- 16*x**3 = 0.
-1, -1/2, 1
Let x(i) = 8*i**3 + 16*i**2 + 8*i + 9. Suppose -41 + 25 = -4*n. Let s(h) = 4*h**3 + 8*h**2 + 4*h + 4. Let g(p) = n*x(p) - 9*s(p). Factor g(u).
-4*u*(u + 1)**2
Suppose 2*f = -i + 2, -i - 4*f + 4 = 2*i. Suppose -3*s + 15 = 3*j, -2*s = 4*j - i*s - 18. Factor 0*q**2 - 9*q + j*q**2 - q**2 + 6.
3*(q - 2)*(q - 1)
Suppose 3*u = 65 - 14. Let n(j) = j**3 - 17*j**2. Let h be n(u). Solve h + 3/5*k + 3/5*k**2 = 0.
-1, 0
Suppose 0 = 5*f - 5*z - 30, -66*f + 65*f - 4*z = 14. Factor 12/5*k - 46/5*k**f + 12*k**3 - 5*k**4 - 1/5.
-(k - 1)**2*(5*k - 1)**2/5
Suppose -2*p + 117 - 109 = 0. Let x(w) be the second derivative of 1/3*w**2 + w + 1/18*w**p - 2/9*w**3 + 0. Suppose x(b) = 0. What is b?
1
Let v(w) = 47 - 38 + 121 + 50*w. Let d be ((30/(-3))/(-1))/(-2). Let n(g) = -g**2 - 50*g - 129. Let c(m) = d*n(m) - 4*v(m). Determine p, given that c(p) = 0.
-5
Let m = -7 + 8. Let t(f) = f**3 - f. Let y(b) = -5*b**3 + 5*b. Let v(p) = m*y(p) + t(p). What is j in v(j) = 0?
-1, 0, 1
Let o(k) be the first derivative of 5*k**4/24 + 5*k**3/9 - 25*k**2/12 - 5*k - 122. Find t such that o(t) = 0.
-3, -1, 2
Let r = 3331 - 3329. Let x be 4/(-2) + (-11)/(-5). Factor 9/5 + 6/5*t + x*t**r.
(t + 3)**2/5
Let q(k) be the third derivative of 2*k**5/165 - 41*k**4/132 + 10*k**3/33 - 53*k**2 - 2*k. Suppose q(f) = 0. Calculate f.
1/4, 10
Suppose o - 92 = -90. Factor 3*n**o - 15*n**4 + 9*n**4 + n + 3*n**3 + 7*n**4.
n*(n + 1)**3
Let f(g) be the second derivative of 16*g**6/195 - 12*g**5/13 + 19*g**4/26 - 7*g**3/39 - 971*g. Factor f(i).
2*i*(i - 7)*(4*i - 1)**2/13
Factor 30*l**2 + 5*l**3 - 65*l + 18*l**2 + 12*l**2.
5*l*(l - 1)*(l + 13)
Let o(c) be the third derivative of c**10/30240 + c**9/1728 - c**5/6 + 14*c**2. Let y(q) be the third derivative of o(q). What is b in y(b) = 0?
-7, 0
Factor 8*k**2 - 185*k**3 - 6*k**4 + 87*k**3 + 90*k**3.
-2*k**2*(k + 2)*(3*k - 2)
What is o in 4 - o**2 - 17*o**2 - 10*o**2 - 24*o = 0?
-1, 1/7
Suppose 7*x - 19*x + 36 = 0. Determine i, given that -3*i**4 - 3*i**x - i**5 + i**5 + 6*i**5 = 0.
-1/2, 0, 1
Let q(n) be the first derivative of -4*n**6/21 + 38*n**5/35 - n**4/2 - 26*n**3/7 - 9*n**2/7 + 96. Determine w, given that q(w) = 0.
-1, -1/4, 0, 3
Solve 2*f - 2*f**3 + 8/3*f**2 + 1/3*f**4 - 3 = 0.
-1, 1, 3
Let l(k) be the third derivative of -k**6/630 + 13*k**5/210 - 31*k**3/6 + 12*k**2 + 2*k. Let f(z) be the first derivative of l(z). Suppose f(j) = 0. What is j?
0, 13
Let i = 156 + -151. Suppose i*o + 10 = 0, 4*h - h + 2*o - 8 = 0. Factor 0*a + 2/7*a**h - 4/7*a**2 + 2/7*a**3 + 0.
2*a**2*(a - 1)*(a + 2)/7
Let y(n) = -4*n**2 - 176*n + 2. Let f be y(-44). Factor 3*g + 3/2 - 15/8*g**f.
-3*(g - 2)*(5*g + 2)/8
Suppose 142 = 6*c - 14. Factor -8*f**2 + 17*f**2 - 2*f + c*f + 30 + 27*f.
