*c**5/15 + c**4/3 + 3*c**2. Suppose d(n) = 0. Calculate n.
0, 2/3, 2
Let d(f) be the third derivative of -f**8/3528 - f**7/315 - f**6/126 + f**5/35 + 3*f**4/28 - 3*f**3/7 + 5*f**2. Find y, given that d(y) = 0.
-3, 1
Let y(b) = b**2 - b - 3. Let l be y(3). Suppose 0*m = 3*m - l. Factor 2*h**2 + 0*h + m - 3*h + 10*h**5 - 9*h**5 + 2*h**3 - 3*h**4.
(h - 1)**4*(h + 1)
Suppose 5*m + 3 + 42 = 0. Let a(y) = -y**3 - 9*y**2 + y + 9. Let r be a(m). Factor -4/5*t**2 + 6/5*t**3 + 0*t + 0 - 2/5*t**5 + r*t**4.
-2*t**2*(t - 1)**2*(t + 2)/5
Let n(w) be the second derivative of w**6/300 + w**5/150 - w**4/60 - w**3/15 - 3*w**2/2 + 3*w. Let j(y) be the first derivative of n(y). What is s in j(s) = 0?
-1, 1
Let 2 - 61*j**2 + 56*j**2 - 2 + 5*j**4 = 0. What is j?
-1, 0, 1
Let c(m) be the second derivative of m**4/24 + m**3/3 + 40*m. Factor c(t).
t*(t + 4)/2
Factor -4*r**3 + 16 - r**3 + 3*r**3 + 8*r - 4*r**2.
-2*(r - 2)*(r + 2)**2
Let x be ((-1)/1)/(1/(-2)). Factor -2*u**2 - 2*u**2 - x*u**2 + 9*u**2 - 3*u.
3*u*(u - 1)
Let u(n) = 196*n**3 + 284*n**2 - 212*n + 28. Let g(p) = -196*p**3 - 285*p**2 + 213*p - 27. Let o(x) = -4*g(x) - 5*u(x). Let o(i) = 0. Calculate i.
-2, 2/7
Let q(w) = 4*w + w + 3 - 1 + 11*w**2 + 8*w**3 + 0*w**3. Let i(p) = -8*p**3 - 10*p**2 - 4*p - 2. Let t(c) = 5*i(c) + 6*q(c). Factor t(f).
2*(f + 1)*(2*f + 1)**2
Let q be (-2)/6 - 35/(-90). Let s(o) be the second derivative of q*o**4 + 0 + 0*o**3 - 1/6*o**2 + 0*o**5 - 1/90*o**6 - 2*o. Determine d, given that s(d) = 0.
-1, 1
Let w(s) = 32*s**2 + 23*s + 6. Let u(n) = -30*n**2 - 23*n - 6. Let h(q) = 5*u(q) + 4*w(q). Suppose h(l) = 0. What is l?
-6/11, -1/2
Let o = 4 - 0. Factor -3 + v**3 - o*v + 3 - 4 + 0*v + v**2.
(v - 2)*(v + 1)*(v + 2)
Determine s so that -1/4*s + 0 - 1/4*s**2 = 0.
-1, 0
Let c(a) = a**3 + 8*a**2 - 4 - 2 - 1 - 10*a + 2. Let v be c(-9). Factor 4/3*h**3 + 0 - 2/3*h**v + 0*h - 2/3*h**2.
-2*h**2*(h - 1)**2/3
Let u(c) be the second derivative of c**6/5 + 21*c**5/40 - 15*c**4/4 + 23*c**3/4 - 3*c**2 + 18*c. What is x in u(x) = 0?
-4, 1/4, 1
Let g(x) = -x - 6. Let i be g(-7). Let t(b) be the first derivative of 0*b + i - 1/3*b**3 + 0*b**2. Factor t(h).
-h**2
Suppose 8 = 4*o - 4. Let f(g) be the third derivative of 0*g + g**2 + 0*g**4 - 1/840*g**7 + 0 + 0*g**o + 0*g**6 + 1/1344*g**8 + 0*g**5. Factor f(v).
v**4*(v - 1)/4
Suppose 2*x + 18 = -x. Let t(i) = -3*i**4 - 13*i**3 - 5*i**2 - 7*i - 7. Let m(j) = 2*j**4 + 12*j**3 + 4*j**2 + 6*j + 6. Let s(u) = x*t(u) - 7*m(u). Factor s(g).
2*g**2*(g - 1)*(2*g - 1)
Let v(b) be the third derivative of 1/80*b**6 + 0 + 0*b - 7*b**2 + 1/80*b**5 + 0*b**4 + 1/280*b**7 + 0*b**3. Determine y, given that v(y) = 0.
-1, 0
Let q = 62 - 59. Find l such that 2/3*l**q + 2/3*l**2 - 2/3*l**5 + 0*l - 2/3*l**4 + 0 = 0.
