**6/18 + 2*c**5/15 - 2*c**3/9 + c**2/6 - 3. Determine n, given that p(n) = 0.
-1, 0, 1
Let a = 111 - 261. Let n be 3 + a/27 + 3. Suppose 0 + n*q - 2/9*q**2 = 0. Calculate q.
0, 2
Let c(v) be the first derivative of -v**4/16 + 33. Factor c(a).
-a**3/4
Let u be (-13)/(-20) + (-6)/12. Let b(c) be the third derivative of 1/4*c**4 + 1/2*c**3 + 0*c + 0 + c**2 - u*c**5. Solve b(l) = 0.
-1/3, 1
Let n(x) = x**2 + 4*x + 5. Let d be n(-3). What is r in 0*r - 1/4*r**d + 0 = 0?
0
Factor -3*u**3 - 12 - 2*u**3 - 28*u**2 + 35*u**2 + 28*u.
-(u - 3)*(u + 2)*(5*u - 2)
Let k(m) be the second derivative of -1/10*m**2 + 1/15*m**4 + 2*m - 1/10*m**3 + 0. Factor k(h).
(h - 1)*(4*h + 1)/5
Let m be (-2)/(-5)*28/2. Factor -22/5*b - 4/5 - m*b**2.
-2*(2*b + 1)*(7*b + 2)/5
Solve -15/4 - 1/4*u**2 - 2*u = 0 for u.
-5, -3
Let p(f) = -f**4 - f**3 - f**2 - 1. Let k(h) = 8*h**4 + 8*h**3 + 7*h**2 + 7. Let w(x) = 3*k(x) + 21*p(x). Let w(b) = 0. Calculate b.
-1, 0
Determine q, given that 5*q**2 - 7*q**2 + 6*q**2 + 4*q**3 = 0.
-1, 0
Find h, given that 0*h**2 + 1/2*h**4 + 0*h + 0 - 1/4*h**3 - 1/4*h**5 = 0.
0, 1
Let k be (354/(-4))/(6/8). Let i be k/(-40) - (-2)/8. What is g in -2/5*g**3 + i*g**4 - 2*g**5 + 0*g - 4/5*g**2 + 0 = 0?
-2/5, 0, 1
Suppose -4*l + g = 23, -2*l - 4 + 0 = 2*g. Let j be (4 - 1)*l/(-3). Factor d**2 + d**2 + 6*d**3 - j*d**3 - d**4.
-d**2*(d - 2)*(d + 1)
Let g(j) = -j. Let z be 27/2 + 27/(-18). Let b(w) = w**4 + 2*w**3 + w - 1. Let d(r) = z*g(r) + 4*b(r). Suppose d(c) = 0. What is c?
-1, 1
Let q = -971/12 - 3047/36. Let b = q - -166. Determine d, given that b*d**3 - 2/9 - 4/9*d + 2/9*d**2 = 0.
-1, -1/2, 1
Let g(m) be the third derivative of -m**5/12 + 35*m**4/12 - 245*m**3/6 - 42*m**2. Solve g(q) = 0 for q.
7
Let x(n) = 0*n + 0*n - 2 + 4*n - 3*n. Let k be x(4). Suppose 2*f**4 - 8*f**3 + 3*f**2 + 7*f**2 + 2*f**2 - 8*f + k = 0. Calculate f.
1
Let x(z) be the second derivative of -63*z**5/80 + 85*z**4/16 - z**3/4 - 3*z**2 + 2*z. Let x(p) = 0. What is p?
-2/7, 1/3, 4
Let l(v) be the second derivative of -v**8/168 - v**7/35 - v**6/20 - v**5/30 + v**2 - 8*v. Let d(i) be the first derivative of l(i). Factor d(x).
-2*x**2*(x + 1)**3
Let v be 1 - 2 - (-5 - -1). Let i = 6 - v. What is f in -2 - 3*f + f + 2*f**i + 3*f**2 - f**2 = 0?
-1, 1
Let k(p) be the second derivative of -p**6/150 + 3*p**5/25 - 3*p**4/4 + 5*p**3/3 - 20*p - 2. Factor k(o).
-o*(o - 5)**2*(o - 2)/5
Let v(c) be the first derivative of -3 - 4/3*c - 2*c**2 - c**3. Determine l, given that v(l) = 0.
-2/3
What is x in -10*x**2 + 4*x + 1 + x**4 - 4*x + 8*x**2 = 0?
-1, 1
Let c be ((-14)/30 + (-6)/(-9))*2. Factor 8/5*d**4 + 12/5*d**3 + 0 + c*d + 2/5*d**5 + 8/5*d**2.
2*d*(d + 1)**4/5
Factor -3000/7 - 990/7*t**2 - 3900/7*t - 93/7*t**3 - 3/7*t**4.
