-1, 1, 2
Let 2/5*l**5 + 0*l**4 - 8/5*l**3 + 4/5*l**2 + 6/5*l - 4/5 = 0. What is l?
-2, -1, 1
Let h be ((-2)/(-5))/((-21)/((-735)/28)). Let a = -101/12 - -26/3. Solve h - 1/4*n**2 + a*n = 0.
-1, 2
Let t = 16 - 16. Let s = -40 + 121/3. Find l, given that 1/3*l**3 + 2/3*l**2 + t*l - s*l**4 + 0 = 0.
-1, 0, 2
Let h be 1 + 1 + -1 + 1. Determine j, given that -2 + 5 - 50*j**h + 47*j**2 = 0.
-1, 1
Let s(t) be the first derivative of -t**6/10 + 6*t**5/25 - 3*t**4/20 + 16. Determine h so that s(h) = 0.
0, 1
Let a(i) be the first derivative of -i**4/42 + 4*i**3/63 - i**2/21 + 5. Suppose a(w) = 0. Calculate w.
0, 1
Let q(d) = -d**3 + 7*d**2 - 5*d - 3. Let k be q(6). Factor 3 - 3*y + 3*y - k*y**2.
-3*(y - 1)*(y + 1)
Factor -3/4*z + 1/2 + 1/4*z**2.
(z - 2)*(z - 1)/4
Solve 60*s**3 + 0*s**4 + 0*s**4 - 63*s**3 - 3*s**4 = 0.
-1, 0
Let x(h) be the first derivative of h**3/5 - 9*h**2/10 + 6*h/5 - 5. Factor x(f).
3*(f - 2)*(f - 1)/5
Let d(m) = m**3 - 47*m**2 + 48*m - 89. Let a be d(46). Suppose -4/7*j + 0 - 2/7*j**a - 6/7*j**2 = 0. Calculate j.
-2, -1, 0
Let h(z) be the second derivative of -3*z + 0 + 1/4*z**4 - 1/2*z**3 + 3/20*z**5 - 1/10*z**6 + 0*z**2. Suppose h(t) = 0. Calculate t.
-1, 0, 1
Let b(o) be the first derivative of -o**4/18 + 4*o**3/9 - o**2 - 3*o - 1. Let f(y) be the first derivative of b(y). Factor f(p).
-2*(p - 3)*(p - 1)/3
Let w(u) be the second derivative of u**5/20 - 11*u**4/12 + 4*u**3 + 18*u**2 + 4*u. Determine s, given that w(s) = 0.
-1, 6
Let z(u) = -16*u**2 - 46*u - 422. Let l(o) = -o**2 + o + 2. Let r(b) = -28*l(b) + 2*z(b). What is n in r(n) = 0?
-15
Let o(x) be the first derivative of -11/9*x**2 - 7/18*x**4 + 6 - 32/27*x**3 - 4/9*x. Factor o(q).
-2*(q + 1)**2*(7*q + 2)/9
Factor 3*g**2 + 10 - 6*g - 6 - 1.
3*(g - 1)**2
Factor 0 + 6/7*x**2 + 0*x - 3/7*x**3.
-3*x**2*(x - 2)/7
Let d(a) = 5*a**2 + 12*a + 7. Let q(t) = 135*t**2 + 325*t + 190. Let k(w) = -55*d(w) + 2*q(w). Factor k(f).
-5*(f + 1)**2
Let l be (16/(16/(-2)))/(-3). Find g such that 6 - 4*g + l*g**2 = 0.
3
Let g(u) = u**4 - u**2 + u - 1. Let v(z) = -5*z**5 - 18*z**4 - 9*z**3 + 6*z**2 - 3*z + 5. Let i(d) = -10*g(d) - 2*v(d). Factor i(k).
2*k*(k + 1)**3*(5*k - 2)
Suppose 5*m - 9 - 6 = 0. Let s(i) be the second derivative of -2*i + 1/3*i**m + 0 - 1/10*i**5 + 0*i**2 + 0*i**4. Find p, given that s(p) = 0.
-1, 0, 1
Let a(d) be the first derivative of -d**6/90 + d**5/5 - 3*d**4/2 - d**3/3 + 4. Let b(c) be the third derivative of a(c). Factor b(v).
-4*(v - 3)**2
Let f be (-4)/6*36/(-96). Suppose 1/4 + 0*z - f*z**2 = 0. Calculate z.
-1, 1
Let n(d) = -2*d - 22. Let j be n(9). Let k be j/(-8) - (4 - 1). Determine p so that -4/9*p + 0 + 2/9*p**k = 0.
0, 2
Let s(o) be the third derivative of -o**7/1050 - 36*o**2. Factor s(b).
-b**4/5
Let f(y) = 2*y**4 - 2*y**3 - 10*y**2 - 14*y - 8. Let t(r) = 4*r**4 - 3*r**3 - 19*r**2 - 27*r - 15. Let q(d) = -7*f(d) + 4*t(d). Suppose q(j) = 0. What is j?
