ative of s(y). Let a(k) = 0. Calculate k.
-1, 0
Let q be 10620/(-84) + 1 + -4. Let l = q + 130. Determine a, given that -l - 18/7*a**2 - 22/7*a = 0.
-1, -2/9
Let v(s) be the first derivative of 4*s**3/3 + 8*s**2 + 13. Let v(p) = 0. Calculate p.
-4, 0
Let k(x) be the second derivative of x**6/10 - 3*x**5/20 + 8*x. Suppose k(n) = 0. What is n?
0, 1
Let y(o) = -9*o**3 + 9*o - 21. Let s(i) = -2*i**3 + 2*i - 5. Let r(j) = -21*s(j) + 5*y(j). Factor r(d).
-3*d*(d - 1)*(d + 1)
Let g(d) = -d. Let l be g(-2). Let v(s) = -s**3 + s - 2. Let k be v(-2). Factor -2*j - l*j**2 + k*j - 2*j.
-2*j**2
Let j(d) be the second derivative of 2*d**6/15 - 4*d**5/5 + 5*d**4/3 - 4*d**3/3 + 32*d. Find u such that j(u) = 0.
0, 1, 2
Suppose 0 = 2*w + 2*w - 2*d - 48, -56 = -4*w - 2*d. Suppose 2*f = -5 + w. Factor 2/5*j**f + 2/5 - 8/5*j - 8/5*j**3 + 12/5*j**2.
2*(j - 1)**4/5
Let u(z) be the second derivative of -z**7/189 + 11*z**6/135 - 43*z**5/90 + 73*z**4/54 - 56*z**3/27 + 16*z**2/9 - 34*z. Factor u(c).
-2*(c - 4)**2*(c - 1)**3/9
Let x(l) be the first derivative of 0*l + 6 + 0*l**2 + 2/15*l**3. Determine z, given that x(z) = 0.
0
Let l be (4/(-7))/(20/84*-6). Suppose -n + 15 = -3*y, 3*n - 21 + 0 = 3*y. Find s, given that l*s**n + 4/5 + 0*s**2 - 6/5*s = 0.
-2, 1
Let w(q) = 2*q + 7. Let n(y) = 2*y + 8. Let g(x) = -3*n(x) + 4*w(x). Let l be g(-2). Factor 2/3*v**2 + 0*v + l - v**3.
-v**2*(3*v - 2)/3
Let t(d) = 20*d**2 + 7*d + 31. Let p(b) = -7*b**2 - 2*b - 10. Let u(i) = 17*p(i) + 6*t(i). Solve u(w) = 0 for w.
-4
Let g(j) be the first derivative of -6*j + 3 + 6*j - 3*j**2 + 3*j**3 - 2*j**3. Factor g(t).
3*t*(t - 2)
Let q(g) be the first derivative of -2*g**5/35 - g**4/14 + 10*g**3/21 - 3*g**2/7 + 1. Factor q(j).
-2*j*(j - 1)**2*(j + 3)/7
Let w(g) = -g**3 + 3*g**3 - 7*g - g**3 + 6 + 7*g**2 + 4. Let l be w(-8). Factor -10/3*f**3 + 4/3*f - l*f**2 + 0.
-2*f*(f + 1)*(5*f - 2)/3
Let r be -1*6/(-33) + 200/352. Factor 3/4*j**4 + 3/4 - 3/4*j**5 - r*j + 3/2*j**3 - 3/2*j**2.
-3*(j - 1)**3*(j + 1)**2/4
Factor -4/3*k**3 - 2/9*k**5 - 2/9*k + 8/9*k**2 + 0 + 8/9*k**4.
-2*k*(k - 1)**4/9
Suppose -102 - 250 = 4*v. Let r = v - -442/5. Factor -4/5*a**3 - r*a**4 - 2/5*a**2 + 0*a + 0.
-2*a**2*(a + 1)**2/5
Factor 1080*n + 450*n**2 + 125/2*n**3 + 864.
(5*n + 12)**3/2
Let a(u) = -u**3 - 1. Let o(n) = -6*n**3 + 7*n**2 - 15*n + 4. Let z(i) = 20*a(i) - 4*o(i). Factor z(v).
4*(v - 3)**2*(v - 1)
Let x(n) be the first derivative of 0*n - 5 - 2/3*n**2 + 7/6*n**4 + 10/9*n**3. Factor x(h).
2*h*(h + 1)*(7*h - 2)/3
Let b(q) = 4*q**2 + 6*q + 6. Let a(k) = -6*k - 6*k + 8 - 9*k**2 - 21 + 0. Suppose -3*h = 6 - 0. Let i(j) = h*a(j) - 5*b(j). Factor i(l).
-2*(l + 1)*(l + 2)
Suppose 4*l - 5*l = -2. Let o be (-297)/(-90) + (-2)/(-10). Factor -4 - 10*g - o*g**3 + 13*g**l.
