.
-3*o**2*(15*o + 2)
Let l(s) be the third derivative of -s**6/720 + s**5/120 + s**4/36 - s**3/3 - 46*s**2. Find p, given that l(p) = 0.
-2, 2, 3
Suppose -2*f + b + 1 = 0, 4*f = f + 2*b - 1. Factor 2*z**2 - 5*z**f - 6*z - 11*z**2 + 2*z**3.
-3*z*(z + 1)*(z + 2)
Suppose 4*n + 3*x + 15 = 0, 5*n - 3*x - 13 - 2 = 0. Let -1/3*t**2 + n + 1/3*t**4 - t**5 + t**3 + 0*t = 0. What is t?
-1, 0, 1/3, 1
Let m = 8 + -5. Let d be m + -4 + 1*3. Let 9*b + 3 - 9*b**3 - 9*b**3 - 5*b**d - 3*b**2 + 9*b**5 + 3*b**4 + 2*b**2 = 0. What is b?
-1, -1/3, 1
Let k be 8/52 + 21/117. Solve 0*z**3 + 0 + 1/6*z**5 + k*z**2 - 1/6*z - 1/3*z**4 = 0.
-1, 0, 1
Let o be ((-66)/(-36))/(2/4). What is c in 2/3*c + 0 + c**5 - o*c**4 + 5*c**3 - 3*c**2 = 0?
0, 2/3, 1
Let w = -11 + 11. Solve w*a**5 - 2*a**2 + 0*a**2 + 0*a**5 + 9*a**3 - 12*a**4 + 5*a**5 = 0.
0, 2/5, 1
Let k(l) be the second derivative of -1/720*l**6 + l + 1/240*l**5 + 0 - 1/2*l**3 + 1/24*l**4 + 0*l**2. Let w(u) be the second derivative of k(u). Factor w(s).
-(s - 2)*(s + 1)/2
Factor -k**3 + 21*k**2 + 8*k + 2*k**2 + 4*k**4 - 3*k**2 + 17*k**3.
4*k*(k + 1)**2*(k + 2)
Let p(n) be the first derivative of n**2 - 1/6*n**4 - n - 1 + 0*n**3. Let d(w) be the first derivative of p(w). Factor d(j).
-2*(j - 1)*(j + 1)
Let a(q) be the second derivative of -q**7/21 - q**6/3 - q**5 - 5*q**4/3 - 5*q**3/3 - q**2 - q. Factor a(f).
-2*(f + 1)**5
Let d = -727/5 - -149. Determine u so that -d*u**3 - 4*u**2 + 0 - 7/5*u**4 - 1/5*u**5 - 8/5*u = 0.
-2, -1, 0
Suppose 2*b - 3*k = -0 + 12, -b - 5*k + 6 = 0. Suppose -y - 1 = -b, 5*p + 20 = 4*y. Determine d so that p + 0*d - 1/2*d**2 = 0.
0
Let c(f) be the first derivative of -3 + 0*f**2 + 0*f + 3/16*f**4 + 0*f**3. Factor c(r).
3*r**3/4
Let n(v) = -3 + 0*v**2 - 4*v**3 + 8*v + 6*v**2 + 3*v**3. Let i be n(7). Let -11*z**5 + 8*z**5 + z**i + 3*z**2 + 3*z**3 - 4*z**4 = 0. What is z?
-1, 0, 1
Suppose -4*k + 5*a - 1 + 3 = 0, -4*k + 18 = 3*a. Let m(x) be the second derivative of -3/20*x**4 + 0 + 3*x + 2/5*x**k - 2/5*x**2. Factor m(j).
-(3*j - 2)**2/5
Let c(i) be the third derivative of -i**8/20160 - i**7/7560 - i**4/6 - 4*i**2. Let v(k) be the second derivative of c(k). Find g such that v(g) = 0.
-1, 0
Let v(r) = -r**3 - 5*r**2 + 4*r + 4. Let l be v(-6). Suppose 0 = -0*s - 4*s + l. Factor -4*f**2 - 6*f**3 - 4*f**5 - 4*f**s - f + 0*f**4 + 3*f**5.
-f*(f + 1)**4
Suppose 2*t + 2*t - 9 = -3*p, -4*p - t + 12 = 0. Let w(s) be the first derivative of 0*s + 2 - 1/12*s**4 - 1/9*s**p + 1/3*s**2. Factor w(i).
-i*(i - 1)*(i + 2)/3
Let t be 4/(4/3) - (13 + -14). Factor 1/2 - 5/2*g + 9/2*g**2 - 7/2*g**3 + g**t.
(g - 1)**3*(2*g - 1)/2
Let h(n) = 5*n**4 + 3*n**3 + 2. Let d(a) = 6*a**4 + 3*a**3 + 3. Let k be 40/(-24) + (-1)/3. Let o(v) = k*d(v) + 3*h(v). Determine r, given that o(r) = 0.
