 l**5/30 + l**4/72 - l**3/2 - 4*l**2. Let m(t) be the first derivative of p(t). Find r, given that m(r) = 0.
1/6
Let m be ((-15)/2 - -1)/(1064/(-304)). Suppose m*v**2 + 4/7 + 1/7*v**4 + 12/7*v + 6/7*v**3 = 0. Calculate v.
-2, -1
Let w(n) = n**2 + 3*n + 3. Let o be w(-3). Let a(r) be the first derivative of 0*r - r**o - 3*r**2 + 3/4*r**4 + 3. Suppose a(i) = 0. What is i?
-1, 0, 2
Let r(c) be the second derivative of c**4/60 - 2*c**3/15 + 2*c**2/5 - 10*c. Factor r(q).
(q - 2)**2/5
Let n(l) be the third derivative of -l**8/588 - 2*l**7/245 + 4*l**5/105 + 24*l**2. Factor n(u).
-4*u**2*(u - 1)*(u + 2)**2/7
Let a(g) = -g. Let v be a(-4). Let d(t) = t - 2. Let q be d(v). Factor -1/2*o**2 - q - 2*o.
-(o + 2)**2/2
Let j(t) be the third derivative of 5/8*t**4 + 1/2*t**3 + 1/5*t**5 + 3*t**2 + 0*t + 0. Factor j(w).
3*(w + 1)*(4*w + 1)
Suppose -44*c = -39*c + 4*s - 22, 0 = -3*c - s + 9. Factor -15/8*b**3 + 1/2*b**4 - 3/8*b - 1/4 + 2*b**c.
(b - 2)*(b - 1)**2*(4*b + 1)/8
Let h = -13/12 + 4/3. Determine k, given that -1/2 - h*k**3 + 3/4*k + 0*k**2 = 0.
-2, 1
Let a be 32/12 + 4/(-6). Let m = 10 + -7. Find d such that -2*d - 5*d**4 - 2*d**5 + a*d**3 - 5*d**5 + 7*d**m + 5*d**2 = 0.
-1, 0, 2/7, 1
Factor 0 - 2/3*c - 2/3*c**2.
-2*c*(c + 1)/3
Let k(z) = z**2 - 1. Let v(b) = -b**3 - b**2 + 3*b + 3. Let m(n) = -3*k(n) - v(n). Find c, given that m(c) = 0.
-1, 0, 3
Suppose -b = -4*p - 3*b - 14, 0 = 2*b + 10. Let i be (0 + p)/(2/(-4)). Factor c**3 + c**2 + 2 - 4*c**3 + 3*c - c**4 - 2*c**i.
-(c - 1)*(c + 1)**2*(c + 2)
Let c(u) = u - 1. Let w(g) = g**2 - g. Let x(o) = 6*c(o) + 3*w(o). Suppose x(t) = 0. Calculate t.
-2, 1
Let f be (-302 - 1)*6/14. Let h = 131 + f. Suppose -h*c**3 - 4/7*c + 2*c**2 - 2/7 = 0. Calculate c.
-1/4, 1
Factor -2*s**3 - 6/5*s**2 + 0 - 2/5*s**4 + 18/5*s.
-2*s*(s - 1)*(s + 3)**2/5
Let s(g) be the second derivative of -g**4/12 - g**3/2 + 2*g**2 - 4*g. Let i be s(-3). Factor 2*l**2 + 9*l + 6*l - i*l**2 - 7*l**2 - 6.
-3*(l - 1)*(3*l - 2)
Let g(l) be the second derivative of -1/3*l**3 - 5*l + 0 + 1/12*l**4 + 1/2*l**2. Factor g(v).
(v - 1)**2
Let g(d) be the third derivative of -d**7/42 - d**6/24 + d**5/12 + 5*d**4/24 - 13*d**2. Let g(o) = 0. Calculate o.
-1, 0, 1
Let h(v) = -2*v - 3*v - 11*v + v**3 - 14*v**2 + 0*v + 18. Let a be h(15). Factor 0*k + 9/7*k**5 - 24/7*k**4 + a*k**3 + 0 - 6/7*k**2.
3*k**2*(k - 1)**2*(3*k - 2)/7
Let -3*y**2 + y**2 - 4 + 6*y**2 = 0. What is y?
-1, 1
Let v(g) be the second derivative of g**6/540 + g**5/270 + 3*g**2/2 - 2*g. Let u(c) be the first derivative of v(c). Let u(z) = 0. Calculate z.
-1, 0
Let k(m) be the first derivative of -m**6/540 - m**5/270 + m**2 - 5. Let o(z) be the second derivative of k(z). Factor o(p).
-2*p**2*(p + 1)/9
Let z(c) be the third derivative of c**7/630 + c**6/120 + c**5/90 + 3*c**2. Let z(h) = 0. What is h?