-(g - 2)**2*(7*g + 2)/2
Let c be 1/((-27)/15 + 2). Let z be (-1 - -5)/(c + -4). Factor 2*v - 10*v**2 + z*v**3 + 4 - 6*v**3 + 0*v + 6*v**4.
2*(v - 1)**2*(v + 1)*(3*v + 2)
Let v(r) be the second derivative of -r**7/5040 - r**6/1440 + r**4/6 + r. Let c(n) be the third derivative of v(n). Factor c(i).
-i*(i + 1)/2
Determine f so that -42*f**3 + 109/3*f**2 - 12*f + 4/3 + 49/3*f**4 = 0.
2/7, 1
Let a(v) be the third derivative of -v**5/105 - v**4/42 - 5*v**2 + 4. Factor a(b).
-4*b*(b + 1)/7
Let s(p) be the second derivative of -p**8/2240 - p**7/840 + p**6/48 - 3*p**5/40 + 3*p**4/4 + 8*p. Let w(o) be the third derivative of s(o). Factor w(n).
-3*(n - 1)**2*(n + 3)
Let b be (-8)/32 + (63/(-4))/(-3). Let p(l) be the second derivative of 0*l**4 + 1/60*l**6 - 1/20*l**b - 1/4*l**2 + 0 + 3*l + 1/6*l**3. Factor p(c).
(c - 1)**3*(c + 1)/2
Let w be (219/225 - 1)/(2/(-3)). Let r(o) be the second derivative of -1/105*o**7 + 0*o**4 + 0 - 1/15*o**3 + 0*o**6 + w*o**5 + 0*o**2 + 2*o. Factor r(y).
-2*y*(y - 1)**2*(y + 1)**2/5
Factor -4/5*b - 2/5 - 2/5*b**2.
-2*(b + 1)**2/5
Let t(l) be the third derivative of l**8/13440 - l**7/1008 + l**6/180 - l**5/60 + l**4/6 - 5*l**2. Let y(s) be the second derivative of t(s). Factor y(q).
(q - 2)**2*(q - 1)/2
Let u = -3829/555 + 11/111. Let y = 7 + u. Let -y*r + 1/5*r**2 - 2/5 = 0. What is r?
-1, 2
Let m = -5 + 13. Suppose 4*f = 8 + m. Factor -4*k + 2*k + 4*k**3 + 2*k**2 - 2*k**f - 2*k**3.
-2*k*(k - 1)**2*(k + 1)
Let u(v) = -v**3 + v**2 + 1. Let l(i) = 12*i**3 - 7*i**2 - 7*i - 3. Let c(m) = 2*l(m) + 10*u(m). Factor c(k).
2*(k - 1)*(k + 1)*(7*k - 2)
Let c be 3 + ((-4)/2 - -1). Factor 2*r - 3*r**c + r**4 + 2*r**3 - 5*r**3 + 3*r**3.
r*(r - 1)**2*(r + 2)
Let x = 18 - 6. Let j be x/30 - 11/(-10). Find l such that 0 + 3/2*l**2 + j*l = 0.
-1, 0
Solve 2*w**5 - 4*w**5 - 2*w**2 + 0*w**5 - 4*w**4 + 6*w**3 - 8*w + 10*w**2 = 0.
-2, 0, 1
Let d(m) = m**2 + m - 8. Let q(i) = i**2 + i + 1. Let u(w) = -d(w) - 2*q(w). Determine x, given that u(x) = 0.
-2, 1
Let k(r) be the first derivative of -2 + 1/24*r**4 + 1/80*r**5 + 2*r + 0*r**2 + 0*r**3. Let v(m) be the first derivative of k(m). Solve v(d) = 0 for d.
-2, 0
Let h(q) be the second derivative of -q**9/12096 - q**8/3360 + 19*q**7/10080 - q**6/480 - q**4/3 + 3*q. Let f(i) be the third derivative of h(i). Factor f(n).
-n*(n - 1)*(n + 3)*(5*n - 2)/4
Let y(u) be the first derivative of -u**5/40 + u**4/12 + 3*u - 1. Let n(p) be the first derivative of y(p). Let n(h) = 0. What is h?
0, 2
Let s(n) = 2*n**3 + 4*n**2 - 5*n - 7. Let d be (-4)/(-6)*(-45)/(-10). Let k(h) = -h**3 - 2*h**2 + 2*h + 3. Let f(v) = d*s(v) + 7*k(v). Factor f(q).
-q*(q + 1)**2
Factor 2 + 4*s**3 + 18*s**2 - 2 - 22*s**2.
4*s**2*(s - 1)
Let z be (-28)/8*4/(-49). Solve 2/7*x**4 - 2/7*x - 2/7*x**2 + z*x**3 + 0 = 0 for x.
