*s**2 + 4/21*s**3 - p. Find u such that a(u) = 0.
-2, 1/2
Let j(k) be the second derivative of k**4/24 - k**3/12 - 5*k. Factor j(r).
r*(r - 1)/2
Let t(v) = v**3 + 11*v**2 - 11*v + 17. Let c be t(-12). Let f(j) = -9*j**2 - 5*j + 9. Let i(p) = 4*p**2 + 2*p - 4. Let q(m) = c*i(m) + 2*f(m). Factor q(z).
2*(z - 1)*(z + 1)
Let f = -1 + 3. Let z be (-6 - f)*9/(-6). Factor -2*u - 7*u**5 + 2*u**2 - 5*u**3 + 2*u**3 - z*u**4 + 2*u.
-u**2*(u + 1)**2*(7*u - 2)
Let x be (3/14)/((-360)/(-7)). Let m(y) be the third derivative of 0*y - 1/24*y**3 - 1/48*y**4 - x*y**5 + 0 + y**2. What is i in m(i) = 0?
-1
Factor -4/15*v**2 - 2/15*v + 0.
-2*v*(2*v + 1)/15
Let u(w) be the second derivative of 0*w**3 + w + 0*w**4 - 1/126*w**7 + 0 + 1/90*w**6 + 0*w**2 + 0*w**5. Find l such that u(l) = 0.
0, 1
Find d, given that -12/7*d + 1/7*d**5 - 4/7 + 3/7*d**4 - 11/7*d**2 - 1/7*d**3 = 0.
-2, -1, 2
Suppose -4*h = -6*h + 6. Factor -3*s**h - 4*s**3 + 3*s**3 - 3*s - 3*s**4 - 9*s**2 - 5*s**3.
-3*s*(s + 1)**3
Let k(m) be the third derivative of m**7/735 + m**6/84 + m**5/70 - 3*m**4/28 + 10*m**2. Suppose k(y) = 0. What is y?
-3, 0, 1
Let k(q) be the first derivative of 7*q**6/2 + 27*q**5/5 - 15*q**4/4 - 9*q**3 - 3*q**2 + 4. What is v in k(v) = 0?
-1, -2/7, 0, 1
Let r(a) be the third derivative of -a**5/40 + a**4/24 + a**3/12 - 19*a**2. Suppose r(i) = 0. Calculate i.
-1/3, 1
Suppose 3/2 - 3/2*j**2 + 1/2*j - 1/2*j**3 = 0. Calculate j.
-3, -1, 1
Let v(u) be the second derivative of -2/11*u**2 + 5/66*u**4 + 1/11*u**3 + 0 - 2*u. Factor v(c).
2*(c + 1)*(5*c - 2)/11
Let z(v) be the second derivative of 3*v**5/20 - 3*v**3/2 + 3*v**2 + 2*v. Factor z(g).
3*(g - 1)**2*(g + 2)
Suppose -4/11 - 2/11*n**2 - 6/11*n = 0. Calculate n.
-2, -1
Let c(x) be the second derivative of -x**6/10 + 7*x**5/20 - x**4/4 - x**3/2 + x**2 - 5*x. Solve c(p) = 0.
-2/3, 1
Suppose 2 = h - 0*h - n, -4*h + 5*n + 5 = 0. Factor 1 + 2*d**3 + 10*d - 2 + 8*d**2 + h.
2*(d + 1)**2*(d + 2)
Let x(c) be the first derivative of -8/45*c**5 + 1 - 2/9*c**4 + 0*c - 1/9*c**3 + c**2. Let z(r) be the second derivative of x(r). Find l such that z(l) = 0.
-1/4
Let t(o) be the second derivative of o**7/14 + o**6/10 - 9*o**5/20 - o**4/4 + o**3 + o + 8. Find l such that t(l) = 0.
-2, -1, 0, 1
Let t(x) be the second derivative of -1/7*x**2 + x - 1/42*x**4 + 2/21*x**3 + 0. Factor t(s).
-2*(s - 1)**2/7
Let t(y) = -y**3 - y. Let x(q) = -12*q**3 + 144*q**2 - 196*q + 108. Let j(w) = 20*t(w) + x(w). Factor j(m).
-4*(2*m - 3)**3
Let l be (-27320)/(-75) - (-6)/(-10). Let r = 369 - l. Suppose -r*j - 7/3*j**4 - 1/3*j**5 - 19/3*j**3 - 4/3 - 25/3*j**2 = 0. What is j?
-2, -1
Let k(b) be the second derivative of -b**4/4 + 5*b**3/2 - 9*b**2 - 41*b. Factor k(w).
