+ 1/8*j**4. Factor s(n).
(n - 2)*(n - 1)**2*(n + 1)
Let m(n) be the first derivative of -n**4/6 + 2*n**3 - 103. Solve m(z) = 0.
0, 9
Let q(t) be the second derivative of 2*t**6/5 - 51*t**5/20 + t**4/4 + 6*t**3 - 124*t + 2. Suppose q(k) = 0. What is k?
-3/4, 0, 1, 4
Solve -2 + 448*a**2 - 421*a**2 - 7*a**3 - 21*a**3 - a + 4*a = 0.
-2/7, 1/4, 1
What is i in -495*i + 995*i + 3*i**2 - 554*i - 120 = 0?
-2, 20
Suppose 0 = -13*d + 8*d + 15. Suppose 3*j - 3*i = 15, -d*i + 6 + 0 = 4*j. Factor 9*o**2 - 2*o - j*o**2 - 4*o**2.
2*o*(o - 1)
Suppose -5*m = 20, 2*k = -m + 5*m + 20. Factor 4 + 8*p - k*p**2 + 5*p**2 + 0.
(p + 2)*(3*p + 2)
Let z(d) be the second derivative of -12*d - 5/24*d**3 + 1/120*d**6 - 1/4*d**2 + 0 - 1/16*d**4 + 1/80*d**5. Find q such that z(q) = 0.
-1, 2
Let c be (-18)/99 + (-24)/(-11). Suppose -4*w - 28 = -4*z, -c*w + 3 + 1 = 0. Factor 8*y**4 + y - z*y**4 + y**2 + y**2 - 2*y**3 + y**5 - 1.
(y - 1)**3*(y + 1)**2
Let t(p) be the first derivative of -p**6/960 - p**5/120 - p**4/64 - 3*p**2/2 + 16. Let o(f) be the second derivative of t(f). Let o(s) = 0. What is s?
-3, -1, 0
Let d(c) be the second derivative of -c**4/4 - 29*c**3 - 171*c**2/2 - 287*c. Find w such that d(w) = 0.
-57, -1
Let f(b) be the third derivative of 7/90*b**5 - 11/90*b**6 + 0*b**3 - 2*b**2 + 0*b**4 - 12 + 1/105*b**7 + 0*b. Determine u so that f(u) = 0.
0, 1/3, 7
Let v be 8/10*(25/(-10) - -5). Suppose -2*p - 3*p = v*b - 14, 8 = 3*p + b. Factor -1/4*k + 1/4*k**p + 0.
k*(k - 1)/4
Let v = 1151 + -1148. Let a(u) be the second derivative of -3/20*u**5 + 1/4*u**4 + 2*u**v + u + 0 - 6*u**2. Solve a(q) = 0.
-2, 1, 2
Suppose 0 = -5*h - 3*u - 2248 + 340, 3*u = -3. Let a = h + 1228/3. Determine l so that 10 + 25/3*l**2 + a*l = 0.
-3, -2/5
Let a(s) be the second derivative of -2*s**7/21 + s**5/5 + s - 94. Factor a(q).
-4*q**3*(q - 1)*(q + 1)
Let z = 4501/3 - 1495. Factor -16/3*n**2 + 0 + 4/3*n**3 + z*n.
4*n*(n - 2)**2/3
Let y = -8/51 + 11/34. Let w(u) be the third derivative of 0*u - 5*u**2 - 1/60*u**5 - y*u**3 + 5/48*u**4 + 0. Suppose w(b) = 0. What is b?
1/2, 2
Let q be (1/(-28)*-7)/(6 + (-546)/96). Factor -2/5*t**3 + 0*t + 0 + q*t**4 + 0*t**2 - 2/5*t**5.
-2*t**3*(t - 1)**2/5
Let w(b) be the first derivative of 1/5*b**3 - 1/25*b**5 - 4/5*b - 12 - 1/10*b**4 + 2/5*b**2. Find o, given that w(o) = 0.
-2, 1
Let c(b) be the first derivative of 4 + 48*b**2 + 1/2*b**4 + 128*b + 8*b**3. Solve c(d) = 0 for d.
-4
Suppose -5*i**5 - 21*i**4 + 2*i**5 + 57*i**2 - 30 - 122*i - 82*i + 63*i**3 + 138 = 0. Calculate i.
-9, -2, 1, 2
Let r be 4/(8/(-3)) + 35/10. Let q(v) = -v**3 - v**2 + 8*v - 1. Let l be q(r). Factor -2/5*k**4 + 6/5*k**2 + 0 + 0*k**l - 4/5*k.
