*i(y) + 3*u(y). Find n such that t(n) = 0.
0, 1, 4
Let h(z) be the third derivative of 0*z**4 + 0*z**3 - 1/735*z**7 - 7*z**2 - 1/70*z**5 + 0 + 1/105*z**6 + 0*z. Factor h(w).
-2*w**2*(w - 3)*(w - 1)/7
Let k(u) = -12*u**3 - 39*u**2 - 33*u - 6. Let w(a) = -12*a**3 - 39*a**2 - 33*a - 6. Let x(v) = 5*k(v) - 4*w(v). Factor x(g).
-3*(g + 1)*(g + 2)*(4*g + 1)
Let k(g) be the first derivative of -1/5*g**5 - g**3 + 0*g + 4 + 3/4*g**4 + 1/2*g**2. Factor k(n).
-n*(n - 1)**3
Let z(m) be the third derivative of -m**7/735 - m**6/70 - 3*m**5/70 + m**4/21 + 4*m**3/7 + 7*m**2. Solve z(i) = 0.
-3, -2, 1
Let x(f) be the third derivative of 0*f**4 + 0*f + 0 - 5*f**2 + 1/9*f**3 - 1/90*f**5. Factor x(u).
-2*(u - 1)*(u + 1)/3
Let x(w) be the second derivative of 9*w**5/20 - 7*w**4/12 - w**3/3 + 4*w. Factor x(s).
s*(s - 1)*(9*s + 2)
Let x(k) = -11*k - 2*k**2 - 8*k**3 - 14*k**2 - 8*k**3. Let h(j) = 3*j**3 + 3*j**2 + 2*j. Let s = 21 + -25. Let r(d) = s*x(d) - 22*h(d). Factor r(y).
-2*y**2*(y + 1)
Factor -8/5*w + 0 - 8/5*w**2 - 2/5*w**3.
-2*w*(w + 2)**2/5
Determine d so that -2/11*d**2 + 6/11 - 4/11*d = 0.
-3, 1
Let g(v) be the second derivative of v**6/90 - v**5/15 + v**4/6 + v**3 - 5*v. Let u(f) be the second derivative of g(f). Let u(m) = 0. Calculate m.
1
Find q, given that -3/4*q - 27/4*q**2 + 1/2 = 0.
-1/3, 2/9
Let d be ((-1)/(-2))/((-42)/(-24)). Factor 2/7*w**2 - d*w + 0.
2*w*(w - 1)/7
Let s(b) be the third derivative of b**8/28 + 2*b**7/15 + b**6/6 + b**5/15 + 3*b**2. Suppose s(g) = 0. What is g?
-1, -1/3, 0
Let n be (-1 - 4) + (-42)/(-6). Let s(o) be the second derivative of -3/2*o**n + 0 - 9/80*o**5 + o**3 + 3*o - 1/16*o**4. Find m such that s(m) = 0.
-2, 2/3, 1
Suppose 56 - 56 = -12*p. Factor -1/4*h - 1/4*h**3 + 1/2*h**2 + p.
-h*(h - 1)**2/4
Let o(d) be the second derivative of -2*d**7/7 + 4*d**6/5 - 3*d**5/20 - 5*d**4/4 + d**3/2 + 3*d**2/2 - d. What is i in o(i) = 0?
-1/2, 1
Let s be 60/675 - 2*2/(-30). Factor 2/9*h**4 + 0*h + 2/9*h**3 - 2/9*h**5 - s*h**2 + 0.
-2*h**2*(h - 1)**2*(h + 1)/9
Let k(r) = -13*r**4 + 15*r**3 + 6*r**2 - 16*r - 3. Let t(x) = -7*x**4 + 8*x**3 + 3*x**2 - 8*x - 2. Let v(s) = 6*k(s) - 11*t(s). Factor v(n).
-(n - 2)*(n - 1)**2*(n + 2)
Let r = -11 + 15. Suppose -6 = 2*n + 2*y, 5*y + 14 + 1 = -r*n. Factor -2/3*t**4 + 0*t + 4/3*t**2 - 2/3 + n*t**3.
-2*(t - 1)**2*(t + 1)**2/3
Suppose -3*r - n = -13, 5*r - 22*n + 26*n = 31. Determine g so that -2/5*g**2 + 0 - 2/5*g**r + 0*g = 0.
-1, 0
Let g(q) be the first derivative of -1/14*q**2 + 2/21*q**3 - 1/28*q**4 + 7 + 0*q. Factor g(p).
-p*(p - 1)**2/7
Suppose 5*k + 2 + 28 = 3*m, -m = 5*k + 30. Let x = -4 - k. Determine v, given that -1 + 4*v - 2*v**5 - v**4 - v**2 + x*v**3 + 3*v**2 - 5*v + v**5 = 0.