-1, 0, 1
Suppose -4*w = -11*w + 7. Let r be (-26)/(-10) - (2 - w). Factor -r + 10*m**3 - 18*m**2 + 48/5*m.
2*(m - 1)*(5*m - 2)**2/5
Let g(b) be the first derivative of 2*b**3/15 + 18. Factor g(w).
2*w**2/5
Suppose -2*k = -6*k + 40. Suppose -9*c + k*c - 3 = 0. Factor 1/2 + 1/2*h**c - 1/2*h - 1/2*h**2.
(h - 1)**2*(h + 1)/2
Let z(c) be the second derivative of -1/6*c**3 - 1/12*c**4 + 0 + 0*c**2 + 3*c. Factor z(x).
-x*(x + 1)
Find q such that 4/7*q**4 - 2/7*q**5 - 4/7*q**2 + 2/7*q + 0*q**3 + 0 = 0.
-1, 0, 1
Let s(g) be the second derivative of g**6/90 + g**5/60 + 5*g. Factor s(i).
i**3*(i + 1)/3
Suppose 3*t - 2*q - 8 = -4*q, -5*t + 4*q = -28. Let m(p) be the third derivative of 0 + 0*p**3 + 0*p**t + 1/270*p**5 + 0*p + p**2. Factor m(c).
2*c**2/9
Let a(u) be the second derivative of -1/45*u**4 + 4*u - 4/15*u**2 + 0 - 7/45*u**3 + 1/150*u**5. Solve a(o) = 0.
-1, 4
Let p be 2 + 1/((-36)/68). Let i(b) be the third derivative of 1/90*b**5 + 0*b + b**2 - p*b**3 + 0*b**4 + 0. Determine r so that i(r) = 0.
-1, 1
Let x(k) be the second derivative of -k**7/252 + k**6/90 - k**5/120 + 4*k. Factor x(y).
-y**3*(y - 1)**2/6
Let w(v) be the third derivative of -v**7/70 + 11*v**6/40 - 6*v**5/5 - 9*v**4/2 + 15*v**2. Determine t so that w(t) = 0.
-1, 0, 6
Let n(l) = 44*l**5 + 4*l**4 - 64*l**3 - 8*l**2 + 12*l - 4. Let c(m) = m**5 - m**4 - m**3 - m. Let v(w) = 8*c(w) - n(w). Find p, given that v(p) = 0.
-1, 1/3, 1
Let r(i) be the first derivative of -3*i**3 + 6*i**2 - 4*i - 1. Factor r(c).
-(3*c - 2)**2
Let m(v) be the first derivative of v**4/20 - v**3/5 + v**2/5 + 14. Suppose m(t) = 0. What is t?
0, 1, 2
Let h be 5/(3*(-2)/(-6)). Suppose 0 = -4*i - h*b - 12, -b + 3*b + 18 = 5*i. Factor 0 - 1/3*k**4 + 1/3*k**i + 0*k + 0*k**3.
-k**2*(k - 1)*(k + 1)/3
Let v(q) be the first derivative of 2*q**3/15 - 3*q**2/5 + 4*q/5 + 63. Find f such that v(f) = 0.
1, 2
Let c(a) be the first derivative of -2*a**5/5 + a**4/2 + 2*a**3/3 - a**2 + 7. Determine j so that c(j) = 0.
-1, 0, 1
Let y(v) be the second derivative of -3*v**5/170 - v**4/102 + 2*v**3/51 + 30*v. Let y(p) = 0. What is p?
-1, 0, 2/3
Suppose -8 = -4*f - 0. Suppose b**f - 5*b - 5*b**2 - 21 + 19 - b**3 = 0. Calculate b.
-2, -1
Let q be (1*3)/((-15)/(-10)). Factor -d**3 - 3*d**2 - 4*d**2 + 4*d**q + 4*d**2.
-d**2*(d - 1)
Let -6*v**2 + 8*v - 8/3 = 0. Calculate v.
2/3
Let v(f) be the third derivative of -1/54*f**4 + 0*f**3 - 1/180*f**6 + 1/1512*f**8 - 3*f**2 + 0 + 1/945*f**7 - 1/54*f**5 + 0*f. What is t in v(t) = 0?
-1, 0, 2
Let h(c) be the third derivative of c**8/84 - c**6/15 + c**4/6 - 6*c**2. Suppose h(y) = 0. Calculate y.
-1, 0, 1
Solve -3/8*c**2 + 3/8 + 0*c = 0.
-1, 1
Let z = -29 - -31. Let f(c) be the second derivative of -1/78*c**4 + 2/13*c**2 - z*c + 0 + 1/39*c**3. Factor f(a).
-2*(a - 2)*(a + 1)/13
Solve -1/2 - 1/4*b**2 - 1/8*b**3 + 7/8*b = 0 for b.