3*(f + 5)*(3*f + 2)
Let g(n) be the first derivative of -3*n**5/4 + 171*n**4/16 + 101*n**3/4 + 117*n**2/8 - 269. Find x, given that g(x) = 0.
-1, -3/5, 0, 13
Let y = 1135/1323 - 1/1323. Factor 2*h - y - 10/7*h**2 + 2/7*h**3.
2*(h - 3)*(h - 1)**2/7
Let b(t) = 18*t**4 + 150*t**3 + 171*t**2 - 57*t. Let x(f) = -37*f**4 - 297*f**3 - 341*f**2 + 115*f. Let q(v) = -5*b(v) - 3*x(v). Factor q(w).
3*w*(w + 2)*(w + 5)*(7*w - 2)
Let p = -133/75 - -1606/525. Let -p*k**2 + 2/7 + k = 0. Calculate k.
-2/9, 1
Let j(a) = -a**2 + 2*a - 1. Let m(c) = -20*c + 36. Let q(l) = -4*j(l) + m(l). Factor q(w).
4*(w - 5)*(w - 2)
Let b(z) be the first derivative of -8 + 4/5*z**2 + 0*z**4 + 1/25*z**5 - 2/5*z**3 - 3/5*z. Factor b(i).
(i - 1)**3*(i + 3)/5
Let m(v) be the third derivative of -v**8/36960 + v**6/1320 + v**5/330 + 7*v**4/24 - 25*v**2. Let r(l) be the second derivative of m(l). Factor r(d).
-2*(d - 2)*(d + 1)**2/11
Let k = -33 - -34. Let n(a) = -2*a**3 + 8*a**2 - 2*a + 24. Let z(s) = s**2 - s + 1. Let p(f) = k*n(f) - 12*z(f). Factor p(r).
-2*(r - 2)*(r + 1)*(r + 3)
Let m(j) be the third derivative of j**5/45 - 5*j**4/18 + 4*j**3/3 - 168*j**2. What is d in m(d) = 0?
2, 3
Let c(q) be the first derivative of 4*q**6/21 + 20*q**5/7 + 59*q**4/7 - 48*q**3/7 + 250. Determine a so that c(a) = 0.
-9, -4, 0, 1/2
Let f(k) be the second derivative of -k**7/14 - k**6/12 + k**5/4 + 5*k**4/12 + 10*k**2 + 18*k. Let t(w) be the first derivative of f(w). Factor t(x).
-5*x*(x - 1)*(x + 1)*(3*x + 2)
Factor 10*i - 10*i**3 + 35/3 - 40/3*i**2 + 5/3*i**4.
5*(i - 7)*(i - 1)*(i + 1)**2/3
Find j such that 0 + 5*j - 10/3*j**3 - 20/3*j**2 - 5/3*j**5 + 20/3*j**4 = 0.
-1, 0, 1, 3
Solve -1/4*r**3 + 5/4*r**4 + 0 + 0*r - 3/4*r**5 - 1/4*r**2 = 0.
-1/3, 0, 1
Let y(u) be the first derivative of u**4/4 + u**3 - 2*u**2 + 81. Factor y(j).
j*(j - 1)*(j + 4)
Let t(m) be the first derivative of m**7/525 + m**6/50 + 4*m**5/75 - m**4/10 - 3*m**3/5 - 17*m**2 + 1. Let c(p) be the second derivative of t(p). Factor c(n).
2*(n - 1)*(n + 1)*(n + 3)**2/5
Determine j so that -3*j**3 + 40*j**2 + 12*j**5 - 18*j**5 - 12*j**4 + 4*j**5 + 36 + 78*j - 9*j**3 = 0.
-3, -1, 2
Suppose l + 2*t + 9 - 19 = 0, t = 5*l + 5. Let h(w) be the third derivative of 0 + 1/120*w**6 + 1/3*w**4 + 2/3*w**3 + l*w + 1/12*w**5 - 4*w**2. Factor h(p).
(p + 1)*(p + 2)**2
Let m(d) = d + 9. Let r be m(-9). Let q(g) be the second derivative of 3*g + 0*g**2 - 1/12*g**3 + r - 1/24*g**4. Factor q(z).
-z*(z + 1)/2
Let u(t) be the second derivative of -t**7/420 + t**6/60 + t**5/200 - 29*t**4/120 + t**3/5 + 9*t**2/5 + 64*t. Solve u(a) = 0.
-2, -1, 2, 3
Let r = 921 - 918. Factor 2/3*k**5 + 0 - 2/3*k + 0*k**r + 4/3*k**4 - 4/3*k**2.
2*k*(k - 1)*(k + 1)**3/3
Suppose 0 = 2*v - 10*v + 88. Suppose -v*l + 17 = -16. Solve 0 - 2/13*c**2 + 4/13*c**l + 0*c + 6/13*c**4 = 0 for c.
