*l**2*(l + 1)*(l + 3)
Let w = 158 - 78. Let -661*h**4 - 920*h**2 - 146*h**4 + 214*h - 623*h**4 - 605*h**5 - 954*h + 3775*h**3 - w = 0. Calculate h.
-4, -2/11, 1
Let a(l) = 20*l**2 + 32*l - 88. Let i(r) = -2*r**2 - r + 3. Let m(n) = a(n) + 8*i(n). Factor m(u).
4*(u - 2)*(u + 8)
Let z(h) be the second derivative of -5*h**4/66 + 47*h**3/33 - 18*h**2/11 + 46*h. Factor z(u).
-2*(u - 9)*(5*u - 2)/11
Let o = 9037 + -9035. Factor 1/7*g**o - 4/7 + 0*g.
(g - 2)*(g + 2)/7
Suppose 10 = z + 2*c, 7 + 3 = z + 3*c. Find o such that -o**3 + z*o**4 - 4*o**3 - 5*o**4 + 0*o**4 = 0.
0, 1
Let o(y) be the third derivative of y**7/11340 - y**6/648 + y**5/90 - 5*y**4/6 - 9*y**2 + 1. Let r(p) be the second derivative of o(p). Factor r(j).
2*(j - 3)*(j - 2)/9
Let x(v) be the second derivative of -v**5/80 + 5*v**4/48 - v**3/6 + 2*v - 161. Find i, given that x(i) = 0.
0, 1, 4
Let k(r) be the first derivative of -r**4/8 + 11*r**3/6 + 7*r**2/2 - 12*r + 11. Let k(j) = 0. What is j?
-2, 1, 12
Factor -14/3*t + 1/3*t**2 - 5.
(t - 15)*(t + 1)/3
Let a = 32837/7785 - 28/1557. Factor -a*f - 3/5*f**2 - 18/5.
-3*(f + 1)*(f + 6)/5
Solve 32/3*a + 0 + 4*a**2 + 1/3*a**3 = 0.
-8, -4, 0
Let q be (19 - 21)*15/(-33). Factor -2/11*a**2 - 8/11 - q*a.
-2*(a + 1)*(a + 4)/11
Let p(m) be the third derivative of m**7/840 - m**6/240 - 59*m**5/240 + 5*m**4/8 + 75*m**3/2 + m**2 + 101. What is l in p(l) = 0?
-5, 6
Let w(g) be the second derivative of -g**7/294 + g**6/30 + g**5/5 + 5*g**4/21 + 101*g. Find u such that w(u) = 0.
-2, -1, 0, 10
Factor 2/3*n**3 - 18*n**2 + 34*n - 50/3.
2*(n - 25)*(n - 1)**2/3
Find o such that 0 + 0*o - 12/7*o**2 + 6/7*o**3 = 0.
0, 2
Let p(l) be the second derivative of l**6/90 - l**5/20 + 2*l**3/9 - 2*l + 30. Suppose p(a) = 0. Calculate a.
-1, 0, 2
Let n(k) be the second derivative of 3*k**4 - 8*k**3/3 + 46*k. Factor n(f).
4*f*(9*f - 4)
Let a(k) = 5*k**3 - 3*k**2 + 6*k + 4. Suppose -5*s = -5*f - 0 + 5, 2*f = 3*s + 1. Let i(w) = w**3 + w. Let l(y) = s*a(y) - 6*i(y). Factor l(q).
-(q - 1)*(q + 2)**2
Let a(s) be the first derivative of s**6/420 + s**5/210 - s**4/84 - s**3/21 - 3*s**2/2 - 8. Let l(h) be the second derivative of a(h). Solve l(j) = 0.
-1, 1
Let o be 0 + -1 + -3 - -6. Suppose -4*r + 10 = o*b, -15 = 3*r - 5*b + 10. Suppose r + 2/3*m**3 + 2/3*m**4 + 2/9*m**5 + 0*m + 2/9*m**2 = 0. What is m?
-1, 0
Let b(y) be the second derivative of -y**7/4620 + y**6/495 + y**5/132 - 7*y**3/3 + 2*y. Let v(p) be the second derivative of b(p). What is d in v(d) = 0?
-1, 0, 5
Let u(q) be the third derivative of q**6/80 + 69*q**5/40 + 153*q**4/2 + 289*q**3 + 1002*q**2. Factor u(y).
3*(y + 1)*(y + 34)**2/2
Let v(t) = 2*t**3 - 7*t**2 - 4*t + 13. Let m be v(5). Let g be 8/(-52) + m/104. Factor g*k**2 + 1/4*k**3 - 1/4*k - 1/2.
