t r(l) be the first derivative of l**5/20 + l**4/4 + 5*l**3/12 + l**2/4 + 3. Determine v, given that r(v) = 0.
-2, -1, 0
Let r(n) be the first derivative of -3*n**4/8 - n**3/2 + 3*n**2 + 6*n - 16. Suppose r(i) = 0. Calculate i.
-2, -1, 2
Let u(h) be the first derivative of h**6/900 - h**5/150 + 5*h**3/3 + 5. Let c(m) be the third derivative of u(m). Factor c(q).
2*q*(q - 2)/5
Let p = 10 + -22. Let n be (0 - -7)*p/(-42). Find g such that 0 + 0*g + 1/5*g**n = 0.
0
Let h(s) be the second derivative of -4*s**5/15 + s**4/6 - 32*s. Factor h(g).
-2*g**2*(8*g - 3)/3
Let z(o) be the first derivative of -o**6/9 + 2*o**5/3 - 7*o**4/6 + 2*o**3/3 + 15. Suppose z(b) = 0. What is b?
0, 1, 3
Suppose 0*j + j - 6 = 2*n, n + 12 = 5*j. Suppose 18*q + q**3 + q**j - 20*q + 0*q**2 = 0. What is q?
-2, 0, 1
Let n(r) be the first derivative of -2*r**3/21 + r**2/7 + 9. Let n(o) = 0. What is o?
0, 1
Let q = -1665/104 + 252/13. Let a = q + -103/40. Determine x, given that -14/5*x**2 + a*x + 0 = 0.
0, 2/7
Let p(l) be the second derivative of -3*l**5/20 - 3*l**4/4 - 3*l**3/2 - 3*l**2/2 + 2*l. Factor p(m).
-3*(m + 1)**3
Let c(y) = 25*y**2 - 15*y - 40. Let v(p) = -3*p**2 + 2*p + 5. Let m(i) = 6*c(i) + 51*v(i). Suppose m(q) = 0. What is q?
-1, 5
Find m such that -2/3*m**2 - 1/3 + 1/9*m**4 + 8/9*m + 0*m**3 = 0.
-3, 1
Let b(s) be the third derivative of 0 + 0*s - 1/9*s**3 - 1/45*s**5 + 1/360*s**6 + 5/72*s**4 - 3*s**2. Factor b(d).
(d - 2)*(d - 1)**2/3
Let y(d) be the third derivative of -d**5/270 + 7*d**4/108 - 10*d**3/27 - 23*d**2. Factor y(r).
-2*(r - 5)*(r - 2)/9
Suppose -3*m + 2*k = -1 - 3, -3*k = m - 5. Suppose -1/4 + l**m + 3/4*l = 0. What is l?
-1, 1/4
Suppose 5*z - 36 = -z. What is s in -4/3*s**3 + 0*s - z*s**4 + 0*s**2 - 14/3*s**5 + 0 = 0?
-1, -2/7, 0
Let t(z) be the second derivative of -10*z**7/21 + 14*z**6/15 + 3*z**5/5 - 7*z**4/3 + 4*z**3/3 + 9*z. Solve t(l) = 0 for l.
-1, 0, 2/5, 1
Let n(j) be the second derivative of j**6/255 - j**5/85 + 2*j**3/51 - j**2/17 - 18*j. Solve n(q) = 0 for q.
-1, 1
Suppose 0 = y - 1, 4*r + 11 + 4 = -y. Let l be (-4)/(-2)*(-6)/r. Let 0 - 2/11*v**2 - 4/11*v + 2/11*v**l = 0. What is v?
-1, 0, 2
Let f(j) be the first derivative of -j**6/30 + j**5/25 + j**4/20 - j**3/15 + 8. What is c in f(c) = 0?
-1, 0, 1
Let j(v) be the first derivative of -3*v**7/1120 + v**6/480 + 10*v**3/3 - 9. Let t(i) be the third derivative of j(i). Determine z so that t(z) = 0.
0, 1/3
Factor -144 + 160 + 2*v**3 - 12*v**2 + 2*v**4 - 4*v - 4*v.
2*(v - 2)*(v - 1)*(v + 2)**2
Let j(q) be the second derivative of q**6/15 - q**4/6 - q. What is p in j(p) = 0?
-1, 0, 1
Let i(u) be the third derivative of 4*u**2 + 1/21*u**5 + 0 + 0*u**3 + 0*u + 1/21*u**4 + 1/70*u**6. Solve i(l) = 0 for l.
-1, -2/3, 0
Let c(j) be the third derivative of j**7/105 + 3*j**6/140 + j**5/105 - 10*j**2. Find h, given that c(h) = 0.