-1, 0
Suppose -10 + 1 = -3*q. Let t be q/(-5) + (1 - 0). Find z such that -1/5*z**4 - 1/5 - 4/5*z + t*z**2 + 8/5*z**3 - 4/5*z**5 = 0.
-1, -1/4, 1
Let z(g) be the second derivative of -1/40*g**6 + g + 0*g**3 + 0 - 1/48*g**4 + 0*g**2 + 1/168*g**7 + 3/80*g**5. Factor z(d).
d**2*(d - 1)**3/4
Let b(z) = -5*z - 2. Let l be b(-2). Solve 9*n**5 - n**4 + n**2 - 2*n**3 - l*n**5 + n**3 = 0 for n.
-1, 0, 1
Let x(l) be the second derivative of l**6/15 + 9*l**5/10 + 4*l**4 + 16*l**3/3 - 15*l. Let x(c) = 0. Calculate c.
-4, -1, 0
Let f(i) = -65*i**5 + 120*i**4 - 120*i**3 + 65*i**2 - 25*i. Let g(a) = -8*a**5 + 15*a**4 - 15*a**3 + 8*a**2 - 3*a. Let l(x) = -3*f(x) + 25*g(x). Factor l(z).
-5*z**2*(z - 1)**3
Let m(c) = -3*c + 6. Let h be m(0). Let x(s) be the first derivative of 7/10*s**2 - 2/5*s + 2/25*s**5 - 1/30*s**h + 1/10*s**4 - 2 - 8/15*s**3. Factor x(t).
-(t - 1)**4*(t + 2)/5
Suppose -3*l + 5*n = -24, 0 = -3*l - 0*n - 5*n - 6. Suppose -12*t**2 + 3*t - 4 + 3*t**l - 7 + 5 + 12*t = 0. What is t?
1, 2
Let h be ((-10)/4)/(1/9). Let q = h + 23. Factor 0*p**2 + 1/2*p**3 + 0 - q*p.
p*(p - 1)*(p + 1)/2
Let d(k) = k**2 + 1 + 0*k**2 + 1 - 4*k**3 - 2*k + 5*k**2. Let m(t) = -t**3 + t + 1. Let s(h) = d(h) - 2*m(h). Factor s(z).
-2*z*(z - 2)*(z - 1)
Let r(n) be the second derivative of -n**7/14 - n**6/5 + n**4/2 + n**3/2 - 8*n. What is u in r(u) = 0?
-1, 0, 1
Let b(x) be the third derivative of -x**6/16 - 11*x**5/48 - 25*x**4/96 + 22*x**2. Factor b(v).
-5*v*(v + 1)*(6*v + 5)/4
Let j(z) = -21*z. Let t be j(-1). Let s be (1/(-2))/(t/(-12)). Find i such that 2/7 - s*i**2 + 0*i = 0.
-1, 1
Let o(b) be the second derivative of b**9/1080 + 3*b**8/1120 + b**7/630 + 7*b**4/12 + 2*b. Let r(j) be the third derivative of o(j). Factor r(x).
2*x**2*(x + 1)*(7*x + 2)
Let l = 39/92 - 4/23. Factor -l*z**2 + 0*z + 1/4*z**3 + 0.
z**2*(z - 1)/4
Suppose -2/3*r**2 - 1/3 - r = 0. What is r?
-1, -1/2
Suppose 2 + 1 = 3*i - 3*w, -4*i = 2*w + 2. Determine d so that -2/3*d + i + d**3 - 1/3*d**2 = 0.
-2/3, 0, 1
Let g(d) be the first derivative of -d**4/12 + d**3/2 - d**2 + 6*d - 7. Let c(y) be the first derivative of g(y). Factor c(m).
-(m - 2)*(m - 1)
Let h(p) be the second derivative of p**9/1512 - p**7/560 + p**6/720 + p**3 + 5*p. Let g(n) be the second derivative of h(n). Factor g(o).
o**2*(o + 1)*(2*o - 1)**2/2
Let t(i) = -10*i**4 + 31*i**3 + 29*i**2 - 20*i - 19. Let j(x) = 5*x**4 - 16*x**3 - 14*x**2 + 10*x + 9. Let v(q) = 11*j(q) + 6*t(q). Factor v(r).
-5*(r - 3)*(r - 1)*(r + 1)**2
Let t(o) be the second derivative of o**5/12 - 5*o**3/6 - 5*o**2/3 + 46*o. Factor t(a).
5*(a - 2)*(a + 1)**2/3
Let b(h) be the third derivative of h**6/120 + h**5/30 - h**4/6 - 4*h**3/3 - 28*h**2. Find g such that b(g) = 0.