-2*k*(k - 1)**2*(k + 2)/5
Let f(i) be the second derivative of -9*i + 0*i**5 + 0*i**2 + 0 + 1/90*i**6 - 1/36*i**4 + 0*i**3. Factor f(u).
u**2*(u - 1)*(u + 1)/3
Let v(a) = 134*a**2 + 76*a + 405. Let k be v(-5). Let -5625*q**3 - 243/2 - k*q**2 - 2025/2*q - 3125/2*q**5 - 9375/2*q**4 = 0. What is q?
-3/5
Let p = -261/4 + 785/12. Let v(l) be the second derivative of -3*l - 1/9*l**3 + 1/45*l**6 + p*l**4 - 1/10*l**5 + 0*l**2 + 0. What is y in v(y) = 0?
0, 1
Suppose 4*b**4 - 192 + 116*b**2 - 32*b - 10*b**3 + 0*b**3 - 5*b**3 - 25*b**3 = 0. What is b?
-1, 3, 4
Suppose 817 - 821 = -f. Find a, given that -11/2*a**2 - a - 8*a**3 - 7/2*a**f + 0 = 0.
-1, -2/7, 0
Let r(a) be the first derivative of a**8/1344 + a**7/280 + a**6/160 + a**5/240 - 7*a**2 + 11. Let x(i) be the second derivative of r(i). Solve x(b) = 0.
-1, 0
Suppose -3*j = 3*j - 18. Solve 0*f**3 - 6*f**j + 5*f**3 = 0 for f.
0
Let l(j) be the third derivative of 16*j**2 + 1/10*j**6 + 0*j**4 + 0 + 0*j**3 - 2/105*j**7 - 2/15*j**5 + 0*j. Factor l(b).
-4*b**2*(b - 2)*(b - 1)
Let a = 11290 - 146768/13. Factor -a*r**5 + 8/13*r**3 + 0*r**2 + 0*r**4 + 0 + 0*r.
-2*r**3*(r - 2)*(r + 2)/13
Let w be ((-10)/4)/((-585)/36). What is j in 0 + 6/13*j + 14/13*j**2 + 10/13*j**3 + w*j**4 = 0?
-3, -1, 0
Let f(y) be the first derivative of 2*y**3/9 - 14*y**2/3 + 98*y/3 + 71. What is n in f(n) = 0?
7
Suppose -3*g - 362 = -3*w - 110, 174 = 2*w - 4*g. Let d = w + -403/5. Let -d*t**2 + 2/5*t + 0 = 0. Calculate t.
0, 1
Suppose -4*a + a = -2*a. Solve a + 0*q + 3/2*q**2 + 3/2*q**3 = 0.
-1, 0
Suppose -8*y + 3*y + 30 = 0. Suppose -y = 51*o - 53*o. Factor 1/2*i**2 + 3/4*i**o + 1/4*i**4 + 0 + 0*i.
i**2*(i + 1)*(i + 2)/4
Let s be 36/21 - 4/(-14). Let q(w) = -2*w + 4. Let l be q(s). Let -10*i**2 + 0 + 2*i**2 + l - 4*i**3 = 0. What is i?
-2, 0
Find v such that -11*v + 333*v + 26*v + 92450 + 2*v**2 + 512*v = 0.
-215
Let a(w) be the first derivative of w**5 + 15*w**4 - 5*w**3 - 95*w**2 - 120*w - 77. Factor a(i).
5*(i - 2)*(i + 1)**2*(i + 12)
Let t(k) be the third derivative of -7/16*k**4 + 1/20*k**5 + 7/80*k**6 - 1/2*k**3 + 9*k**2 + 0 + 0*k. Factor t(z).
3*(z - 1)*(z + 1)*(7*z + 2)/2
Let d be (0/(-9) + 4 + (-8)/2)/(-1). Factor 0 - 1/3*n + d*n**2 - 1/3*n**5 + 2/3*n**3 + 0*n**4.
-n*(n - 1)**2*(n + 1)**2/3
Factor -1 + 34*i**2 - 15 + 52*i - 20*i**2.
2*(i + 4)*(7*i - 2)
Suppose -p + 10 = 2. Suppose -p = -2*v - 2. Factor 0*x**v + 4/3*x**2 - 2/3*x + 2/3*x**5 + 0 - 4/3*x**4.
2*x*(x - 1)**3*(x + 1)/3
Let t(w) be the third derivative of -w**7/210 + w**6/45 - 4*w**3/3 - 7*w**2. Let g(z) be the first derivative of t(z). What is u in g(u) = 0?
0, 2
Let v = -166 - -151. Let h be ((-1)/v*3)/((-8)/(-10)). Factor -1/8*t**2 - h + 3/8*t.
-(t - 2)*(t - 1)/8
Let k = 678 + -674. Let r(g) be the second derivative of 1/12*g**k + 0*g**2 - 1/6*g**3 + 9*g + 0. Factor r(q).
q*(q - 1)
Let a = 59 - 62. Let l be (a/6*2)/1 - -3. Factor l*z**2 + 8/3 + 26/3*z.