-2, -1, 0
Let u(i) be the first derivative of -i**6/720 + i**4/48 + i**3 + 2. Let x(g) be the third derivative of u(g). Let x(w) = 0. What is w?
-1, 1
Suppose 25*s + 23*s**3 + 12*s**2 + 4 - 32*s**3 - 10 - 10*s = 0. What is s?
-1, 1/3, 2
Let r(w) be the second derivative of -w**8/1344 - w**7/210 - w**6/120 + 5*w**2/2 + 6*w. Let i(d) be the first derivative of r(d). Factor i(p).
-p**3*(p + 2)**2/4
Let d be ((-63)/27)/(20/(-6)). Let j(t) be the first derivative of 0*t - 5/8*t**4 + 2 - 1/4*t**6 - d*t**5 - 1/6*t**3 + 0*t**2. Factor j(r).
-r**2*(r + 1)**2*(3*r + 1)/2
Let v(s) be the second derivative of 0*s**4 + 1/30*s**5 + 0*s**2 + 1/45*s**6 + 0 + 0*s**3 - 5*s. Factor v(a).
2*a**3*(a + 1)/3
Let b(c) = -c**2 - 8*c - 8. Let m be b(-6). Let j(h) = -h**2 + 5*h - 4. Let d be j(m). Factor v**3 + 0 + d*v - 1/2*v**2 - 1/2*v**4.
-v**2*(v - 1)**2/2
Let l = 71/150 - -2/75. Let t(n) be the second derivative of n + 1/3*n**4 + 0*n**2 + 0*n**3 + 0 + l*n**5. Suppose t(j) = 0. Calculate j.
-2/5, 0
Find j such that 0*j**3 + 18*j**2 + 41*j + 55*j + 2*j**3 + 128 + 6*j**2 = 0.
-4
Let x = 67 - 67. Let r(a) be the second derivative of -1/60*a**6 + 1/168*a**7 + 0*a**5 - 1/24*a**3 + 1/24*a**4 + x + 0*a**2 + 2*a. Factor r(b).
b*(b - 1)**3*(b + 1)/4
Suppose -5*s = -w - 5, -s + 20 = 2*w + 4*s. Let u = 430/3 - 142. Factor -3*n**4 + 2*n**3 + 0*n + u*n**w - 1/3*n**2 + 0.
n**2*(n - 1)**2*(4*n - 1)/3
Determine t, given that 0*t**2 - 4*t**4 + 6*t**2 - 3*t**5 - 107*t - 2*t**4 + 110*t = 0.
-1, 0, 1
Find o, given that -4/3*o**3 + 0 + 4/3*o - 14/3*o**2 + 14/3*o**4 = 0.
-1, 0, 2/7, 1
Let z(m) be the third derivative of 0*m + 1/72*m**4 + 1/120*m**6 + 1/630*m**7 + 1/60*m**5 + 0*m**3 - 3*m**2 + 0. Determine l, given that z(l) = 0.
-1, 0
Let z(o) = o**2 - 6*o - 4. Let s be z(7). Suppose -2*p = -s*p. What is m in 1/5*m**2 + p + 1/5*m = 0?
-1, 0
Let d = -2/81 - -143/324. Let w(r) be the second derivative of -d*r**4 - 1/3*r**3 - 3/20*r**5 + 0*r**2 + 0 + 2*r. Let w(c) = 0. Calculate c.
-1, -2/3, 0
Let x(i) = -9*i**4 + 8*i**3 + 5*i**2 + 6*i + 5. Let l(z) = -z**3 - z - 1. Let f(v) = -5*l(v) - x(v). Suppose f(d) = 0. Calculate d.
-1/3, 0, 1
Let o(t) = -t**2 + t - 1. Let r(p) = 5*p**2 - 5*p + 10. Let m(x) = -6*o(x) - r(x). Let c be m(3). Factor 0*j + 2*j**2 - 8 + 8*j - 4*j**c.
-2*(j - 2)**2
Factor 0 - 3/2*y**4 + y**2 - 1/2*y**3 + 0*y.
-y**2*(y + 1)*(3*y - 2)/2
Factor -2 + 2/3*t**2 + 4/3*t.
2*(t - 1)*(t + 3)/3
Let y(l) be the third derivative of -l**6/60 - 7*l**5/240 + l**4/96 - 50*l**2. Factor y(i).
-i*(i + 1)*(8*i - 1)/4
Let h(s) be the third derivative of -s**5/90 - s**4/18 - s**3/9 + 7*s**2. Factor h(g).
-2*(g + 1)**2/3
Let y(o) be the first derivative of -o**5/40 - o**4/8 - o**3/4 - o**2/4 + 2*o - 1. Let f(g) be the first derivative of y(g). What is j in f(j) = 0?
