60*j**6. Factor s(u).
(u - 6)*(u + 1)**2/8
Let f(v) be the first derivative of -2*v**3/3 + 46*v**2 + 192*v + 233. Factor f(t).
-2*(t - 48)*(t + 2)
Suppose 5*r = 8*r - 12. Determine j, given that -2 + 9*j + 7*j + 8*j + 10 - 24*j**3 + 14*j**r - 22*j**2 = 0.
-1, -2/7, 1, 2
Suppose 2*c - 5*d + 0 + 11 = 0, -22 = -5*c - 4*d. Suppose c*r - 8 = -2*r. What is u in 6*u**2 + 5*u**2 - 5*u**r - 12 - 4*u + 2*u**2 = 0?
-1, 3/2
Let n(o) = 3*o**2 - 3 + 0 - 5*o**2 + 9*o - 2*o. Let x be n(3). Factor x + 1/3*b - 1/3*b**2.
-b*(b - 1)/3
Let r = -15186/5 - -3038. Factor 4/5*i**3 + 0 + 8/5*i**2 + r*i.
4*i*(i + 1)**2/5
Let w(x) be the first derivative of x**4/24 - 10*x - 5. Let z(g) be the first derivative of w(g). Factor z(q).
q**2/2
Suppose j - 11 = 46. What is z in 2*z**4 + j*z - 3*z**3 + 2*z**2 - z**4 - 57*z = 0?
0, 1, 2
Let t be 48/(-20)*(-20)/6. Suppose t - 23 = -5*s. Factor -6*n**4 - 12*n**2 + 12*n**s + 6*n**5 + 13*n**4 + 14*n**4.
3*n**2*(n + 2)**2*(2*n - 1)
Let m(o) be the first derivative of o**4/28 + 4*o**3/7 + 41*o**2/14 + 30*o/7 - 584. Factor m(l).
(l + 1)*(l + 5)*(l + 6)/7
Let k = -39 - -48. Factor 10*t**2 - 15*t**4 - 4 + 5*t**5 + 13*t**3 - 15*t + k - 3*t**3 + 0*t**5.
5*(t - 1)**4*(t + 1)
Let p(s) be the third derivative of s**5/300 - 7*s**4/120 + s**3/5 + 186*s**2. Find i such that p(i) = 0.
1, 6
Let f(s) be the first derivative of 1/12*s**4 - 32/3*s + 23 + 2/3*s**3 + 0*s**2. Determine g, given that f(g) = 0.
-4, 2
Suppose 4*g + 2 - 10 = 0. Factor -2*d + 5*d**2 - d**g + 3*d**2 - 9*d**2 + 4.
-2*(d - 1)*(d + 2)
Let z(r) = r**2 - 4*r. Let y be z(3). Let m be (-1)/(2/(-3 + y)). Factor -x**3 - 2 - 3*x**4 + 5*x**4 - 4*x - 3*x**m + 8*x**3.
2*(x - 1)*(x + 1)**3
Let l(d) be the second derivative of d**7/147 - 2*d**6/105 - 2*d**5/35 + 4*d**4/21 + 303*d. Factor l(j).
2*j**2*(j - 2)**2*(j + 2)/7
Let i(j) = 8*j + 16. Let b be i(-7). Let m be (0 - 2/b)/((-20)/(-80)). Find q, given that 2/5 + 1/5*q**3 - 12/5*q**2 - m*q + 2*q**4 = 0.
-1, -1/2, 2/5, 1
Let r = 4198639/307901 + 1/27991. Suppose -210/11*b**2 + 0 + r*b + 6*b**3 - 6/11*b**4 = 0. What is b?
0, 1, 5
Let a be (4/(-128))/((-1)/4). Let l(b) be the first derivative of -1/2*b + 4 - 1/4*b**2 + 1/6*b**3 + a*b**4. Factor l(n).
(n - 1)*(n + 1)**2/2
Suppose -4*s + 0*s = -12. Suppose 6*m - 3*m - s = 0. Let -m - 5*y**2 + 12*y - 2 - 1 + 0 = 0. What is y?
2/5, 2
Let x(r) = 73*r**4 + 195*r**3 + 168*r**2 + 22*r - 12. Let i(g) = 74*g**4 + 195*g**3 + 169*g**2 + 21*g - 11. Let z(m) = -3*i(m) + 4*x(m). Factor z(c).
5*(c + 1)**3*(14*c - 3)
Let d(w) = w**3 + w + 1. Let y(u) = u**4 + 16*u**3 + 90*u**2 + 107*u - 217. Let m(g) = -d(g) - y(g). Find t, given that m(t) = 0.
-6, 1
Let a = -27301/19 - -1437. Factor -a*b**2 - 2/19*b + 0.
