p*l**2 - l**3 = 0.
0, 1
Let g be ((-3)/8*2)/(1/(-4)). Factor -2/3*l**4 + 0 + 10/3*l**g + 8/3*l - 16/3*l**2.
-2*l*(l - 2)**2*(l - 1)/3
Let c(q) be the second derivative of 0 + 8/5*q**5 - 2*q**2 - 3/7*q**7 + 1/3*q**4 + 8*q + 0*q**6 - 7/3*q**3. Let c(o) = 0. What is o?
-1, -2/3, -1/3, 1
Let a(n) be the third derivative of -1/12*n**4 + 0*n**3 + 0 + 1/60*n**5 + n**2 + 0*n. Determine c so that a(c) = 0.
0, 2
Let r(c) be the third derivative of -7/720*c**6 + 0*c + 1/9*c**3 + 1/72*c**5 + 1/9*c**4 - 6*c**2 + 0. Find n, given that r(n) = 0.
-1, -2/7, 2
Factor 0 + 0*c**3 + 0*c**2 - 1/3*c**4 + 0*c.
-c**4/3
Let z(d) = -d**3 - 11*d**2 + 11*d - 9. Let n be z(-12). Let b = -3 + 5. Factor 1/3*k**n + 1/3 + k + k**b.
(k + 1)**3/3
Let k = 3 + 4. Let v(c) be the third derivative of 0 + 0*c**3 + 1/240*c**6 + 2*c**2 + 0*c**5 + 0*c + 0*c**4 + 1/420*c**k. Factor v(b).
b**3*(b + 1)/2
Let f(a) be the third derivative of a**7/1680 - a**5/240 - a**3/6 + 3*a**2. Let p(b) be the first derivative of f(b). Let p(o) = 0. Calculate o.
-1, 0, 1
Let g(p) be the second derivative of -p**4/42 + 2*p**3/7 + p**2 - p - 2. Factor g(r).
-2*(r - 7)*(r + 1)/7
Let z = -1418 - -9948/7. Solve 4/7 + 20/7*a**3 + 38/7*a**2 + z*a = 0 for a.
-1, -1/2, -2/5
Let t(p) = 10*p**4 + 3*p**5 - 9 - 3*p**3 + 6 + 0*p**3 - 4*p**4. Let a(l) = l**4 + l**2 - 1. Let q(k) = 3*a(k) - t(k). Find d, given that q(d) = 0.
-1, 0, 1
Let o be (2/75)/((-4)/(-5)). Let r(z) be the second derivative of 2/3*z**2 - 1/9*z**3 + 1/45*z**6 + 0 - 2*z + o*z**5 - 1/6*z**4. Factor r(p).
2*(p - 1)**2*(p + 1)*(p + 2)/3
Solve 1/4*h**3 - 1/4*h + 0*h**2 + 0 = 0 for h.
-1, 0, 1
Factor 47*t**2 + 49*t**2 - 4 - 92*t**2.
4*(t - 1)*(t + 1)
Let y(v) = -v**3 - v**2 + v + 3. Let n be y(0). Factor u**2 + n*u**2 - 6*u**2 + u**4 + u**2.
u**2*(u - 1)*(u + 1)
Let o(q) be the second derivative of q**6/30 + 3*q**5/40 - q**4/8 + q**3/6 - 3*q. Let c(j) be the second derivative of o(j). Determine t, given that c(t) = 0.
-1, 1/4
Suppose x = m - 3, -3*m + 5*x + 9 = -0*x. Let i be 2*(18/(-3))/(-6). Factor 1/2*c**4 + 0 + c**i + 0*c - 3/2*c**m.
c**2*(c - 2)*(c - 1)/2
Suppose 3*r + 7 = -5*m + 2, 4*r = -5*m - 10. Determine f so that -4*f + 2*f + 2*f + m*f**3 = 0.
0
Let n(w) be the second derivative of 0*w**5 + 0 + 0*w**3 + 0*w**4 + 0*w**2 - 1/10*w**6 + 5*w. Determine p so that n(p) = 0.
0
Let x(s) be the third derivative of 7*s**6/80 + 2*s**5/5 + s**4/4 + 5*s**2. Solve x(b) = 0.
-2, -2/7, 0
Suppose -4*n - 3*x + 10 = -35, 0 = -3*n - x + 30. Suppose 0 = 3*y - n. Factor 5/4*t - 1/4 + 5/2*t**y - 5/4*t**4 - 5/2*t**2 + 1/4*t**5.
(t - 1)**5/4
Find n, given that n**3 + 10*n**3 - 3*n**3 - 4*n**3 = 0.
0
Let s(w) be the first derivative of w**5/50 + 3*w**4/40 - w**2/5 - 17. Factor s(n).
n*(n - 1)*(n + 2)**2/10
Factor -1144/3*i**3 - 208/3*i - 284*i**2 - 484/3*i**4 - 16/3.