-1, -2/7, 0
What is n in 2/3 - 2/3*n**3 - 2/3*n**2 + 2/3*n = 0?
-1, 1
Let p(g) be the third derivative of -g**5/90 - g**4/36 + 2*g**3/9 - 5*g**2. Solve p(c) = 0.
-2, 1
Let z be 220/(-672) - (-2)/6. Let j(f) be the third derivative of 1/105*f**7 + 0 - 1/30*f**5 + 0*f + 1/60*f**6 - 2*f**2 - z*f**8 + 0*f**3 + 0*f**4. Factor j(b).
-2*b**2*(b - 1)**2*(b + 1)
Let j(t) be the second derivative of 0*t**2 - t + 1/10*t**6 + 1/10*t**5 - 7/12*t**4 + 1/3*t**3 + 0. Factor j(l).
l*(l - 1)*(l + 2)*(3*l - 1)
Let l be 286/65 - (-4)/(-10). Solve 32*w - 32*w - l*w**3 + 4*w**5 - 4*w**2 + 4*w**4 = 0 for w.
-1, 0, 1
Let a be 3 - -1 - 19/(-19). Suppose 4*q - 4 = -d - 0*d, -3*d = -5*q + a. Factor d + 3*t**3 + 0*t - 3/2*t**4 - 3/2*t**2.
-3*t**2*(t - 1)**2/2
Let l(x) be the first derivative of -6*x**5/55 + 4*x**3/11 - 6*x/11 + 24. Factor l(s).
-6*(s - 1)**2*(s + 1)**2/11
Let q(c) = c - 7. Let d be q(0). Let w be 3 - (1 - 8/d). What is m in 2/7*m**3 + w*m**2 + 6/7*m + 2/7 = 0?
-1
Let r(f) = -f**3 - 5*f**2 - 6*f - 5. Suppose -2*a - 12 = a. Let m be r(a). Find j such that 3*j**m + 7*j - 6*j**2 - j - 3*j = 0.
0, 1
Let k(t) be the second derivative of -t**6/40 + t**5/40 + t**4/12 - t**3/12 - t**2/8 + 25*t. Solve k(h) = 0 for h.
-1, -1/3, 1
Let g(d) = -d**3 - 1 - 3*d**2 + 2*d**2 + 3 + d. Let c be g(0). Solve y**5 + 3*y**3 + y**c - 1 + 1 + 3*y**4 = 0 for y.
-1, 0
Suppose 16/13 + 2/13*k**3 + 24/13*k + 12/13*k**2 = 0. Calculate k.
-2
Determine u so that -u**2 - 1/2*u**5 + 1/2*u**4 - 1/2*u + u**3 + 1/2 = 0.
-1, 1
Let b(k) be the third derivative of -5*k**8/112 - 12*k**7/35 - 23*k**6/25 - 24*k**5/25 - 2*k**4/5 + 14*k**2. Factor b(a).
-3*a*(a + 2)**2*(5*a + 2)**2/5
Let o(n) be the third derivative of -n**6/300 + n**5/150 + n**4/30 - 6*n**2. Factor o(x).
-2*x*(x - 2)*(x + 1)/5
Let c(h) be the third derivative of h**7/1050 + h**6/200 + h**5/150 + 2*h**2. Factor c(m).
m**2*(m + 1)*(m + 2)/5
Let s(f) be the first derivative of f**7/168 - f**6/120 - f**5/80 + f**4/48 - f - 1. Let k(v) be the first derivative of s(v). Determine u, given that k(u) = 0.
-1, 0, 1
Let j(o) be the first derivative of -o**6/33 - 6*o**5/55 - 3*o**4/22 - 2*o**3/33 + 7. Factor j(h).
-2*h**2*(h + 1)**3/11
Factor 2/5 + 1/5*b**3 + 0*b**2 - 3/5*b.
(b - 1)**2*(b + 2)/5
Factor 0*i - 7*i**4 + 0*i + 11*i**4.
4*i**4
Let c = 77 + -72. Let y(i) be the second derivative of 1/42*i**4 + 1/70*i**c - 1/7*i**2 + 0 - 1/21*i**3 - 2*i. Factor y(g).
2*(g - 1)*(g + 1)**2/7
Let q(v) = 20*v**2 - 600*v + 4516. Let m(t) = 4*t**2 - 120*t + 903. Let d(h) = 16*m(h) - 3*q(h). Find a such that d(a) = 0.
15
Let z(p) = 0 - 4 + 20*p**2 - 4*p + 4*p**2 - 14*p**3. Suppose 0 = 3*b + b - 4. Let j(g) = g**3 - g + 1. Let y(k) = b*z(k) + 4*j(k). Factor y(s).