-3*(t + 1)*(t + 10)**3/7
Suppose 0 = 3*c + c. Let b = -40/7 - -6. Find l such that b*l**3 - 2/7*l + 0 + c*l**2 = 0.
-1, 0, 1
Let x = -66 - -333/5. Factor x - 1/5*p**3 + 1/5*p - 3/5*p**2.
-(p - 1)*(p + 1)*(p + 3)/5
Let y = 273/1108 - -1/277. Let f(m) = m**3 - 8*m**2 - m + 8. Let v be f(8). Let -1/4*q**2 + y + v*q = 0. What is q?
-1, 1
Let c(t) be the third derivative of 1/60*t**5 + 0*t - 2*t**2 + 1/24*t**4 - 1/3*t**3 + 0. Factor c(j).
(j - 1)*(j + 2)
Suppose 3*m = 4*r - 7, -29*m + 28*m = r - 7. Factor 9/4*q**2 - m*q**3 - 1/2*q + 0 + 5/4*q**4.
q*(q - 1)**2*(5*q - 2)/4
Let k(a) be the first derivative of 0*a + 1/10*a**4 + 0*a**2 - 5 + 2/15*a**3. Factor k(u).
2*u**2*(u + 1)/5
Let p(m) = 20*m**2 - 36*m + 16. Let b(o) = -o**2 + o - 1. Let r(q) = 24*b(q) + p(q). Factor r(s).
-4*(s + 1)*(s + 2)
Let k be (-12)/4 + 4 + -1. Let c(j) be the second derivative of 1/15*j**4 - 2*j + 1/15*j**3 + 1/105*j**7 + k - 1/25*j**5 - 1/5*j**2 - 1/75*j**6. Factor c(f).
2*(f - 1)**3*(f + 1)**2/5
Let r(l) be the first derivative of -14/3*l**3 + 5 + 0*l - 2*l**2. Let r(i) = 0. What is i?
-2/7, 0
Let c(x) be the first derivative of 7*x**5/30 + 17*x**4/36 + x**3/18 - x**2/3 + x + 3. Let u(a) be the first derivative of c(a). Find m, given that u(m) = 0.
-1, -1/2, 2/7
Let g be 0 + 0 + 1 + 1. Suppose g*z - 2*v - 6 = 0, -4*v + 5 = 5*z - 10. Factor -2/7*k**z - 2/7*k**2 + 4/7*k + 0.
-2*k*(k - 1)*(k + 2)/7
Let u be (9/15)/(1/5). Suppose -m + u = -0. Factor m - 3 + 2*j**2.
2*j**2
Suppose -5 - 3 = -2*q. Suppose -24 = i - 5*i. Solve 9/2*h**2 + 0 + 5/2*h**q - h - i*h**3 = 0.
0, 2/5, 1
Let j(z) be the second derivative of 0*z**5 + 5*z - 1/3*z**4 + 0 + 1/15*z**6 + z**2 + 0*z**3. What is b in j(b) = 0?
-1, 1
Let w be (7/7)/(-1 + 0). Let v = 1 - w. Factor 1/3*f**3 + 0 + 1/3*f + 2/3*f**v.
f*(f + 1)**2/3
Let r be 0 + 0 + 16/4. Factor 0 - 2/7*x**3 - 2/7*x**r + 2/7*x**2 + 2/7*x.
-2*x*(x - 1)*(x + 1)**2/7
Factor -2/17*w**2 + 18/17*w + 0.
-2*w*(w - 9)/17
Factor n + 1/2*n**2 + 1/2.
(n + 1)**2/2
Let l be (-10)/(-2) + 6/4*-2. Factor 2/3*t + 0 + 4*t**3 + 2/3*t**5 - 8/3*t**l - 8/3*t**4.
2*t*(t - 1)**4/3
Suppose 0 = v - 8*v + 7. Suppose -9 = -5*s + v. Factor -3/4*w + 0*w**s + 1/2 + 1/4*w**3.
(w - 1)**2*(w + 2)/4
Let h(i) be the third derivative of -i**8/20160 - i**7/2520 - i**6/720 - i**5/30 + i**2. Let t(v) be the third derivative of h(v). Factor t(p).
-(p + 1)**2
Let i = -43 - -48. Let s(w) be the third derivative of 1/24*w**4 + 0*w + 0 + 2*w**2 - 1/60*w**i + 0*w**3. Find l such that s(l) = 0.
0, 1
Let z(h) = 2*h**5 - 2*h**2 - 3*h - 3. Let w be (-2)/(-4)*-1*-2. Let b(r) = r**5 - r**4 + r**3 - r**2 - r - 1. Let y(q) = w*z(q) - 3*b(q). Factor y(g).
-g**2*(g - 1)**3
Suppose -12 = -4*m, 0 = -4*f - 2*m + 14 - 0. Find i such that 12*i**3 + i - 7*i**4 - 6*i**2 - f*i + 3*i**2 - i = 0.