-1, 2
Let l(c) be the first derivative of 2*c**6 - 21*c**5/5 + 3*c**4/2 + c**3 + 4. Let l(d) = 0. What is d?
-1/4, 0, 1
Factor -187 - 6*i**3 - 2*i**5 + 2*i**2 + 6*i**4 + 187.
-2*i**2*(i - 1)**3
Determine t so that -22/7*t**4 + 4/7*t + 6/7*t**5 + 0 - 18/7*t**2 + 30/7*t**3 = 0.
0, 2/3, 1
Suppose 10 = -0*s - s + 4*v, -5*s + 4*v = 2. Factor -5*g**s + 7 - g + 7 + 8*g - 4*g**3 - 12.
-(g - 1)*(g + 2)*(4*g + 1)
Let d(h) = h**4 - h**3 - h**2 - h + 2. Let y(z) = 45*z**4 - 1125*z**3 + 6342*z**2 + 3387*z + 426. Let l(x) = 3*d(x) + y(x). Factor l(q).
3*(q - 12)**2*(4*q + 1)**2
Let v(z) = -5*z**5 + 5*z**4 + 5*z**3 - 3*z**2 + 2*z + 2. Let n(q) = 5*q**5 - 5*q**4 - 5*q**3 + 2*q**2 - 3*q - 3. Let f(l) = -2*n(l) - 3*v(l). Factor f(c).
5*c**2*(c - 1)**2*(c + 1)
Let x(q) be the first derivative of -3 + 2/3*q**3 - 2/5*q**5 + 0*q + 0*q**2 + 0*q**4. Factor x(k).
-2*k**2*(k - 1)*(k + 1)
Factor 1/2*i**2 + 0*i + 0.
i**2/2
Let v be 2/(-3)*-1 - (-160)/75. Let -v*r + 6/5*r**4 + 14/5*r**3 - 2/5*r**2 - 4/5 = 0. Calculate r.
-2, -1, -1/3, 1
Let c be 10/42*9/225. Let m(x) be the second derivative of c*x**6 + 0 + 0*x**2 + 1/14*x**4 + 3/70*x**5 + 1/21*x**3 - 4*x. Find v such that m(v) = 0.
-1, 0
Let p(n) = 3*n**2 - 12*n - 3. Let y(f) = 2*f - 3*f + 3 - 4. Let d(u) = -p(u) + 3*y(u). Find j such that d(j) = 0.
0, 3
Factor 1/2*l**5 + 0*l + 3*l**4 + 6*l**3 + 0 + 4*l**2.
l**2*(l + 2)**3/2
Let p(a) be the second derivative of -a**5/10 - a**4/6 + a**3/3 + a**2 + 6*a. Factor p(i).
-2*(i - 1)*(i + 1)**2
Let q(s) be the second derivative of -s**4/28 + 3*s**3/14 + 4*s. What is b in q(b) = 0?
0, 3
Let f(u) be the first derivative of -1/15*u**5 + 1/12*u**4 + 1/60*u**6 - 2 + 0*u + 0*u**3 - u**2. Let o(a) be the second derivative of f(a). Factor o(w).
2*w*(w - 1)**2
Suppose -2*t - 2*t = -12. Factor -3*d**4 + d**5 + 6*d**3 + t*d**4 - 2*d**2 - 6*d**4 + d**5.
2*d**2*(d - 1)**3
Let u = 1/56 + 31/56. Suppose -u*d + 4/7*d**3 - 2/7 + 0*d**2 + 2/7*d**4 = 0. What is d?
-1, 1
Let t(y) = 96*y**2 + 153*y + 24. Let l(k) = 12*k**2 + 19*k + 3. Let x = 14 - 18. Let j(n) = x*t(n) + 33*l(n). Factor j(c).
3*(c + 1)*(4*c + 1)
Suppose 2*q - 2 = -8. Let o be 0 - ((-33)/9 - q). Factor -2/3 + 2/3*y**2 - o*y**3 + 2/3*y.
-2*(y - 1)**2*(y + 1)/3
Let g(c) be the third derivative of c**8/30240 - c**7/3780 + c**6/1080 - c**5/540 + c**4/8 - c**2. Let o(z) be the second derivative of g(z). Factor o(q).
2*(q - 1)**3/9
Factor -2/5*g + 4/5 - 4/5*g**2 + 2/5*g**3.
2*(g - 2)*(g - 1)*(g + 1)/5
Let t(r) be the second derivative of -27*r**7/14 + 81*r**6/10 - 27*r**5/2 + 23*r**4/2 - 11*r**3/2 + 3*r**2/2 + 6*r. What is c in t(c) = 0?