(k - 1)*(k + 1)*(k + 2)/4
Let d(u) = -7*u**4 - 14*u**3 + 11*u**2 + 14*u - 5. Let z(n) = -n**4 + n**2 + 1. Let p = -27 + 25. Let i(j) = p*d(j) - 2*z(j). Let i(r) = 0. What is r?
-2, -1, 1/4, 1
Suppose -2*k = 0, -3*k = -3*h + 2*k + 9. Let m(w) = -w - 1. Let i(p) = -3*p**2 + 3*p - 6. Let s(u) = h*m(u) - i(u). Find v, given that s(v) = 0.
1
Factor -20*x**2 - 4*x**2 - 4*x**4 + 3*x**2 + 3*x**5 + 13*x**4 + 54*x - 24 + 11*x**3 - 32*x**3.
3*(x - 1)**3*(x + 2)*(x + 4)
Let p(u) be the first derivative of u**3/3 - 29*u**2 + 841*u + 67. Suppose p(y) = 0. What is y?
29
Let i be (-2)/15 - (-124)/30. Suppose w - o = -0 - 2, -o - 7 = -i*w. Determine k, given that -4/3*k + 0*k**w + 2/3*k**4 - 2*k**2 + 0 = 0.
-1, 0, 2
Let h(u) be the first derivative of -u**7/560 + u**5/160 - 10*u**2 - 16. Let g(r) be the second derivative of h(r). Let g(o) = 0. Calculate o.
-1, 0, 1
Let l(i) be the second derivative of 0*i**2 - 1/6*i**3 - 1/10*i**5 - 4*i + 0 - 3/8*i**4. Let l(c) = 0. What is c?
-2, -1/4, 0
Factor -30*s**2 - 5*s**2 + 270*s - 148 - 95 - 23*s**2 - 17*s**2.
-3*(5*s - 9)**2
Let p be 18336/(-40)*(-30)/28. Let w = p + -490. Solve 0 - 2/7*c + w*c**3 + 6/7*c**2 = 0 for c.
-1, 0, 1/4
Let f(a) be the third derivative of -a**8/1512 - 4*a**7/945 - a**6/180 + 4*a**2 - 4. Let f(v) = 0. Calculate v.
-3, -1, 0
Let k(x) be the second derivative of x**4/30 + 92*x**3/15 + 2116*x**2/5 + 29*x - 1. Determine n, given that k(n) = 0.
-46
Let w(v) = 7*v - 22. Let q be w(4). What is t in -q*t**3 - 8*t + 0*t - 2*t**2 + 9*t**3 + t - 2 = 0?
-1, -1/3, 2
Solve -68694/17*s - 2/17*s**3 - 2450086/17 - 642/17*s**2 = 0.
-107
Let f(c) be the third derivative of -c**6/420 - 29*c**5/210 - 20*c**4/21 - 52*c**3/21 - 589*c**2. Let f(d) = 0. Calculate d.
-26, -2, -1
Find b, given that 33/2*b**2 - 3/2*b**3 - 27*b + 0 = 0.
0, 2, 9
Let i = -61313/5 - -12303. Suppose 98/5*g**5 + 124/5*g**2 - i*g**3 - 28*g**4 + 16/5 + 104/5*g = 0. What is g?
-1, -2/7, 1, 2
Let x(v) be the second derivative of -5/3*v**3 + 5/12*v**4 + 0 + v + 3/4*v**5 - 1/6*v**6 + 0*v**2 - 5/42*v**7. Solve x(g) = 0 for g.
-2, -1, 0, 1
Let q = 783 - 779. Let g(z) be the first derivative of 3 + q*z**3 - 3*z**4 - 2*z**2 + 4/5*z**5 + 0*z. Factor g(t).
4*t*(t - 1)**3
Let y(k) be the first derivative of -k**3/3 - 71*k**2 - 5041*k - 400. Suppose y(l) = 0. Calculate l.
-71
Let x = -3/868 - -5223/4340. Factor 6/5*y**2 + 0*y**3 - x*y**4 - 3/5*y + 3/5*y**5 + 0.
3*y*(y - 1)**3*(y + 1)/5
Determine f, given that -148*f**5 + 154*f**5 + 2 + 60*f**2 + 14 + 3*f**4 - 56*f - 19*f**4 - 10*f**3 = 0.
-2, 2/3, 1, 2
Let n(g) be the second derivative of -g**4/27 - 7*g**3/27 - 5*g**2/9 - 63*g. Find c, given that n(c) = 0.
-5/2, -1
Let h(b) be the second derivative of 1/30*b**4 + 1/100*b**5 - 2/15*b**3 - 3*b + 0 - 4/5*b**2. Factor h(x).