-1, 0, 1/3
Let n = -5620/27 - -208. Let m = n + 35/54. Factor 0 + 1/2*k - m*k**3 + 0*k**2.
-k*(k - 1)*(k + 1)/2
Let y = -66 + 66. Let i(h) be the first derivative of y*h + 2/3*h**3 + h**2 - 1. Factor i(n).
2*n*(n + 1)
Let w(d) be the first derivative of -4*d**3/3 - 122*d**2 + 248*d - 588. Determine g so that w(g) = 0.
-62, 1
Let g(l) = -15*l**3 + 825*l**2 - 1062*l + 273. Let z(c) = -4*c**3 + 206*c**2 - 265*c + 68. Let x(y) = -5*g(y) + 21*z(y). Suppose x(k) = 0. Calculate k.
1/3, 1, 21
Let v(g) be the third derivative of -g**5/150 + g**4/15 - g**3/5 + 15*g**2 + 3. Factor v(n).
-2*(n - 3)*(n - 1)/5
Let f(t) = 6*t + 18. Let n(h) be the first derivative of h**3/3 + 5*h**2/2 + 20*h - 3. Let m(l) = -4*f(l) + 3*n(l). Solve m(v) = 0.
-1, 4
Let c(q) be the second derivative of 14*q - 1/2*q**3 + 0 + 1/48*q**4 + 9/2*q**2. Factor c(g).
(g - 6)**2/4
Let l(p) = -p**3 + 13*p**2 + 4. Let n be l(13). Suppose m + n*m = 2*m. Determine u so that 0*u + 8/3*u**2 - 8/3*u**3 + m + 2/3*u**4 = 0.
0, 2
Let g(a) be the second derivative of -25/36*a**3 + 0 - 5/72*a**4 - 5/3*a**2 - 5*a. Factor g(w).
-5*(w + 1)*(w + 4)/6
Suppose -2*f = 2*u - 112, 4*f - 220 = -6*u + u. Factor 3*j + 122*j + 38 - 8 + f*j**2 - 35*j**3.
-5*(j - 3)*(j + 1)*(7*j + 2)
Find p such that 3*p + 0 + 7/2*p**4 - 5/2*p**3 - 7/2*p**2 - 1/2*p**5 = 0.
-1, 0, 1, 6
Let y(c) be the third derivative of c**7/1890 + c**6/540 - c**5/180 - c**4/54 + 2*c**3/27 - c**2 - c. Factor y(i).
(i - 1)**2*(i + 2)**2/9
Let w(t) = 17*t**2 + 196*t + 207. Let a(s) = -5*s**2 - 66*s - 69. Let h(i) = 14*a(i) + 4*w(i). Suppose h(g) = 0. What is g?
-69, -1
Let q = -13 + 18. Solve v**3 + 0*v + v + 2 + 3 - 3 - 7*v**2 - 2*v**q + 5*v**4 = 0.
-1, -1/2, 1, 2
Let t(y) be the second derivative of -y**8/4480 - y**7/1344 - y**6/2880 + y**5/960 + 3*y**3/2 - 37*y. Let u(j) be the second derivative of t(j). Factor u(b).
-b*(b + 1)**2*(3*b - 1)/8
Let v = 44951/19964 - 8/4991. Factor -3 - v*k**2 - 14*k.
-(k + 6)*(9*k + 2)/4
Let q be (918/4284)/(0 - (-9)/48). Factor -4/7*f + 4/7*f**3 - 8/7 + q*f**2.
4*(f - 1)*(f + 1)*(f + 2)/7
Let t(n) be the first derivative of 1/8*n**4 + 1/2*n + 7 - 1/24*n**6 + 7/8*n**2 + 2/3*n**3 - 1/10*n**5. Find h such that t(h) = 0.
-1, 2
Let r(n) = 93*n. Let f be r(1). Factor 6*a + 0*a + 10*a - 97*a**3 + f*a**3.
-4*a*(a - 2)*(a + 2)
Let m(f) be the first derivative of -f**3/6 - f**2/4 + 6*f + 319. Factor m(b).
-(b - 3)*(b + 4)/2
Suppose 0 + 3/4*y**2 - 3/4*y**4 - 9/4*y + 9/4*y**3 = 0. Calculate y.
-1, 0, 1, 3
Let b(m) = 7*m - 33. Let g be b(5). Factor -15*w - g*w**2 + 6*w**2 + 0*w**2 - 9*w**2 - 10.
-5*(w + 1)*(w + 2)
Find v such that 32/19*v + 28/19*v**2 + 6/19 - 8/19*v**5 - 24/19*v**3 - 34/19*v**4 = 0.
-3,