-2*b*(b + 1)/19
Let k(n) be the first derivative of n**8/1680 + n**7/840 - 7*n**6/1440 + n**5/240 + 3*n**3 - 19. Let l(s) be the third derivative of k(s). Solve l(p) = 0.
-2, 0, 1/2
Let t(a) = -a**4 - 10*a**3 - 27*a**2 - 2*a + 10. Let u(q) = -q**2 - q - 3. Let j(c) = t(c) - 6*u(c). Suppose j(k) = 0. What is k?
-7, -2, 1
Let r(g) be the third derivative of 0*g**3 + 1/10*g**7 - 11*g**2 + 0 + 11/20*g**5 - 1/4*g**4 + 0*g - 2/5*g**6. Factor r(w).
3*w*(w - 1)**2*(7*w - 2)
Let m(w) be the third derivative of -11*w**5/60 + 19*w**4/24 + 8*w**3/3 + 25*w**2. Let c(o) = -12*o**2 + 18*o + 15. Let b(h) = -2*c(h) + 3*m(h). Factor b(d).
-3*(d - 3)*(3*d + 2)
Let q(y) = y + 10. Let c be q(-7). Determine r so that 4*r**c - r + 7*r - 3*r**3 + 2 - 9*r = 0.
-2, 1
Suppose -26*r - 96*r**2 - 165 + 3*r**3 - 175*r + 63 = 0. What is r?
-1, 34
Factor -23*t**3 + 5*t**3 - 3*t**4 + 4*t**4 + 33*t**2 - 6*t - 10*t.
t*(t - 16)*(t - 1)**2
Let c(d) = -d - 7. Let h be c(-9). Suppose 4*x + h = 10. Solve 3*a**4 - 3*a**3 + a**x - 3*a**2 - 3*a**3 + 6*a - a**2 = 0.
-1, 0, 1, 2
Factor -3/2 + 29/4*p + 5/2*p**3 - 33/4*p**2.
(p - 2)*(p - 1)*(10*p - 3)/4
Let m(h) be the second derivative of 0*h**2 + 37*h - 7/4*h**5 + 0 - 5/4*h**4 + 0*h**3 - 5/6*h**6 - 5/42*h**7. Let m(d) = 0. What is d?
-3, -1, 0
Suppose 4*i - 14 + 2 = -z, 0 = -i + 2*z + 3. Factor 2*f + 0*f**3 + 2*f**2 + 3*f**3 - 5*f**i - 1 - 1.
-2*(f - 1)**2*(f + 1)
Suppose -11 = -5*c + n, -5 = 2*c + 2*n - 19. Let b = 5 + -1. Factor 3*j + 1 + j**4 - 7 + j**2 + 4 - 3*j**c + 0*j**b.
(j - 2)*(j - 1)**2*(j + 1)
Let c(s) be the first derivative of 1/16*s**4 - 1/4*s**3 - 6 + 3/8*s**2 - 1/4*s. Factor c(i).
(i - 1)**3/4
Let o(x) be the first derivative of 135/2*x**2 - 1/6*x**6 - 15/2*x**4 - 2*x**5 + 0*x**3 + 9 - 13*x. Let g(q) be the first derivative of o(q). Factor g(j).
-5*(j - 1)*(j + 3)**3
Let j(d) be the first derivative of 5*d**3/3 + 165*d**2/2 - 170*d + 202. Suppose j(s) = 0. What is s?
-34, 1
Let g(d) be the first derivative of -2*d**3 + 4*d + 2/5*d**5 - 8 + 1/2*d**4 - d**2. Factor g(l).
2*(l - 1)**2*(l + 1)*(l + 2)
Determine v, given that 11*v**2 - 30*v**4 + 135 - 45*v + 40*v**3 + 5*v**5 - 8*v**2 - 268 + 7*v**2 + 153 = 0.
-1, 1, 4
Suppose 0 = -2*f - 3*p + 2 + 14, -4*f + 4*p + 72 = 0. Factor -61*c - 52*c - 308*c**2 - 196*c**3 - 16 - 29*c + f*c.
-4*(c + 1)*(7*c + 2)**2
Suppose -12*m - 32 = 28. Let d(h) = h**3. Let u(g) = -6*g**3 + g**2. Let p(c) = m*d(c) - u(c). Solve p(v) = 0 for v.
0, 1
Let f = 1089 + -1079. Let u(x) be the second derivative of -2/3*x**4 + f*x + 0 - 2/5*x**5 - 1/8*x**2 - 5/12*x**3. Solve u(q) = 0 for q.
-1/2, -1/4
Find h such that 0 + 256/3*h + 32/3*h**2 + 1/3*h**3 = 0.
-16, 0
Let n(m) be the first derivative of -m**4/4 - 7*m**3/3 - 5*m**2 + 136. Factor n(j).