-3*(w - 3)*(w - 2)
Let q be ((-4)/(-18))/((80/(-6))/(-1)). Let d(l) be the second derivative of 0*l**3 - l + 0 + 0*l**4 - q*l**6 - 1/40*l**5 + 0*l**2. Suppose d(y) = 0. What is y?
-1, 0
Let c(k) = k**3 - k**2. Let l(x) = 15*x**3 - 18*x**2 - 2*x. Let g(p) = 22*c(p) - 2*l(p). Factor g(w).
-2*w*(w - 2)*(4*w + 1)
Let x(q) = -q**2 + 20*q + 53. Let l(v) = -v**2 + 40*v + 105. Let g(h) = 3*l(h) - 5*x(h). Solve g(f) = 0 for f.
-5
Let n(p) be the third derivative of 1/150*p**5 - 1/60*p**4 + 0*p + p**2 + 0 + 0*p**3. Factor n(s).
2*s*(s - 1)/5
Let v(q) = q**3 + 5*q**2 + 3. Let m be v(-5). Let n(c) = -c - 2. Let a be n(-2). Determine p so that p + a - 7/2*p**m - 5/2*p**2 = 0.
-1, 0, 2/7
What is m in 11*m**2 - 4*m**4 + 5*m**4 - m**5 - 12*m**2 + m**3 = 0?
-1, 0, 1
Let k = -38 + 41. Let x(s) be the first derivative of -7/8*s**4 + 1/2*s**5 + 0*s**2 + 0*s + k + 1/3*s**3. Factor x(l).
l**2*(l - 1)*(5*l - 2)/2
Let y(h) be the first derivative of 1/18*h**4 + 4/27*h**3 + 0*h + 1 + 0*h**2. Factor y(d).
2*d**2*(d + 2)/9
Suppose 0*m**2 + 0 - 1/8*m + 1/8*m**3 = 0. Calculate m.
-1, 0, 1
Suppose 0*z + 3*z = 0. Suppose 5*s + 9 = -d + 34, 0 = 2*d - 2*s + 10. Let -2/3*j**3 + 0 + d*j + z*j**2 = 0. What is j?
0
Let c(s) be the first derivative of -7*s**6/10 + 36*s**5/25 - 9*s**4/20 - 2*s**3/5 + 2. Factor c(b).
-3*b**2*(b - 1)**2*(7*b + 2)/5
Let g = 287/24420 - -2/407. Let d(z) be the third derivative of 1/3*z**3 + 0*z + 1/24*z**4 - g*z**5 + 0 + z**2. Factor d(c).
-(c - 2)*(c + 1)
Let i(v) be the third derivative of v**6/160 - 9*v**2. Suppose i(r) = 0. Calculate r.
0
Suppose -3*p**2 + p - 8*p + 3*p - 27 - 14*p = 0. Calculate p.
-3
Let k = 471 - 18841/40. Let b = 7/40 - k. Factor 1/5*c - 2/5 + b*c**2.
(c - 1)*(c + 2)/5
Solve -c**4 - 2*c**2 + 2*c**4 + 3*c**3 + c**4 - 5*c**3 + 2*c = 0 for c.
-1, 0, 1
Let w(b) be the first derivative of -b**5/10 + b**3/6 + 3. Factor w(i).
-i**2*(i - 1)*(i + 1)/2
Let x(p) be the second derivative of -3*p**5/160 + 3*p**4/32 + 3*p**3/8 - 3*p**2/2 - 11*p. Factor x(v).
-3*(v - 4)*(v - 1)*(v + 2)/8
Let x(b) be the second derivative of -1/84*b**7 + 0*b**6 + 0*b**4 - 1/12*b**3 + 0*b**2 + 0 + 1/20*b**5 + b. Suppose x(h) = 0. Calculate h.
-1, 0, 1
Let q(x) be the first derivative of -x**5/5 - x**4/4 + x**3/3 + x**2/2 - 6. What is b in q(b) = 0?
-1, 0, 1
Factor 13 - 15*s**2 + 2 + 3*s**3 + 36*s**2 + 33*s.
3*(s + 1)**2*(s + 5)
Suppose 0 = 3*i - 3 - 9. Let h(v) be the first derivative of -2/25*v**5 + 2/15*v**3 + 0*v**i + 0*v + 0*v**2 - 2. Find j such that h(j) = 0.
-1, 0, 1
Let c(m) be the second derivative of -2*m**6/5 - 11*m**5/5 - 8*m**4/3 + 8*m**3/3 + 13*m. Factor c(i).
-4*i*(i + 2)**2*(3*i - 1)
Let f(b) be the first derivative of b**4/4 + b**3/3 - b**2 - 11. Suppose f(x) = 0. What is x?
-2, 0, 1
Factor 2 + 7*u + 3*u**2 + 6 + 2*u - 2.