2*(z + 4)*(3*z + 1)/3
Let v be (-26)/91 - (-116)/14. Determine t, given that 17*t**3 - 11*t**3 - v*t - 4*t**5 - 9*t**4 + 6*t**3 + 5*t**4 + 4*t**2 = 0.
-2, -1, 0, 1
Suppose -4*i - f + 2 = -3, 4*f - 20 = 0. Let k be (i/(-2))/(-1 - -3). Factor 27/2*q - 18*q**2 + 3/2*q**5 - 3*q**3 + 6*q**4 + k.
3*q*(q - 1)**2*(q + 3)**2/2
Let f(u) be the second derivative of u**5/5 - 9*u**4 + u - 272. Let f(t) = 0. Calculate t.
0, 27
Let r(h) be the second derivative of -6*h**2 + 0 + 3/4*h**4 + 3/5*h**5 - 2*h**3 + 9*h + 1/10*h**6. Solve r(k) = 0.
-2, -1, 1
Let y = -100 + 90. Let p be ((-100)/120)/(y/6). Factor s - p - 1/2*s**2.
-(s - 1)**2/2
Factor 3/4*t**2 + 99/4*t - 51/2.
3*(t - 1)*(t + 34)/4
Let y(v) be the second derivative of 1/2*v**2 - 28*v - 77/120*v**6 + 73/48*v**4 - 17/80*v**5 + 7/24*v**7 - 4/3*v**3 + 0. Solve y(x) = 0 for x.
-1, 2/7, 1
Let x(g) be the second derivative of -3/4*g**4 - 3*g**2 - 9/2*g**3 - 1/20*g**5 + 3*g + 0. Let y(j) be the first derivative of x(j). Suppose y(i) = 0. What is i?
-3
Let q(u) be the first derivative of 32*u**2 - 6*u**3 - 12*u**2 - 8*u + 1 + 6. Factor q(n).
-2*(n - 2)*(9*n - 2)
Factor 100*s + 55*s**3 - 20*s**3 - 31*s**3 - 48 - 56*s**2.
4*(s - 12)*(s - 1)**2
Let a(f) be the second derivative of -f**6/10 + 3*f**5/20 + 3*f**4/4 - f**3/2 - 3*f**2 - 3*f - 5. Factor a(o).
-3*(o - 2)*(o - 1)*(o + 1)**2
Let d(w) be the third derivative of 0*w + 0 + 11*w**2 + 0*w**4 - 1/180*w**5 + 1/18*w**3. What is v in d(v) = 0?
-1, 1
Let m = -102 + 305. Let r = m + -2231/11. What is a in -10/11*a + r*a**3 + 4/11 - 2/11*a**4 + 6/11*a**2 = 0?
-2, 1
Let m be (-15)/10*(-24)/9. Let w be (m/2)/(2 + -1). What is n in 0*n**2 + n**w + 0 + 4*n - 3 - 2*n = 0?
-3, 1
Let h(l) be the second derivative of 3*l**5/20 - l**4/2 + l**3/2 + 10*l - 5. What is v in h(v) = 0?
0, 1
Let g(i) be the first derivative of i**4/2 + 2*i**3 - 4*i**2 - 24*i + 99. Suppose g(x) = 0. Calculate x.
-3, -2, 2
Let j(b) be the third derivative of -b**5/450 + 35*b**4/18 - 6125*b**3/9 - 2*b**2 + 52. Factor j(i).
-2*(i - 175)**2/15
Let r be -3*5/(-3)*(2 + -1). Solve 97*y**5 + 158*y**2 - 96 + 592*y + 280*y**4 - 778*y**3 - 410*y**3 + 99*y**r - 742*y**2 = 0 for y.
-3, -1, 2/7, 2
Suppose 14*o - 52 = -12*o. Let x(v) be the first derivative of 0*v + 0*v**o - 5 - 4/3*v**6 + 0*v**3 + 4/5*v**5 + 0*v**4. Find z such that x(z) = 0.
0, 1/2
Let j(f) = 3*f**4 - 11*f**3 + 21*f**2 - 9*f + 8. Let o(y) = 6*y**4 - 23*y**3 + 42*y**2 - 18*y + 14. Let m(k) = -7*j(k) + 4*o(k). Factor m(u).
3*u*(u - 3)*(u - 1)**2
Factor 6*b**3 - 2*b**4 + 4*b**3 + 0*b**2 + 0*b**3 - 8*b**2.
-2*b**2*(b - 4)*(b - 1)
Factor 4/7*a + 4/7 - 1/7*a**2 - 1/7*a**3.
-(a - 2)*(a + 1)*(a + 2)/7
Let d(o) be the second d