-j*(j + 2)*(j + 5)
Let n(w) = w**4 + w**3 + w**2 - 4. Let f(q) = -25*q**4 - 47*q**3 - 4*q**2 + 4*q + 16. Let b(a) = -f(a) - 4*n(a). Determine m so that b(m) = 0.
-2, -1/3, 0, 2/7
Solve 640*i**3 - 3835*i**2 + 5280*i - 20*i**4 - 12*i**4 + 11*i**4 - 4*i**4 + 2880 - 705*i**2 = 0.
-2/5, 2, 12
Let y(b) = -10*b**3 + 3*b**2 - 7*b. Let v be 3/(-9)*(21 + -6). Let j(k) = 7*k**3 - 2*k**2 + 5*k. Let z(r) = v*y(r) - 7*j(r). Suppose z(n) = 0. What is n?
0, 1
Solve 0 + 135/7*y - 3/7*y**2 = 0.
0, 45
Let z = -8 + 10. Factor 6*j**z + 2*j - j**4 - j**4 - 6*j.
-2*j*(j - 1)**2*(j + 2)
Suppose 47 = z - 5*d, 4*z - 2*d + 23 = 175. Let t = -109/3 + z. Factor -4/3*m - 1/6*m**3 + 5/6*m**2 + t.
-(m - 2)**2*(m - 1)/6
Suppose 20*d + 22 = 25*d + 3*n, 3*d + 4*n = 11. Let -1/2 + 7/2*o**3 + 1/4*o**d - 3/2*o**4 + 9/4*o - 4*o**2 = 0. Calculate o.
1, 2
Let y(l) = 3*l**3 + 4*l**2 - l - 18. Let r(z) = 5*z**3 + 7*z**2 - z - 32. Let s(n) = 4*r(n) - 7*y(n). Let s(u) = 0. Calculate u.
-2, 1
Let m(j) be the first derivative of -3*j**5/20 - j**4 - 2*j**3 + 34*j - 20. Let h(v) be the first derivative of m(v). Determine a, given that h(a) = 0.
-2, 0
What is g in -10 + 8/5*g**2 - g - 1/5*g**3 = 0?
-2, 5
Let l(k) be the first derivative of -k**6/2 + 3*k**5 - 21*k**4/4 + 3*k**3 - 48. Let l(x) = 0. What is x?
0, 1, 3
Factor 3*d**2 - 15*d - 5 + 14 - 10*d - 11*d + 24.
3*(d - 11)*(d - 1)
Let h be (-3)/((-55)/15 + 4). Let f(s) = 21*s + 191. Let g be f(h). Factor -9/4*k**g + 0 - 3/4*k - 9/4*k**3 - 3/4*k**4.
-3*k*(k + 1)**3/4
Find q such that -14*q**5 - 102*q**4 - 186*q**2 - 365*q - 389*q + 718*q - 238*q**3 = 0.
-3, -1, -2/7, 0
Suppose 0 = -78*l + 77 - 77. Let 0 + l*o - 2/23*o**2 = 0. What is o?
0
Let o(t) be the first derivative of -t**4 + 40*t**3/3 - 24*t**2 - 288*t + 43. Solve o(l) = 0 for l.
-2, 6
Let x be ((-4)/8)/((-3)/24). Let f(a) be the first derivative of 3/4*a**2 - 1/2*a**3 + 3*a - x. Suppose f(k) = 0. What is k?
-1, 2
Let u(v) be the second derivative of -v**5/6 - 7*v**4/6 - 4*v**3/9 - 40*v. Determine p so that u(p) = 0.
-4, -1/5, 0
Let x = -14 - -18. Let s(j) be the second derivative of 0*j**2 + 1/45*j**6 - j + 0 + 0*j**x - 1/126*j**7 + 0*j**3 - 1/60*j**5. Factor s(c).
-c**3*(c - 1)**2/3
Let x be 312/192 + -5 + (-117)/(-24). Let q = -1 + 5/4. Factor x*a - 9/4 - q*a**2.
-(a - 3)**2/4
Suppose -o - 61 = -64. Let h(f) be the first derivative of -7/10*f**2 + 8 - 2/5*f - 2/15*f**o + 3/20*f**4. Factor h(q).
(q - 2)*(q + 1)*(3*q + 1)/5
Let f(p) be the first derivative of 5*p**3/3 - 25*p**2/2 - 30*p + 92. Factor f(m).
5*(m - 6)*(m + 1)
Let s(o) be the first derivative of o**3/6 + 12*o**2 - 49*o/2 + 292. Factor s(w).
(w - 1)*(w + 49)/2
Let d be (-18)/63 + (-4)/(-14). Let s(f) be the first derivative of -3 + 1/6*f**6 + 0*f**2 + 1/15*f**5 + d*f + 0*f**4 + 0*f**3. Factor s(j).
j**4*(3