-2, 2
Find g, given that 3*g**2 - 8*g**2 + 0*g**4 + 3*g**4 + 2*g**4 = 0.
-1, 0, 1
Let k = 9 + -6. Suppose 0*l - 3*l - k*v = -12, 0 = -l - 5*v. Solve -6*d**4 - 4*d**5 + 6*d**2 + d**l + 4*d - d = 0 for d.
-1, 0, 1
Let k(l) be the third derivative of l**7/2940 - l**6/1260 - l**3/3 - 3*l**2. Let y(j) be the first derivative of k(j). Factor y(u).
2*u**2*(u - 1)/7
Let j(p) be the first derivative of -3 + 0*p - 2/5*p**5 + 1/2*p**2 - 1/6*p**6 + 2/3*p**3 + 0*p**4. Let j(n) = 0. What is n?
-1, 0, 1
Let w(d) = -3*d**5 + 7*d**4 - 7*d**3 - 2*d**2. Let m = 0 + 1. Let h(r) = -r**5 + r**4 - r**3. Let u(j) = m*w(j) - 5*h(j). What is i in u(i) = 0?
-1, 0, 1
Suppose -2 = 5*b - q + 1, -4*b + 4*q - 12 = 0. Factor b - 1/2*i**5 - 5/2*i**4 - i - 9/2*i**3 - 7/2*i**2.
-i*(i + 1)**3*(i + 2)/2
Find m such that 9/8*m + 15/8*m**3 + 0 - 3/8*m**4 - 21/8*m**2 = 0.
0, 1, 3
Let k(b) = -14*b**4 + 4*b**3 - 4*b**2 - 16*b - 12. Let x(g) = g**4 + g**2 + 1. Let z(p) = -k(p) - 12*x(p). Determine u, given that z(u) = 0.
-2, 0, 2
Suppose 8 + 1 = 3*h. Factor -3*m + 3*m**3 + 0*m**h - 3*m**2 + 0 + 3 + 0*m.
3*(m - 1)**2*(m + 1)
Let o(x) = -151962*x**3 + 24639*x**2 - 1335*x + 27. Let j(t) = 151963*t**3 - 24638*t**2 + 1336*t - 28. Let m(w) = 3*j(w) + 4*o(w). Let m(z) = 0. Calculate z.
2/37
Let s(y) be the first derivative of 2*y**3/21 + 2*y**2/7 + 2*y/7 - 10. What is j in s(j) = 0?
-1
Let a(i) = 7*i**4 - 4*i**3 - 5*i**2 + 4*i - 2. Let k(o) = o**4 - o**2. Let j = -15 - -5. Let v = j - -15. Let s(d) = v*k(d) - a(d). Factor s(h).
-2*(h - 1)**3*(h + 1)
Factor -1/2*x**3 + 0 + 1/2*x**5 - 1/2*x**2 + 1/2*x**4 + 0*x.
x**2*(x - 1)*(x + 1)**2/2
Factor -4*s**3 + 2*s + 15*s**2 - 29 + 34 - 17*s - s**3.
-5*(s - 1)**3
Let x = 4 + -7. Let y = x - -5. Let -8/3*t + 2*t**y + 2/3 = 0. Calculate t.
1/3, 1
Let n(y) be the third derivative of -y**5/240 + y**4/96 + y**3/12 - 10*y**2. Let n(p) = 0. What is p?
-1, 2
Let u(j) be the first derivative of -j**7/2520 + j**6/1080 + j**5/360 - j**4/72 + j**3/3 - 2. Let g(z) be the third derivative of u(z). Factor g(s).
-(s - 1)**2*(s + 1)/3
Let r be ((-4)/(-162))/((-1)/(-3)). Let l(a) be the first derivative of -4/9*a + 5/9*a**2 + 2 - r*a**3 - 5/18*a**4 + 2/15*a**5. Find z such that l(z) = 0.
-1, 2/3, 1
Let m = -1578/5 - -318. Factor 3/5*b**2 - m*b + 12/5.
3*(b - 2)**2/5
Suppose -2*n + 6 = 0, 2*n + 17 = -4*m + 39. Let a = -113 + 115. Find i such that 9/5*i**a + 24/5*i + 3/5*i**m - 12/5 - 33/5*i**3 + 9/5*i**5 = 0.
-2, -1, 2/3, 1
Let p = 59 - 57. Determine k, given that -k - 1/4*k**p - 1 = 0.
-2
Let t(o) be the first derivative of -3*o**4/28 - 4*o**3/7 - 9*o**2/14 + 30. Factor t(l).
-3*l*(l + 1)*(l + 3)/7
Let y(d) = -d**3 + 3*d**2 - d. Let a be y(2). Suppose -8/3 + 8/3*t - 2/3*t**a = 0. What is t?
2
Let g(t) = t - 5. Let d be g(5)