-2*s*(s - 2)*(5*s - 2)
Let v(b) be the second derivative of 0 + 2/5*b**6 + 9/20*b**5 + 5/42*b**7 + 0*b**3 + 1/6*b**4 + 0*b**2 + b. Factor v(a).
a**2*(a + 1)**2*(5*a + 2)
Let f be 3*-1 - 15*(-7)/21. Let l = -6 + 9. Let 0*c + 0*c**l - 3/5*c**f + 3/5*c**4 + 0 = 0. Calculate c.
-1, 0, 1
Let j(h) = h**4 + 2*h**3 + 5*h**2 - 5*h + 3. Let c(x) = -2*x**4 - 2*x**3 - 6*x**2 + 6*x - 4. Let b(t) = -3*c(t) - 4*j(t). Determine m so that b(m) = 0.
-1, 0, 1
Let d(h) be the first derivative of h**5/20 + h**4/4 - 2*h**2 - 1. Let l(m) be the second derivative of d(m). Let l(i) = 0. What is i?
-2, 0
Suppose -3*b - y = 18, -3*y + 0 = -b - 16. Let d be b/(-5)*84/98. Suppose 2*o - 2*o**3 + 8/5*o**4 - 2/5 - d*o**2 = 0. What is o?
-1, 1/4, 1
Let t be (-16 + 14)*3/(-21). Factor -2/7 - t*j**2 - 4/7*j.
-2*(j + 1)**2/7
Factor 0 + 2/13*d**5 + 0*d - 6/13*d**3 + 0*d**4 + 4/13*d**2.
2*d**2*(d - 1)**2*(d + 2)/13
Let s(o) = 8*o**5 - 8*o**3 + 4*o**2 - 4*o - 4. Let n(c) = -c**5 - c**4 + c**3 + c + 1. Let t(q) = -4*n(q) - s(q). Let t(x) = 0. Calculate x.
-1, 0, 1
Let m(g) be the third derivative of -g**6/660 + g**5/66 - g**4/33 - 17*g**2. Factor m(h).
-2*h*(h - 4)*(h - 1)/11
Let j(y) be the second derivative of y**7/280 - y**6/120 + y**5/240 + y**2/2 - y. Let x(a) be the first derivative of j(a). Factor x(m).
m**2*(m - 1)*(3*m - 1)/4
Let n(q) be the second derivative of 8/5*q**2 - 44/15*q**3 - 1/2*q**5 + 2*q + 7/3*q**4 + 0. Let n(m) = 0. What is m?
2/5, 2
Let s(j) be the third derivative of j**6/24 + 5*j**5/2 + 125*j**4/2 + 2500*j**3/3 + 22*j**2 + 2. Factor s(m).
5*(m + 10)**3
Let g be 2*(-4 + (-27)/(-6)). Factor 1/2*m**2 - g - 1/2*m.
(m - 2)*(m + 1)/2
Let b(w) be the second derivative of 0 - 6*w + 1/21*w**3 - 1/70*w**5 + 2/7*w**2 + 1/7*w**6 - 17/42*w**4. What is u in b(u) = 0?
-1, -1/3, 2/5, 1
Let g be 5/((-1540)/(-808)) - 4/(-14). Factor -18/11*t**2 + g*t + 8/11.
-2*(t - 2)*(9*t + 2)/11
Suppose 63*f + 6 = 65*f. Solve -2/3*o**2 - 2/9*o - 2/9*o**4 + 0 - 2/3*o**f = 0.
-1, 0
Let l(q) = -80*q**2 - 810*q - 3715. Let v(m) = -9*m**2 - 90*m - 413. Let f(z) = -4*l(z) + 35*v(z). Factor f(i).
5*(i + 9)**2
Let z(l) be the first derivative of -2/15*l**5 - 1/6*l**6 + 0*l**2 + 7 + 0*l**3 + 0*l + 1/12*l**4. Factor z(x).
-x**3*(x + 1)*(3*x - 1)/3
Let d(c) = -7*c**2 - 19*c. Let j(p) = 2*p**2 + 5*p. Let i(b) = -6*d(b) - 22*j(b). Solve i(t) = 0 for t.
0, 2
Factor 0 + 0*t**2 - 2/5*t**3 - 8/5*t**5 + 0*t + 8/5*t**4.
-2*t**3*(2*t - 1)**2/5
Let r(v) be the second derivative of -1/9*v**3 - v + 0*v**6 + 1/15*v**5 - 1/63*v**7 + 0*v**4 + 0*v**2 + 0. Factor r(z).
-2*z*(z - 1)**2*(z + 1)**2/3
Let s(l) be the third derivative of -l**5/15 - l**4/6 - 8*l**2. Solve s(g) = 0 for g.
-1, 0
Let s = 78