-1, 0, 1
Let u(x) be the second derivative of x**7/336 - x**5/160 + x. Let u(r) = 0. Calculate r.
-1, 0, 1
Let h(a) = -4*a**2 + 23*a - 11. Let u be h(5). Suppose 0 - 2/3*o**u + 4/3*o**3 + 2/3*o**2 - 4/3*o = 0. Calculate o.
-1, 0, 1, 2
Suppose 0 = -0*g + 3*g - 12. Let q be ((-10)/4)/((-2)/g). Suppose -d**3 + 0 - 2*d**2 + 2 + 3*d**3 - q*d + 3*d = 0. What is d?
-1, 1
Let i(g) = 2*g**3 + 4*g. Let p(w) = 3*w. Let n(x) = 4*x. Let l(t) = -5*n(t) + 7*p(t). Let v(d) = i(d) - 6*l(d). Suppose v(o) = 0. Calculate o.
-1, 0, 1
Let a(v) = v**2 - 2*v - 3. Let s be a(3). Factor 1/3*j**2 + 1/3*j**3 + s + 0*j.
j**2*(j + 1)/3
Let d(v) = 7*v**5 - 7*v**4 - 7*v**3 - 3*v**2 - 5*v - 5. Let o(u) = 8*u**5 - 8*u**4 - 8*u**3 - 4*u**2 - 6*u - 6. Let a(l) = 6*d(l) - 5*o(l). Factor a(z).
2*z**2*(z - 1)**2*(z + 1)
Suppose -19 = 4*s - 35. Solve f**2 - 1/2*f**5 + 0*f**s + 2*f**3 - 1 - 3/2*f = 0.
-1, 1, 2
Let d(y) be the second derivative of -1/12*y**4 + 0*y**3 + 0*y**2 + 0 + 3*y. Find m, given that d(m) = 0.
0
Let o(d) be the first derivative of -2*d**6/9 + 8*d**5/15 - 8*d**3/9 + 2*d**2/3 - 15. Factor o(b).
-4*b*(b - 1)**3*(b + 1)/3
Let o be (0 - (0 + -1))*0. What is y in o - 2 + y - y**2 - 3*y + 1 = 0?
-1
Factor 46*r**2 - 20*r**2 + 8 - 8*r - 24*r**2.
2*(r - 2)**2
Find p, given that 2*p + 4*p - 3*p + 5*p**2 - 6*p**2 = 0.
0, 3
Let g be 99/27 - (2 - -1). Factor -3*d - 7/3*d**2 - g.
-(d + 1)*(7*d + 2)/3
Let s be (-2)/((-1)/2 - 0). Suppose -s*d = -6*d. Determine y so that 2*y**3 + 1/2*y**2 + 0*y + d = 0.
-1/4, 0
Factor 0*r**2 - 1/7*r + 1/7*r**3 + 0.
r*(r - 1)*(r + 1)/7
Let v(h) be the first derivative of -h**6/420 - h**5/210 + 3*h**2/2 + 1. Let o(z) be the second derivative of v(z). Factor o(g).
-2*g**2*(g + 1)/7
What is s in 18 + 3/2*s**2 + 12*s = 0?
-6, -2
Let c(q) = 3122*q**2 + 497*q + 23. Let g(l) = 3123*l**2 + 498*l + 22. Let x(o) = 2*c(o) - 3*g(o). What is k in x(k) = 0?
-2/25
Suppose -14*i = -16*i. Let n(d) be the second derivative of 1/42*d**4 + 0 - 1/70*d**5 + i*d**2 + 0*d**3 - 2*d. Factor n(w).
-2*w**2*(w - 1)/7
Let s(t) = -t**3 - 10*t**2 + 4. Let q be s(-10). Let y(w) = 2*w**2 - 3. Let m(a) = 3*a**2 - 4. Let u(x) = q*y(x) - 3*m(x). Factor u(n).
-n**2
Let o(j) be the third derivative of j**7/210 - j**6/60 + j**5/60 + 3*j**2. Find c, given that o(c) = 0.
0, 1
Let o = -2 - 0. Let r(n) = 3*n**2 + 0 - 3*n - 4 + n**2 + 7*n**3. Let g(a) = 29*a**3 + 17*a**2 - 11*a - 17. Let y(p) = o*g(p) + 9*r(p). Factor y(i).
(i - 1)*(i + 1)*(5*i + 2)
Let a be (-280)/231 + (-2)/(-3). Let t = 29/33 + a. Factor -1/3*r - 2/3 + t*r**2.
(r - 2)*(r + 1)/3
Let q = 0 + -3. Let a(t) = -t**3 - 3*t**2 - 2*t - 1. Let z be a(q). Factor -4/3*k**2 + 10/3*k**3 - 8/3*k**4 + 0*k + 0 + 2/3*k**z.
2*