-4, 1
Let -1/4*z**4 + 0 + 1/4*z + 3/4*z**3 - 3/4*z**2 = 0. What is z?
0, 1
Let y(d) = -7*d**2 - 10*d - 7. Suppose -5*f + 0*o + 72 = o, 0 = f - 5*o - 30. Let r(g) = 27*g**2 + 39*g + 27. Let q(n) = f*y(n) + 4*r(n). Factor q(p).
3*(p + 1)**2
Suppose -h = v + 10, -3*v + v + 2*h - 12 = 0. Let p = -6 - v. Determine b so that 1 - 2 - p*b**3 - b**5 - 2*b**2 + 0 + 3*b + 3*b**4 = 0.
-1, 1
Let m(t) be the second derivative of -t**4/8 - 5*t**3/2 - 75*t**2/4 - 10*t. Factor m(v).
-3*(v + 5)**2/2
Let k(c) be the second derivative of 1/48*c**4 + 1/8*c**3 - c + 0 + 0*c**2. Factor k(w).
w*(w + 3)/4
Let j = 7 + -4. Determine g so that -4*g + 1 + j*g - g - 2 + 3*g**2 = 0.
-1/3, 1
Let -4*c**3 + 21*c**5 - 17*c**5 + 8*c**2 - 4*c**3 - 4*c**3 = 0. What is c?
-2, 0, 1
What is w in -2*w**3 + 36/7*w**2 + 2/7*w**4 - 40/7*w + 16/7 = 0?
1, 2
Let y(n) be the third derivative of 1/10*n**4 - 1/200*n**6 + 0*n + 31/150*n**5 - 4/15*n**3 - 3*n**2 + 0 - 3/50*n**7. Find i such that y(i) = 0.
-2/3, 2/7, 1
Factor -8/3*g**3 - 10/3*g**2 - 2/3*g**4 + 0 - 4/3*g.
-2*g*(g + 1)**2*(g + 2)/3
Let b(w) = 2*w**4 + 4*w**3 + w**2 - 4*w - 3. Let d(i) = -5*i**4 - 11*i**3 - 3*i**2 + 11*i + 8. Let h(q) = 8*b(q) + 3*d(q). Solve h(c) = 0 for c.
-1, 0, 1
Find b such that -b**2 + b**3 - 2*b**2 + 7*b**3 - b**2 = 0.
0, 1/2
Let r = -4 + 5. Let w(t) = t**2 - t - 1. Let u(z) = -z**4 + 2*z**3 + 2*z**2 - 3*z - 3. Let d(j) = r*u(j) - 3*w(j). Factor d(b).
-b**2*(b - 1)**2
Let v be (-2 - 4)/((-1)/(-2)). Let t be (4/7)/(v/(-28)). Factor 2*q**3 + 4*q - t - 13/3*q**2 - 1/3*q**4.
-(q - 2)**2*(q - 1)**2/3
Let t(y) = -10*y**4 - 48*y**3 + 51*y**2 + 289*y + 231. Let g(q) = -5*q**4 - 23*q**3 + 26*q**2 + 144*q + 116. Let p(u) = 9*g(u) - 4*t(u). Factor p(b).
-5*(b - 3)*(b + 2)**3
Let s(n) be the second derivative of -n**5/70 - n**4/14 - n**3/7 - n**2/7 + 7*n. Factor s(q).
-2*(q + 1)**3/7
Let l(f) = -10*f**5 + 4*f**4 + 16*f**3 - 10*f**2. Let m(d) = d**5 - d**2. Let o(a) = l(a) + 6*m(a). Suppose o(z) = 0. Calculate z.
-2, 0, 1, 2
Suppose -2*y - 22 = -3*y. Let k be (11/y)/((-2)/(-8)). Find f such that 1/4*f**3 + 0 - 1/4*f**k + 0*f = 0.
0, 1
Let z = -3 + 6. Factor -2 + 6*y**z - 3*y + y**2 + 3*y - 3*y - 2*y.
(y - 1)*(2*y + 1)*(3*y + 2)
Let k(q) be the second derivative of -q**6/10 - 7*q**5/20 + 2*q**3/3 - 27*q. Factor k(v).
-v*(v + 1)*(v + 2)*(3*v - 2)
Let b(a) be the second derivative of a**4/18 + 16*a**3/9 + 64*a**2/3 - 27*a. Factor b(p).
2*(p + 8)**2/3
Determine q, given that 16/5*q**2 + 4/5*q - 5*q**4 + q**3 + 0 = 0.
-2/5, 0, 1
Factor 0 + 0*z**2 - 6/11*z**3 + 8/11*z - 2/11*z**4.
-2*z*(z - 1)*(z + 2)**2/11
Let g(z) = 2*z. Let n be g(2). Factor 1 - n*l**4 - 2*l**3 - 1 - 2*l