-1, 1
Let v(n) = n**3 + 5*n**2 - 8*n - 9. Suppose 0 = -9*x + 4*x - 30. Let g be v(x). Solve 2*p**2 - 7*p**4 + 9*p**g - 2*p**2 - 2*p**2 = 0.
0, 2/7, 1
Suppose -75*f = -71*f - 8. Suppose 1/5*r**f + 0*r - 1/5*r**3 + 0 = 0. Calculate r.
0, 1
Let y(b) be the second derivative of -2*b**3/3 + b**2 - 3*b. Let z be 1*(2 - 4) - -4. Let s(p) = p**3 + 9*p - 5. Let t(a) = z*s(a) + 5*y(a). Factor t(v).
2*v*(v - 1)*(v + 1)
Suppose 4*c - 9*c = -15. Suppose f - 68 = -2*b - 3*f, 4*b - 121 = -c*f. Factor -3*g**5 + 12*g**2 + b*g**3 - 2 - 2*g + 3*g**4 + 9*g**5 + 19*g**4.
2*(g + 1)**4*(3*g - 1)
Let j(g) = -3*g**3 + 3*g**2 + 3*g + 5. Suppose 2*o - 3*o + 5 = 0. Let w(c) = -2*c**3 + 2*c**2 + 2*c + 3. Let f(z) = o*j(z) - 8*w(z). Solve f(t) = 0.
-1, 1
Let d(b) be the third derivative of -13/15*b**5 - 2/105*b**7 + 0*b + 0 - 4*b**2 + 2*b**4 - 8/3*b**3 + 1/5*b**6. Factor d(w).
-4*(w - 2)**2*(w - 1)**2
Let n(g) be the third derivative of -1/70*g**7 + 0*g**3 - 2*g**2 + 1/20*g**5 + 0 + 1/40*g**6 - 1/8*g**4 + 0*g. Determine t, given that n(t) = 0.
-1, 0, 1
Let h = -18 + 23. Let r(n) be the second derivative of -1/36*n**4 + n - 1/60*n**h + 1/18*n**3 + 0*n**2 + 0 + 1/90*n**6. Factor r(m).
m*(m - 1)**2*(m + 1)/3
Let k(c) be the second derivative of -5*c**7/42 + 5*c**6/6 - 5*c**5/2 + 25*c**4/6 - 25*c**3/6 + 5*c**2/2 - 13*c. Factor k(a).
-5*(a - 1)**5
Let u(a) be the second derivative of -a**7/189 - a**6/135 + a**5/30 + a**4/54 - 2*a**3/27 + 5*a. Let u(g) = 0. Calculate g.
-2, -1, 0, 1
Let g(j) be the second derivative of 6*j + 0*j**3 + 0 + 0*j**2 + 0*j**4 + 1/45*j**5 - 1/189*j**7 + 1/135*j**6. Factor g(q).
-2*q**3*(q - 2)*(q + 1)/9
Let v(m) be the third derivative of m**6/180 - m**5/20 + m**4/6 + m**3/2 - 2*m**2. Let c(n) be the first derivative of v(n). Factor c(u).
2*(u - 2)*(u - 1)
Suppose -u + 0 + 2 = 0. Factor u*a**3 - 3*a**2 - 1/2*a**4 - 1/2 + 2*a.
-(a - 1)**4/2
Let w(d) = -d**4 + d**3 - d + 1. Let l(n) = 12*n**4 - 10*n**3 + 10*n - 12. Let b(r) = 2*l(r) + 28*w(r). Suppose b(a) = 0. Calculate a.
-1, 1
Let c(x) be the first derivative of 4*x**3/3 + 2*x**2 - 24*x + 5. Find t such that c(t) = 0.
-3, 2
Let n(k) be the first derivative of k**3/3 - 5*k**2 + 25*k + 6. Let n(o) = 0. Calculate o.
5
Let u(c) = -6*c**3 - 8*c + 7. Let d(q) = -q**3 + q**2 + 1. Let a(i) = -14*d(i) + 2*u(i). Suppose a(x) = 0. What is x?
-1, 0, 8
Let u(r) = -5*r**2 - 3*r - 1. Let o(n) be the first derivative of n**3/3 + n**2/2 + n - 1. Let s(t) = -3*o(t) - u(t). Find p such that s(p) = 0.
-1, 1
Suppose 4/5*w**4 + 0 - 2/5*w**2 + w**3 - 3/5*w = 0. Calculate w.
-1, 0, 3/4
Let q(g) be the third derivative of 1/735*g**7 - 2/21*g**3 + 1/210*g**5 + 1/28*g**4 - 1/140*g**6 - 5*g**2 + 0*g + 0. Factor q(n).
2*(n - 2)*(n - 1)**2*(n + 1)/7
Factor 4/9*z**2 + 4/9 - 8/9*z.
4*(z - 1)**2/9
Let d = -96/25 + 5189/1350. Let t(i) be the third derivative of d*i**5 + 0*i + 2*i**2 + 0 - 2/27*i**3 + 1/108*i**4. Factor t(a).