-4*(i + 1)**2*(11*i + 2)**2/3
Let h be 2/3 + 0*(-4)/12. Factor 2/3*w**5 - 2/3*w**3 - h*w**2 + 0*w + 0 + 2/3*w**4.
2*w**2*(w - 1)*(w + 1)**2/3
Let f be (-10)/4*48/40. Let y be f/(-5) - (-17)/5. Determine t so that -1/4*t**y + 1/4*t - 1/4*t**3 + 3/4*t**2 - 1/2 = 0.
-2, -1, 1
Let v(u) = -u**2 + 6*u - 2. Suppose -3*s + 15 = c, -2*s + 2 = 4*c - 8. Let l be v(s). Determine r, given that -1/4*r**2 + 1/2*r - 1/2*r**l + 1/4 = 0.
-1, -1/2, 1
Suppose 4*f - 8 = -2*y, 5*y - 2*f = -5*f + 20. Factor -y*x**4 + 34*x**2 - 28*x**2 - 17*x**4 + 15*x**3.
-3*x**2*(x - 1)*(7*x + 2)
What is w in 6/11*w**3 + 24/11*w + 30/11*w**2 + 0 = 0?
-4, -1, 0
Suppose -4*k + 10 = k. Suppose 4*f + 2*y - 5 + 3 = 0, 2*f = -2*y + 2. Let 0*p**k + 1/6*p**5 + 0*p**4 - 1/3*p**3 + f + 1/6*p = 0. Calculate p.
-1, 0, 1
Let n be 9/(-3) + -1 + -2. Let f be 1*((-20)/n + -3). Factor 0 + f*j**2 + 0*j.
j**2/3
Let k = 6 + -11. Let v(c) = -150*c**3 - 23*c**2 + 96*c - 31. Let n(i) = 100*i**3 + 15*i**2 - 64*i + 21. Let q(x) = k*v(x) - 7*n(x). Solve q(o) = 0 for o.
-1, 2/5
Let k(h) be the third derivative of h**7/3780 + h**6/540 + h**4/8 - 4*h**2. Let a(p) be the second derivative of k(p). Factor a(d).
2*d*(d + 2)/3
Suppose -g - 10 = -6*g. Suppose 3*q = 4*q - g. Factor 0 + 0*s**q + 1/4*s - 1/4*s**3.
-s*(s - 1)*(s + 1)/4
Let u(c) be the third derivative of -c**6/300 + c**5/150 + 36*c**2. Factor u(f).
-2*f**2*(f - 1)/5
Let g(v) be the first derivative of 1/27*v**6 - 1/9*v**4 + 2/45*v**5 - 4/27*v**3 + 2/9*v + 1/9*v**2 - 2. Factor g(r).
2*(r - 1)**2*(r + 1)**3/9
Determine c so that -8/5*c**2 + 8/5*c - 6/5*c**3 + 0 = 0.
-2, 0, 2/3
Factor 56*s**5 + 11*s**4 - 46*s**4 - 36*s**5 - 10*s**3.
5*s**3*(s - 2)*(4*s + 1)
Let w(m) be the third derivative of m**8/10080 - m**7/1260 + m**6/360 + m**5/20 + 2*m**2. Let v(f) be the third derivative of w(f). Let v(q) = 0. What is q?
1
Let n(g) be the first derivative of g**8/5040 + g**7/840 + g**6/540 - 4*g**3/3 - 4. Let u(s) be the third derivative of n(s). Factor u(a).
a**2*(a + 1)*(a + 2)/3
Let d = 1703/21 - 81. Let g(b) be the first derivative of -1/7*b**4 + d*b**3 + 0*b + 0*b**2 - 1 - 2/5*b**5 - 4/21*b**6. Factor g(z).
-2*z**2*(z + 1)**2*(4*z - 1)/7
Factor 14/5*z**2 + 32/5*z + 8/5.
2*(z + 2)*(7*z + 2)/5
Let a(d) be the second derivative of -d**6/75 + 3*d**5/25 - d**4/30 - 8*d**3/5 - 16*d**2/5 - 12*d. Suppose a(r) = 0. Calculate r.
-1, 4
Factor -8*o - 4*o**4 + 2/3*o**5 + 22/3*o**3 + 16/3 - 4/3*o**2.
2*(o - 2)**3*(o - 1)*(o + 1)/3
Let q(p) be the second derivative of p**4/36 + p**3/18 - 8*p. Factor q(r).
r*(r + 1)/3
Let x(d) be the second derivative of d**6/45 + d**5/6 + d**4/2 + 7*d**3/9 + 2*d**2/3 - 3*d. Factor x(k).
2*(k + 1)**3*(k + 2)/3
Let y(s) be the second derivative of s**5/50 - 3*s**4/10 + 8*s**3/5 - 4*s**2 - 28*s. Factor y(w).
