*v**2*(v - 2)*(v + 4)
Factor 2/5 - 13/5*j + 6/5*j**2.
(j - 2)*(6*j - 1)/5
Factor -17*q - 2403 - 4*q**2 + 14947 + 7*q**2 - 2*q**2 - 207*q.
(q - 112)**2
Let d(y) = 3*y + 23. Suppose 0 = 6*c + 2*c + 56. Let r be d(c). Solve -2*v**2 + 2/3*v**3 - 2/3 + r*v = 0 for v.
1
Suppose 17*p = 12*p + 120. Suppose -3*j + 2 + 17 = 2*g, -3*j - 3*g + p = 0. Factor -7*x**3 + 5*x**2 + x**j - 81*x + 79*x + 3*x**2.
-2*x*(x - 1)*(3*x - 1)
Suppose 0 = -2*d + 5*d + 27. Let h = 14 + d. Factor 28*a**2 - h*a**3 + 3*a**3 + 12 + 6*a**3 + 24 + 60*a.
4*(a + 1)*(a + 3)**2
Let w = -1283/155100 + 6/517. Let z(t) be the third derivative of 0*t + 0*t**3 + 1/150*t**5 - w*t**6 + 0 - 5*t**2 + 0*t**4. Factor z(p).
-2*p**2*(p - 1)/5
Let v be ((4 - 5)/3 - 12/72)*0. Find u, given that v + 4/7*u**2 + 0*u + 4/7*u**3 = 0.
-1, 0
Suppose 18*k - 24 = 10*k. Suppose 0 = -v + 8 - 3. Factor 5/2*l**k + 0 + 5/2*l**2 - v*l.
5*l*(l - 1)*(l + 2)/2
Factor 26*l**2 - 119 + 222*l - 100 + 24*l**2 - 53*l**2.
-3*(l - 73)*(l - 1)
Let v(o) be the first derivative of o**6/21 - 3*o**4/14 - 4*o**3/21 + 126. Suppose v(d) = 0. What is d?
-1, 0, 2
Let -24 - t - 2*t**2 - 4 + 19*t = 0. What is t?
2, 7
Let j(y) be the third derivative of 1/24*y**6 - 5/24*y**4 + 1/12*y**5 - 31*y**2 - 5/6*y**3 + 0 + 0*y. Factor j(m).
5*(m - 1)*(m + 1)**2
Let o(f) be the third derivative of -f**5/300 + 7*f**4/60 - 49*f**3/30 - 72*f**2. Solve o(y) = 0.
7
Find m, given that -903 + 1252 - 15*m**3 - 1349 + 290*m**2 - 1300*m = 0.
-2/3, 10
Let z be (-1)/(-5) - (-32)/40. Suppose -20*i + z + 2 - i**2 + 22*i = 0. Calculate i.
-1, 3
Suppose 59 - 8 = 17*j. Let b(t) be the first derivative of -t**4 + 2*t**2 + 4/5*t**5 + 1 - 4/3*t**j + 0*t. Find x such that b(x) = 0.
-1, 0, 1
Let b = -32380 + 32382. Factor -8/3*t + 0 - 4/3*t**b.
-4*t*(t + 2)/3
Suppose 0 = -17594*a + 17577*a. Determine l so that a + 2/7*l**2 + 2/7*l = 0.
-1, 0
Let g(d) = 3*d**3 - 28*d**2 + 11*d - 22. Let o be g(9). Let l be 1 - ((-5 + o)/3 - 0). Factor 10/9*z**2 + 2/9*z**l + 0 - 4/9*z - 8/9*z**3.
2*z*(z - 2)*(z - 1)**2/9
Let l(x) be the second derivative of 1/660*x**6 + 0*x**3 + 0*x**4 + 3/2*x**2 + 13*x + 0 - 1/330*x**5. Let c(k) be the first derivative of l(k). Solve c(f) = 0.
0, 1
Factor 12355*n**2 - 34*n - 28 - 6254*n**2 + 19*n**3 - 3*n**3 + 4*n**4 + 114*n - 6173*n**2.
4*(n - 1)**3*(n + 7)
Let t = -32 + 45. Suppose 5*h - 12 = t. Find c such that -h*c + 4*c - 2*c**2 - 2 - 3*c = 0.
-1
Let l(s) be the first derivative of -1/9*s**3 - 12 + 0*s - 1/24*s**4 + 1/4*s**2. Factor l(g).
-g*(g - 1)*(g + 3)/6
Let m be ((-2)/4)/((66/(-24))/11). Factor 0 + 0*d + 2/11*d**m - 2/11*d**4 + 0*d**3.
-2*d**2*(d - 1)*(d + 1)/11
Let l(o) be the second derivative of 2*o**7/21 + 17*o**6/30 + 4*o**5/5 + o**4/4 - 135*o. Factor l(g).
g**2*(g + 1)*(g + 3)*(4*g + 1)
Let n(l) = 2*l**3 - 2*l. Let y(r) = -r**4 - 29*r**3 - 18*r**2 + 20*r. Let b(x) = -30*n(x) - 3*y(x). Factor b(k).
3*k**2*(k + 3)*(k + 6)
Let m(d) be the first derivative of d**6/2 - 8*d**5/5 - 14*d**4 - 32*d**3/3 + 24*d**2 + 20. Determine v, given that m(v) = 0.
-2, 0, 2/3, 6
Let d(u) = -u - 1. Let n be d(-3). Determine t so that 23*t + 3*t**n + 27*t - 59*t = 0.
0, 3
Let d(g) be the first derivative of 0*g + 13/20*g**5 + g**3 - 1 - 1/10*g**6 + g**2 - 11/8*g**4. Let k(z) be the second derivative of d(z). Factor k(a).