2*(a - 1)*(a + 2)/9
Factor -2*h**4 + 0*h**2 + 2*h**2 + 9*h**3 + 2*h - 11*h**3.
-2*h*(h - 1)*(h + 1)**2
Let w be (-15)/10 + 2/(-4). Let h = w + 4. Factor 32*q**2 + 6 - 2 + 28*q - 3*q**h + 20*q**2.
(7*q + 2)**2
Suppose -65*w + 246 = -24*w. Factor 3/2*l**2 + 6 + w*l.
3*(l + 2)**2/2
Let v(o) be the first derivative of 1/6*o**6 + 0*o**2 + 2/21*o**3 + 0*o + 11/28*o**4 - 4 + 16/35*o**5. Factor v(n).
n**2*(n + 1)**2*(7*n + 2)/7
Suppose 6*s = 5*s. Let b(w) be the third derivative of 0*w**7 - 1/840*w**8 + 0 + s*w**5 + 0*w**4 + 1/300*w**6 + 0*w**3 + 0*w - 2*w**2. Factor b(a).
-2*a**3*(a - 1)*(a + 1)/5
Let a(h) be the third derivative of -5*h**2 - 1/6*h**4 + 1/15*h**5 - 4/3*h**3 + 0 + 0*h. Solve a(x) = 0.
-1, 2
Let w(p) be the first derivative of -2*p**3/3 - 3*p**2 - 4*p - 1. Determine v, given that w(v) = 0.
-2, -1
Let i = -31005/14 - -2216. Let o = i - 6/7. Factor 0 + o*y + 1/2*y**2.
y*(y + 1)/2
Let i = -338/3 + 114. Determine v so that v - i*v**2 + 1/3 = 0.
-1/4, 1
Let n(w) be the third derivative of w**5/18 + w**4/54 - w**3/27 - 32*w**2. Let n(c) = 0. What is c?
-1/3, 1/5
Suppose 12/7*c**3 - 9/7*c + 0*c**4 - 6/7*c**2 - 3/7*c**5 + 6/7 = 0. What is c?
-2, -1, 1
Solve -1/3*q**2 + 4/3*q + 0 = 0 for q.
0, 4
Let b(k) be the second derivative of 4/3*k**3 + 5/12*k**4 - 2*k**2 + 0 + k. What is a in b(a) = 0?
-2, 2/5
Let r = -253/3 + 89. Suppose -r*f**2 + 2*f**4 + 0*f + 8/3 + 2/3*f**3 - 2/3*f**5 = 0. Calculate f.
-1, 1, 2
Factor 3*a**4 + 10*a**3 + 24*a**2 + 0*a + 12*a + 5*a**3.
3*a*(a + 1)*(a + 2)**2
Let u(j) be the third derivative of -j**5/10 - 7*j**4/16 + j**3/2 - 2*j**2. Factor u(o).
-3*(o + 2)*(4*o - 1)/2
Let h be (-8)/(-20) - 24/(-15). Suppose -2*j + 12 = h. Factor -2*s**3 - 9*s + 3*s**3 + j*s**3 - 3 + 3*s**3 + 3*s**2.
3*(s - 1)*(s + 1)*(3*s + 1)
Factor 0 - 3/2*c**3 + 0*c - 1/2*c**2.
-c**2*(3*c + 1)/2
Let h = 2 + -2. Suppose -u + 21 = i - 6*u, h = 5*i + 3*u + 7. Let 2*z - 1 - 2*z**3 + i = 0. What is z?
-1, 0, 1
Let w(n) be the second derivative of 0 + 0*n**3 - 3/50*n**5 - 1/15*n**4 + 2*n + 1/105*n**7 + 0*n**2 + 0*n**6. Factor w(a).
2*a**2*(a - 2)*(a + 1)**2/5
Factor -96*o + 0*o**3 + 72 - 3/2*o**4 + 36*o**2.
-3*(o - 2)**3*(o + 6)/2
Suppose -2*s + y + 5 = -3*s, 3*s + 4*y + 20 = 0. Factor 2*a**4 - 2*a**5 + 0*a**5 + s*a**5.
-2*a**4*(a - 1)
Let n(j) be the second derivative of 1/18*j**3 + 1/90*j**5 - 4*j - 1/24*j**4 + 1/2*j**2 + 0. Let u(p) be the first derivative of n(p). Factor u(a).
(a - 1)*(2*a - 1)/3
Suppose -4*h + 13 = -p - 5, -22 = -p - 4*h. Suppose i = -0 + p. Factor 11/3*d**i - 2/3*d - 4*d**3 + 0 - 3*d**4.
-d*(d + 2)*(3*d - 1)**2/3
Suppose m + 4 = 3*m. Factor -8*n - 9*n**m + n**2 