-2/7, 0, 1
Let f(c) = 6*c**2 - 2*c + 1. Let v be f(1). Let n(u) = -6*u - 1. Let g be n(-1). Let 5*w**v - 2*w + 3*w**4 - 4*w**2 + w**4 - 3*w**g = 0. What is w?
-1, 0, 1
Let b(d) be the first derivative of 0*d**3 + 0*d**2 + 0*d + 1/22*d**4 + 4 - 4/55*d**5 - 1/11*d**6. Solve b(n) = 0 for n.
-1, 0, 1/3
Suppose 0*u - 4/7*u**2 + 36/7 = 0. Calculate u.
-3, 3
Let i = 1/102 - -301/510. Suppose 0 = -5*h + 3*x + 2*x + 35, 3*x + 13 = h. Solve 0 - 3/5*p**3 + 3/5*p + i*p**h - 3/5*p**2 = 0.
-1, 0, 1
Let v(q) be the first derivative of 3/4*q**3 + 0*q - 2 - 15/16*q**4 + 3/4*q**2. Factor v(z).
-3*z*(z - 1)*(5*z + 2)/4
Let x be (-9)/5*54/(-162). Suppose 3/5*m**2 + 0 - x*m = 0. Calculate m.
0, 1
Let r = -85 - -256/3. Let q(x) be the third derivative of -r*x**3 + 0*x + 0 - 1/6*x**4 - x**2 - 1/30*x**5. Factor q(h).
-2*(h + 1)**2
Let v(l) be the second derivative of -l**7/168 - l**6/120 + l**5/80 + l**4/48 + 27*l. Factor v(t).
-t**2*(t - 1)*(t + 1)**2/4
Let o(l) = -l**2 + 4*l + 8. Let n be o(5). Factor -97/4*s**2 + 8*s + 25/4*s**5 + 139/4*s**n - 95/4*s**4 - 1.
(s - 1)**3*(5*s - 2)**2/4
Let a(f) be the first derivative of f**4/2 + 4*f**3/3 - 8. Let u(d) = -d**4 - 3*d**3 - 4*d**2 - 1. Let x(n) = -3*a(n) - 2*u(n). Factor x(c).
2*(c - 1)**2*(c + 1)**2
Let i(h) = 20*h + 5. Let a be i(2). Suppose 0*b - 8 = -2*b. Determine g so that 15/2*g**b + 243/2 + a*g**3 + 1/2*g**5 + 135*g**2 + 405/2*g = 0.
-3
Let d be (26/39)/((-8)/(-6)). Suppose 1/2*y + 0 - y**2 + d*y**3 = 0. What is y?
0, 1
Suppose -4*a = k + 19, -17 = -2*k + 4*a - a. Let g be 3/(k + 25/2). Factor 0 - 2/9*s**2 + g*s.
-2*s*(s - 1)/9
Let l(j) be the first derivative of j**4/36 + j**3/3 + 3*j**2/2 - 7*j - 5. Let p(m) be the first derivative of l(m). Determine d, given that p(d) = 0.
-3
Let r(p) = -3*p**2 + p + 2. Let k(c) = 7*c**2 - 3*c - 4. Suppose -t + 5*z - 7 = 18, 3*t + 3 = -3*z. Let n(a) = t*r(a) - 2*k(a). Factor n(h).
(h - 1)*(h + 2)
Let p be 1/(-3)*18/(-3). Factor 10*z**2 - 12*z**2 + 2*z**3 - 4*z**2 + 6*z - p.
2*(z - 1)**3
Let p(x) be the first derivative of x**6/30 - x**5/10 + x - 3. Let v(z) be the first derivative of p(z). Solve v(y) = 0 for y.
0, 2
Suppose 0 = -5*d + 2*o + 88, 4*d - 4*o - 64 = d. Suppose -4*c + 0*c + d = 0. Find m such that c*m - 1 - 4 - 2*m**2 + 3 = 0.
1
Let w(a) be the first derivative of -2*a**4/3 + 22*a**3/9 - 10*a**2/3 + 2*a + 5. Factor w(u).
-2*(u - 1)**2*(4*u - 3)/3
What is p in 2/13*p**2 - 2/13*p + 0 = 0?
0, 1
Suppose -3 = i - 2*i. Suppose -q = i*g - 3, -2*q + 6 = -3*g - 2*g. What is a in g*a + 0 - 2/7*a**2 + 4/7*a**3 - 2/7*a**4 = 0?
0, 1
Let h(x) be the second derivative of 3*x**5/80 - x**4/16 - x**3/8 + 3*x**2/8 - x. Let h(q) = 0. What is q?
-1, 1
Suppose 11*n + 44 = 15*n. Let r(i) = i**3 - 5*i