-1
Let g(x) be the first derivative of 9*x**4/32 - x**3/2 - 15*x**2/16 + 3*x/4 + 12. Factor g(s).
3*(s - 2)*(s + 1)*(3*s - 1)/8
Solve -10/17*f**3 + 0 + 8/17*f - 8/17*f**2 + 6/17*f**4 = 0.
-1, 0, 2/3, 2
Let p(a) be the first derivative of 0*a**4 + 1/6*a**3 - 1/3*a**2 - 1/60*a**5 + 2 - 2*a. Let x(l) be the first derivative of p(l). Solve x(j) = 0.
-2, 1
Suppose -19*h**2 + 2*h**5 - 12*h**3 - 6*h + 5*h**2 - 2*h**2 = 0. Calculate h.
-1, 0, 3
Let h be 1 - ((-171)/6 - -1). Let v = -28 + h. Let -1 + v*s**2 + 1/2*s = 0. What is s?
-2, 1
Let a(i) be the third derivative of -i**7/42 + i**6/24 + i**5/4 - 25*i**4/24 + 5*i**3/3 - 8*i**2. What is b in a(b) = 0?
-2, 1
Factor -8*i**4 + 12*i**3 + 0 + 4/3*i**5 + 0*i - 16/3*i**2.
4*i**2*(i - 4)*(i - 1)**2/3
Let b(r) be the first derivative of r**7/147 - r**6/140 - r**5/105 - r**2 - 1. Let p(z) be the second derivative of b(z). Solve p(k) = 0.
-2/5, 0, 1
Suppose -5*q + 8*q - 6 = 0. Suppose 3*m + 5*m + 2 + 6*m**2 + 2 - 2*m**q = 0. Calculate m.
-1
Suppose -11 = b - 2*d - 3*d, 4*b - 5*d - 1 = 0. Let o = b + -1. Factor -32*u + 51*u**o + 18*u**2 - 24 - 47*u + 15*u**4 + 19*u.
3*(u - 1)*(u + 2)**2*(5*u + 2)
Let z = -130/3 - -44. Factor 4/3 - z*x - 2/3*x**2.
-2*(x - 1)*(x + 2)/3
Let l(z) = -z**3 + 8*z**2 + 2*z - 12. Let s be l(8). Let o be (-3)/s - 11/(-4). Determine g so that -2/11 - 2/11*g**o - 4/11*g = 0.
-1
Factor -19 - 20 - 24 + 75 - 3*o**2.
-3*(o - 2)*(o + 2)
Let q = -308 + 308. Factor 1/5*h**4 + q - 4/5*h**3 - 2/5*h + h**2.
h*(h - 2)*(h - 1)**2/5
Let d(o) be the second derivative of -o**2 - 1/60*o**5 - o + 1/12*o**4 + 0*o**3 + 0. Let c(y) be the first derivative of d(y). Factor c(a).
-a*(a - 2)
Let m(c) be the third derivative of -c**5/210 - c**4/42 + c**3/7 - 2*c**2. Factor m(n).
-2*(n - 1)*(n + 3)/7
Let x(l) = -l**3 + 5*l**2 - 2*l - 5. Let i be x(4). Let v(a) be the first derivative of 3 - 26/5*a**i - 8/5*a + 22/5*a**2 + 9/4*a**4. Let v(o) = 0. Calculate o.
2/5, 2/3
Suppose 8 = -q - 4*n, -7*q + 12*q + 2*n = -4. Determine p so that 2/7*p**2 + q + 2/7*p**3 + 0*p = 0.
-1, 0
Determine w, given that -1/5*w**4 + 1/5*w**2 + 0*w - 1/5*w**3 + 0 + 1/5*w**5 = 0.
-1, 0, 1
Let v(j) be the third derivative of 1/15*j**5 + 1/12*j**6 + 0*j + 0 + 0*j**3 - 1/4*j**4 + 5*j**2. Factor v(r).
2*r*(r + 1)*(5*r - 3)
Let n be 7 + (-3)/(1 + 2). Factor 0*x + 2*x - n + 6*x**2 - 3*x**3 - 2*x + 3*x.
-3*(x - 2)*(x - 1)*(x + 1)
Let r = 19/5 + -52/15. Factor 0*j**4 + 1/3*j**5 + r*j + 0 + 0*j**2 - 2/3*j**3.
j*(j - 1)**2*(j + 1)**2/3
Suppose 3*u - 18 = -f, 0 = u - 2 - 2. Let k = f - 6. Factor 2/3*i**4 + k + 0*i**2 - 1/3*i**3 - 1/3*i**5 + 0*i.
-i**3*(i - 1)**2/3
Factor 2*i**3 + 4*i**2 + 0*i