1/3, 1
Let b(q) be the first derivative of 2*q**5/45 - q**4/9 + 2*q**3/27 + 2. Factor b(l).
2*l**2*(l - 1)**2/9
Let g(m) be the first derivative of m**4/4 + 3*m**3/2 + 3*m**2 - 2*m + 4. Let x(s) be the first derivative of g(s). Find c, given that x(c) = 0.
-2, -1
Let c be 252/70 + 4/10. Let i(r) be the third derivative of -1/15*r**3 + 0*r + 0*r**c - 4*r**2 + 0 + 1/150*r**5. Factor i(m).
2*(m - 1)*(m + 1)/5
Solve -162/17*j**5 - 314/17*j**3 + 0 - 8/17*j - 88/17*j**2 - 396/17*j**4 = 0.
-1, -2/9, 0
Let p be (-6)/(-8)*36/54. Let 0 - 1/2*c**3 + 1/2*c - 1/2*c**2 + p*c**4 = 0. What is c?
-1, 0, 1
Let g(n) = 2*n**2 + 4*n - 1. Let c be g(-3). Let b = c + -5. Solve 2/7*x - 4/7*x**4 + 4/7*x**2 + 0 + b*x**3 - 2/7*x**5 = 0.
-1, 0, 1
Let y = 5 - 3. Suppose -7*a + 8 = -3*a. Factor -5*j**a + 2*j**3 + j**5 + 2*j**2 + j**3 + 2*j**y - 3*j**4.
j**2*(j - 1)**3
Let u(r) = r**3 - 1. Let s(p) = 15*p**3 + 3*p**2 + 6*p - 18. Suppose -t = -4*t - 12, 2*t = -z - 7. Let g(f) = z*s(f) - 18*u(f). Suppose g(m) = 0. Calculate m.
-1, 0, 2
Let v(o) = -7*o**2 - 2*o - 1. Let h be (6/18)/(2/(-18)). Let d(m) = -4*m**2 - m - 1. Let u(g) = h*v(g) + 5*d(g). Find z such that u(z) = 0.
-2, 1
Suppose 2*u = 2*a - 46, -4*a + 4*u - 5*u = -97. Let p = -95/4 + a. Factor -p*r**2 - 1/4*r + 0.
-r*(r + 1)/4
Let z = 13 - 8. Find o, given that -3*o**2 - o**2 - 2 + o**2 + z*o**2 = 0.
-1, 1
Let k(z) = -z**3 - 3*z**2 + 3*z - 3. Let n be k(-4). Suppose -h - n = h + 5*b, -5*h - 4*b + 6 = 0. Determine g so that 9/4*g**h - 1/2*g - 7/4*g**3 + 0 = 0.
0, 2/7, 1
Let m = 86 - 171/2. Factor -m*j**3 + j**2 - 1 + 1/2*j.
-(j - 2)*(j - 1)*(j + 1)/2
Let a(t) = -5*t**2 + t + 4. Suppose 2*k = 4*k - 12. Let d(m) = -3*m**2 + 8*m**2 - 4*m**2 - 2 + m**2. Let u(q) = k*a(q) + 14*d(q). Suppose u(x) = 0. What is x?
1, 2
Let n = 227/446 - 2/223. Factor 0*h + 0*h**2 + 0 - n*h**3.
-h**3/2
Factor 1/3*n**4 + 0 - 1/3*n**2 + 2/3*n**3 - 2/3*n.
n*(n - 1)*(n + 1)*(n + 2)/3
Let b be (30/35)/((-48)/(-112)). Factor 0 - 1/2*c**b + 3/2*c.
-c*(c - 3)/2
Let w(c) = 4*c**3 + 4*c**2 + 7*c + 5. Let t(j) be the third derivative of j**6/24 + j**5/12 + j**4/3 + j**3 - 5*j**2. Let z(f) = -5*t(f) + 6*w(f). Factor z(q).
-q*(q - 1)*(q + 2)
Let m be -1 + 0 + (-15)/(-5). Solve 0*x**2 - 5 + 3 + m*x**2 = 0 for x.
-1, 1
Let h = 2 + 1. Factor 4*z - 2*z - 4*z + 2 + 2*z**h - 2*z**2.
2*(z - 1)**2*(z + 1)
Let a(p) = -9*p**2 - 7*p + 11. Let i(h) = -5*h**2 - 4*h + 6. Let g(c) = -c**3 + 4*c**2 - 3*c + 1. Let q be g(4). Let x(z) = q*i(z) + 6*a(z). Factor x(s).
s*(s + 2)
Suppose -30/7*k + 6/7*k**3 - 2*k**2 + 36/7 + 2/7*k**4 = 0. Calculate k.
-3, 1, 2
Let i(v) be the first derivative of -v**7/1260 + v**5/360 - 5*v**2/2 + 8. Let d(x) be the second derivative of i(x). Factor d(u).
-u**2*(u - 1)*(u +