(x - 2)*(x + 2)**2/5
Let i = -122 - -125. Let u(n) be the second derivative of 3/80*n**5 + 0*n**i - 1/16*n**4 - 4*n + 0 + 0*n**2. Solve u(z) = 0.
0, 1
Determine g, given that 16 + 27/10*g - 1/10*g**2 = 0.
-5, 32
Let k(j) be the third derivative of 0*j**3 + 3/160*j**6 - 3/280*j**7 + 0*j**4 + 0*j + 1/448*j**8 - 1/80*j**5 + 12*j**2 + 0. Suppose k(b) = 0. Calculate b.
0, 1
Suppose -19 = 2*a + 5*t, -3*a = -5*a - 4*t - 20. Let r be 18/27 + ((-13)/a - 1). Suppose 1/2 + 1/4*p**2 - r*p = 0. Calculate p.
1, 2
Let u(i) = 2*i**3 + 42*i**2 - 464*i. Let z be u(8). Factor -y**4 + z*y + 3/2*y**2 - 1/2*y**3 + 0.
-y**2*(y - 1)*(2*y + 3)/2
Let u(w) be the first derivative of 2*w**5/5 - 5*w**4/2 - 14*w**3 + 85*w**2 + 200*w + 38. Factor u(a).
2*(a - 5)**2*(a + 1)*(a + 4)
Suppose 13*b + 2*b**2 + 0*b**2 - 8 - 40*b + 12*b = 0. What is b?
-1/2, 8
Let u(r) = 8*r**4 - 6*r**3 + r**2 + 15*r - 3. Let b(z) = 14*z**4 - 14*z**3 + z**2 + 29*z - 5. Let j(a) = -3*b(a) + 5*u(a). Factor j(m).
-2*m*(m - 6)*(m - 1)*(m + 1)
What is i in -16/13*i**2 + 4/13*i**3 - 18/13 + 2/13*i**4 - 36/13*i = 0?
-3, -1, 3
Factor -y + 15/8*y**2 + 1/8*y**4 - 2 + y**3.
(y - 1)*(y + 1)*(y + 4)**2/8
Let g(r) be the second derivative of -7*r**7/15 - 28*r**6/5 - 16*r**5/25 + 824*r**4/15 + 304*r**3/5 + 128*r**2/5 - 118*r. Solve g(s) = 0 for s.
-8, -2, -2/7, 2
Determine w, given that 2/3*w**5 - 24*w**3 + 70/3*w + 32/3*w**4 + 4/3*w**2 - 12 = 0.
-18, -1, 1
Let j(u) = 3*u - 12. Let h be j(5). Suppose 18 = -p + 7*o - h*o, -5*p - 2*o + 20 = 0. Suppose -9/2*v**p - 3/2*v**3 - 9/2*v - 3/2 = 0. Calculate v.
-1
Let m(u) be the first derivative of -6/55*u**5 - 16 + 2/11*u**3 + 1/11*u**2 + 0*u - 1/22*u**4. Solve m(c) = 0 for c.
-1, -1/3, 0, 1
Let g(k) = -7*k**2 + 1654*k + 136127. Let s(l) = 27*l**2 - 4964*l - 408382. Let a(o) = -7*g(o) - 2*s(o). Let a(c) = 0. What is c?
-165
Let x(m) = m**2 - m. Let z(a) = 2*a**2 - 2*a. Let h(t) = 3*x(t) - 3*z(t). Suppose h(w) = 0. What is w?
0, 1
Let d = -754 - -757. Let o(h) be the first derivative of 3/10*h**5 + 9 + d*h**4 + 18*h**2 + 11*h**3 + 27/2*h. Find a, given that o(a) = 0.
-3, -1
Let s(m) = 3*m**4 - 4*m**3 - 15*m**2 + 9*m + 7. Let j(k) = k**4 - k**3 - 5*k**2 + 3*k + 2. Let n(b) = 21*j(b) - 6*s(b). Factor n(t).
3*t*(t - 1)**2*(t + 3)
Let z(u) be the first derivative of -u**6/5 + 4*u**5/5 - 14*u**4/15 + 16*u**3/45 - 141. Suppose z(m) = 0. What is m?
0, 2/3, 2
Let h(m) be the third derivative of m**6/24 + m**5/12 - 5*m**4/6 - 10*m**3/3 - 29*m**2. Factor h(d).
5*(d - 2)*(d + 1)*(d + 2)
Let d = -727 - -1455/2. What is t in 2*t + 3/4 - d*t**3 + 3/4*t**2 = 0?
-1, -1/2, 3
Let k(c) = -32*c**4 + 164*c**3 + 84*c**2 - 104*c + 24. Let h(v) = -33*v**4 + 165*v**3 + 83*v**2 - 104*v + 23. Let b(m) = -4*h(m) + 3