-3*(a - 2)*(a - 1)*(4*a - 1)
Let o(r) be the second derivative of 32*r + 3/2*r**4 + 1/10*r**6 + 1 + 6/5*r**5 - 20*r**3 + 75/2*r**2. Suppose o(k) = 0. What is k?
-5, 1
Let g be 1 + 1 - 9/((-405)/1240). Let z = 1307/36 - g. Let -33/4*j - z*j**2 - 3/2 = 0. Calculate j.
-1, -2/9
Let x(a) be the second derivative of -a**4/4 + 11*a**3/2 + 39*a**2 - 129*a. Solve x(l) = 0 for l.
-2, 13
Let l(g) be the first derivative of -27 - 4/11*g + 3/11*g**4 + 14/33*g**3 - 1/11*g**2. Determine y so that l(y) = 0.
-1, -2/3, 1/2
Let z(q) = q**2 + 2*q + 1. Let j(c) = c**2 + c. Let s(n) = 2*n - 19. Let o be s(12). Let u(b) = o*z(b) - 10*j(b). Factor u(g).
-5*(g - 1)*(g + 1)
Let q(z) be the first derivative of 12 + 4/3*z - 1/9*z**3 + 0*z**2. Find m, given that q(m) = 0.
-2, 2
Let x(m) be the first derivative of -10*m**3 - 45/4*m**4 - 5/2*m**2 - 23 + 0*m - 4*m**5. Factor x(w).
-5*w*(w + 1)**2*(4*w + 1)
Suppose 0 = k - 5*k + 2*n + 16, 4*n = 0. Let v(r) be the third derivative of -5*r**2 + 0*r**3 + 0*r + 0 + 1/15*r**5 - 1/60*r**6 - 1/12*r**k. Factor v(x).
-2*x*(x - 1)**2
Let s be 14/56 - (1 + 21/(-12)). Let r(a) be the first derivative of 7/6*a**2 - 2/3*a - 5/9*a**3 + s. Find g such that r(g) = 0.
2/5, 1
Factor 0 - 2/9*a**2 + 64/9*a.
-2*a*(a - 32)/9
Let r be (5 - 5)/(-2)*3/6. Factor 0*t**4 - 3/7*t - 6/7*t**3 - 8/7*t**2 + r + 1/7*t**5.
t*(t - 3)*(t + 1)**3/7
Factor -59/3*t**2 - 899/3*t - 841/3 - 1/3*t**3.
-(t + 1)*(t + 29)**2/3
Let z be (-3)/(-9) + (-44)/(-12). Suppose 3*h**3 + 5*h**3 + 5*h**4 + h**5 - 3*h**z - 7*h**3 = 0. What is h?
-1, 0
Suppose -5*j = -90 - 10. Let x = j - 77/4. Solve x*p**3 + 0*p + 0 - 1/2*p**2 - 1/4*p**4 = 0 for p.
0, 1, 2
Let u(x) be the second derivative of x**6/30 + 3*x**5/5 - 7*x**4/3 + 408*x - 2. Factor u(i).
i**2*(i - 2)*(i + 14)
Suppose -3*f + 2 + 13 = 0. Suppose d + 60 = f*d. Factor -1 + 0*k**3 + 2*k**2 - 11*k - 6*k**3 + d*k**2 + 3.
-(k - 2)*(2*k - 1)*(3*k - 1)
Let n(f) be the third derivative of 13*f**6/240 - 17*f**5/120 - 11*f**4/24 + 2*f**3/3 - 78*f**2 + 3*f. Solve n(x) = 0 for x.
-1, 4/13, 2
Suppose u - 5*u + 10*u**5 - 784*u**2 + 19*u**4 - 9*u**3 + 768*u**2 + 0*u = 0. What is u?
-2, -1/2, -2/5, 0, 1
Let z(b) be the first derivative of 2*b**6/3 - 4*b**5/5 - 3. What is l in z(l) = 0?
0, 1
Let x(o) be the first derivative of o**5/15 - o**4/6 - 8*o**3/9 - 214. Let x(j) = 0. What is j?
-2, 0, 4
Find q such that -20/3*q + 32/3 + 2/3*q**2 = 0.
2, 8
Let p(a) be the second derivative of -a**6/10 - 93*a**5/10 - 1021*a**4/4 - 930*a**3 - 1350*a**2 + 53*a - 2. Factor p(u).
-3*(u + 1)**2*(u + 30)**2
Let m(g) be the first derivative of -5*g**6/6 - 4*g**5 - 25*g**4/4 - 10*g**3/3 - 27. Factor m(y).
-5*y**2*(y + 1)**2*(y + 2)
Factor 51/2*d + 0 + 53/2*d**3 - 103/2*d**2 - 1/2*d**4.
-d*(d - 51)*(d - 1)**2/2
Let p(w) be the third derivative of w**7/4200 + w**6/600 + w**5/300 - w**3/2 + 6*w**2. Let a(i) be the first derivative of p(i). Let a(v) = 0. What is v?
-2, -1, 0
Suppose 5*z - 26 = z + p, -3*p = 4*z - 34. Let u(x) = 11*x - 75. Let b be u(z). Solve 1/4*h**b + 3/4 + h = 0 for h.
-3, -1
Let k(y) = -y**2 - 1. Let n(d) = 71*d**2 - 726*d - 31*d**2 + 303 + 2361 - 2*d**3 + 28*d**2. Let g(b) = 2*k(b) + n(b). Factor g(a).
-2*(a - 11)**3
Let k(a) be the third derivative of -a**9/181440 + a**8/20160 + a**7/15120 - a**6/720 - a**5/10 + 4*a**2. Let i(r) be the third derivative of k(r). Fac