2*(w - 5)*(w - 2)**2/5
Solve -2/7*d**2 + 0*d + 0 - 4/7*d**3 - 2/7*d**4 = 0 for d.
-1, 0
Let h be 1*(-2)/(3*-2). Suppose -5*w - 3*i + 7 + 6 = 0, 3*w - 2*i = 4. Factor -1/3*v**w + 0 + h*v.
-v*(v - 1)/3
Suppose -22*m**3 + 4*m + 2*m**4 + 19*m**3 - 3*m**4 = 0. Calculate m.
-2, 0, 1
Let f = 1731/7 - 247. Suppose 4/7*x**3 + 0*x**2 + 2/7 - f*x**4 - 4/7*x = 0. What is x?
-1, 1
Let y be (-18)/(1/((-2)/3)). Solve 7*p**3 + p**3 - 3*p**4 + 8*p + p**4 - 2 - y*p**2 = 0 for p.
1
Factor 0 - 8/5*v**2 - 2/5*v**3 - 8/5*v.
-2*v*(v + 2)**2/5
Determine f, given that -36*f**2 + 27*f**5 - 4*f**2 + 23*f**5 + 205*f**4 + 10*f**3 = 0.
-4, -1/2, 0, 2/5
Let v(n) = 2*n**3 - n**2 + n. Let g be v(1). Suppose 1/5*k**3 - 1/5*k**g + 1/5 - 1/5*k = 0. What is k?
-1, 1
Let n(z) be the second derivative of 2*z**7/9 - 23*z**6/30 - 43*z**5/60 + 53*z**4/18 + 10*z**3/3 + 4*z**2/3 - 30*z. Find h such that n(h) = 0.
-1, -2/7, -1/4, 2
Let n(u) be the second derivative of 0 - 1/5*u**3 + 2*u - 1/50*u**5 + 1/10*u**4 + 1/5*u**2. Suppose n(k) = 0. Calculate k.
1
Let r(o) be the first derivative of -2*o**7/63 - 2*o**6/45 + o**5/15 + o**4/9 + 9*o + 7. Let v(m) be the first derivative of r(m). Factor v(x).
-4*x**2*(x - 1)*(x + 1)**2/3
Let v be (17/(-119))/(2/(-7)). What is z in -1/4*z**2 - 1/4 + v*z = 0?
1
Suppose -2*b + 3 = 5. Let v be b + 3/((-2)/(-2)). Solve 0*h**2 - 3*h**4 + 9*h**4 - 6*h**3 + 2*h**2 - v*h**5 = 0 for h.
0, 1
Let h(l) = l**3 + 7*l**2 - 7*l + 3. Let w be h(-8). Let x = 21/4 + w. What is g in 1/4*g**2 - 5/4*g**4 + 0 - 1/2*g**5 + x*g - 3/4*g**3 = 0?
-1, 0, 1/2
Let b = 15 - 11. Suppose z + 2*j - b*j = 7, 0 = 5*j + 10. Factor 0 - 1 + 2*n**2 - n**5 - n**z - n + 3*n**3 - n**4.
-(n - 1)**2*(n + 1)**3
Factor -2/5*j**2 - 6/5*j**3 - 2/5*j**5 - 6/5*j**4 + 0 + 0*j.
-2*j**2*(j + 1)**3/5
Let c(q) be the second derivative of -q**8/3360 - q**7/1260 - q**4/6 - 2*q. Let a(m) be the third derivative of c(m). Factor a(p).
-2*p**2*(p + 1)
Let k(d) be the third derivative of -d**6/30 - 3*d**5/5 - 9*d**4/2 - 18*d**3 - 38*d**2. Let k(v) = 0. What is v?
-3
Find d, given that 7*d**3 - 15*d**3 + 6*d**3 + 2*d - 3*d**4 + d**4 + 2*d**2 = 0.
-1, 0, 1
Let o(z) = z**2 + 8*z - 18. Let l be o(-10). Factor -2/3 + 4/3*h - 2/3*h**l.
-2*(h - 1)**2/3
Let t(v) be the first derivative of 4*v**3 + 8*v**2 + 4*v + 7. Factor t(n).
4*(n + 1)*(3*n + 1)
Let o(p) = 7*p**2 - p - 10. Let h(c) = -15*c**2 + 3*c + 21. Let y(s) = -4*h(s) - 9*o(s). Factor y(b).
-3*(b - 1)*(b + 2)
Suppose -2*m + 4*m = 6. Factor -4*u**2 + 8*u**3 + 9*u**4 + u**3 + 7*u**2 + m*u**5.
3*u**2*(u + 1)**3
Let o = -44 + 48. Let s(a) be the third derivative of 0*a**3 + 0*a**5 - 1/1344*a**8 + 3*a**2 + 0 + 0*a + 0*a**7 + 1/2