3*(u + 1)*(u + 2)
Let l = 13367/8460 + -74/47. Let f(v) be the third derivative of 0 + 0*v**3 + v**2 + 0*v + l*v**6 + 0*v**4 - 1/90*v**5. Solve f(x) = 0.
0, 1
Let u = 2/33 - -1/44. Let i(z) be the third derivative of 0*z**3 + u*z**4 + 3*z**2 - 2/15*z**5 - 1/60*z**6 + 0*z + 0 + 4/105*z**7. Find g such that i(g) = 0.
-1, 0, 1/4, 1
Let g(m) be the first derivative of -1/2*m**2 + 3 - m + 0*m**3 + 1/12*m**4. Let i(w) be the first derivative of g(w). Find o such that i(o) = 0.
-1, 1
Let d(y) be the first derivative of -2*y**3/9 - 2*y**2/3 - 2*y/3 + 7. Find s, given that d(s) = 0.
-1
Let i(f) be the second derivative of -1/6*f**2 + f - 1/36*f**4 + 0 - 1/9*f**3. What is r in i(r) = 0?
-1
Let k(v) = -v**4 - 5*v**3 + 5*v**2 + 5*v. Let b(j) = 2*j**4 + 16*j**3 - 16*j**2 - 16*j. Let u(l) = 2*b(l) + 7*k(l). Solve u(f) = 0.
-1, 0, 1
Let n(d) be the first derivative of 3*d**4/16 + 3*d**3/4 + 9*d**2/8 + 3*d/4 + 4. Suppose n(u) = 0. What is u?
-1
Factor 2*c**3 - 6*c**2 - c**3 + 2*c**3 + 12*c**2.
3*c**2*(c + 2)
Let w be (-24)/(-9)*(-9)/(-6). Let a(c) be the second derivative of -1/10*c**5 - 1/30*c**6 + 1/2*c**2 + 1/3*c**3 + 0 + 0*c**w + 2*c. What is t in a(t) = 0?
-1, 1
Solve 0 - 6/7*r**5 - 2/7*r + 8/7*r**3 - 4/7*r**2 + 4/7*r**4 = 0.
-1, -1/3, 0, 1
Let g(n) be the second derivative of 5*n - 2/15*n**6 + 0*n**2 + 0 + 2/5*n**5 - 16/3*n**3 + 4/3*n**4. Let g(a) = 0. Calculate a.
-2, 0, 2
Let y(s) = -s**3 - 14*s**2 - 14*s - 11. Let k be y(-13). Let t(h) be the second derivative of -2*h + 1/6*h**4 + 9*h**k + 0 + 2*h**3. Let t(p) = 0. What is p?
-3
Let z(p) be the third derivative of 0*p + 0*p**4 - 1/240*p**5 + 0 + 3*p**2 + 1/160*p**6 - 1/280*p**7 + 0*p**3 + 1/1344*p**8. Factor z(h).
h**2*(h - 1)**3/4
Let m(i) = -4*i + 12*i**3 + 3*i**2 + 5*i**4 + 3 - 3. Let x(g) be the third derivative of g**7/210 + g**4/24 + 4*g**2. Let n(f) = m(f) + 2*x(f). Factor n(v).
v*(v + 1)**2*(7*v - 2)
What is p in 0 - 2*p**3 - 10/3*p**2 - 4/3*p + 2/3*p**4 + 2/3*p**5 = 0?
-1, 0, 2
Let q(t) be the third derivative of -2*t**6/105 - 2*t**5/21 - 11*t**4/56 - 3*t**3/14 - 15*t**2. Find y, given that q(y) = 0.
-1, -3/4
Factor 0*y**2 + y**2 + 0 + 6 + 7*y.
(y + 1)*(y + 6)
Let w(t) be the third derivative of t**8/1680 - t**7/420 + t**6/360 - 2*t**3/3 - 2*t**2. Let h(c) be the first derivative of w(c). Factor h(x).
x**2*(x - 1)**2
Let o(z) = -12*z**4 - 4*z**3 - 24*z**2 + 20*z - 20. Let t(y) = -y**3 - y**2 + y - 1. Let a(u) = o(u) - 20*t(u). Factor a(m).
-4*m**2*(m - 1)*(3*m - 1)
Let a(s) = -s**3 - 10*s**2 - 4*s. Let v(f) = 9*f**3 + 81*f**2 + 33*f. Let o(q) = 33*a(q) + 4*v(q). Suppose o(b) = 0. Calculate b.
0, 2
Let i(q) = 2*q**3 - 14*q**2 + 16*q - 4. Let v(l) = -l**2 + l. Let r(k) = -i(k) + 6*v(k). Find y, given that r(y) = 0.
1, 2
Let a be (-4)/(