**4 = 0.
-1, 0, 1
Let z(t) = -t**2 - 10*t. Let v be z(-10). Factor v*x - 1/4*x**2 + 1/4.
-(x - 1)*(x + 1)/4
Let p(o) be the first derivative of 64*o**5/35 + 24*o**4/7 - 20*o**3/7 + 4*o**2/7 - 4. Solve p(y) = 0.
-2, 0, 1/4
Suppose 5*g - c = 13, -3*g + 7 = c + 4. Let 4*x**g - 4*x + 2 - 5*x**2 + 3*x = 0. Calculate x.
-2, 1
Let d(t) be the first derivative of -t**7/630 + t**6/360 - 3*t**2/2 - 3. Let k(u) be the second derivative of d(u). Determine s, given that k(s) = 0.
0, 1
Solve 0 - 3/4*o**5 - 3/2*o**2 + 3/2*o**4 + 0*o**3 + 3/4*o = 0 for o.
-1, 0, 1
Let -1 + c**2 + 3/2*c = 0. What is c?
-2, 1/2
Let g(l) = l**4 + l + 1. Let q(n) = -2*n**4 - 4*n**3 - 6. Suppose 2*a + 3*a = 20. Suppose 9*p - a*p = -s + 8, 6 = 2*s. Let z(y) = p*q(y) + 4*g(y). Factor z(r).
2*(r - 1)**3*(r + 1)
Let t be 0 + 2 - (-18)/18. Factor 0*k + 1/3*k**t + 0 + 0*k**2.
k**3/3
Let x(v) = -v**5 + v**3 + v**2 + 1. Let w(a) = -2*a**5 - a**4 - 6*a**3 + 8*a**2 + 16*a - 9. Let y(c) = 5*w(c) - 15*x(c). Find i, given that y(i) = 0.
-2, 1, 3
Suppose 2/5*l**2 - 2/5 - 2/5*l + 2/5*l**3 = 0. Calculate l.
-1, 1
Suppose 0*z = 6*z. Factor 0*l**2 + 2*l**5 + z*l - 4/7*l**3 + 0 + 10/7*l**4.
2*l**3*(l + 1)*(7*l - 2)/7
Suppose 0*i = -i + 5*c - 23, 0 = -5*i + 2*c. Factor -2/7 + 0*j**i + 3/7*j - 1/7*j**3.
-(j - 1)**2*(j + 2)/7
Solve -10*u**4 + 20*u**2 - 25*u**4 + 24*u**3 - 84*u**3 = 0 for u.
-2, 0, 2/7
Factor 3/5*w**4 - 12/5*w**3 - 6/5*w + 0 + 3*w**2.
3*w*(w - 2)*(w - 1)**2/5
Let h(x) be the second derivative of x**7/1680 - x**5/80 - x**4/24 - x**3/6 - 3*x. Let o(s) be the second derivative of h(s). Determine z, given that o(z) = 0.
-1, 2
Factor 3/5*l**2 - 3/5*l**4 + 0 + 1/5*l - 1/5*l**3.
-l*(l - 1)*(l + 1)*(3*l + 1)/5
Factor -2500 - 4*l + l**2 + 0*l + 2504.
(l - 2)**2
Let k(l) = -l**5 - l**4 + l. Let i(p) = 72*p**3 + 6*p**4 - 83*p**5 - 6*p + 12*p**2 + 63*p**4 - 58*p**5. Let o(n) = -i(n) - 6*k(n). Factor o(z).
3*z**2*(z - 1)*(7*z + 2)**2
Let f = -7 - -12. Suppose r - 1 = -2*c + 4, -3 = -4*c + f*r. What is w in 2*w - 1 + c - 4*w + w**2 = 0?
1
Let s = -13 + 23. Let y be ((-3)/s)/(12/(-90)). Factor 1/4*c**2 + 3/2*c + y.
(c + 3)**2/4
Let l(t) be the second derivative of t**3/6 + 15*t**2/2 - 4*t. Let u be l(-12). What is o in -o**2 + 0*o + o**2 + 6*o + u*o**2 - 9 = 0?
-3, 1
Let w(v) be the third derivative of v**8/112 - 3*v**7/70 + v**5/5 - 5*v**2. Factor w(x).
3*x**2*(x - 2)**2*(x + 1)
Let h(t) = 5*t**4 + 17*t**3 - 9*t**2 - 8*t - 5. Let a(s) = 2*s**4 + 8*s**3 - 4*s**2 - 4*s - 2. Let g(v) = -9*a(v) + 4*h(v). Find o, given that g(o) = 0.
-1, 1
Let s(l) be the third derivative of -l**6/240 + l**5/20 - l**4/4 + 2*l**3/3 + 3*l**2. What is d in s(d) = 0?
2
Let s(b) be the first derivative of -18*b**5/5 + 10*b**4 - 26*b**3/3 + 2*b**2 + 4. Factor s(t).
-2*t*(t - 1)**2*(9*t - 2)
Suppose 6 = 3*u - k, -5 = 4*u + 3*k - 26. Suppose 0 = -3*w - 4 + 13. Factor 2*o**u - 5*o**3 + 2*o + o**w.
-2*o*(o - 1)*(o + 1)
Let f(m) = m**5 + m**2 + 1. Let q(i) = -4*i**5 - i**4 - 3*i**3 - 5*i**2 + i - 6. Let d(b) = 6*f(b) + q(b). Solve d(y) = 0.
-1, -1/2, 0, 1
Let s(u) be the second derivative of 0*u**3 + 1/30*u**6 - 1/42*u**7 + 0 + 4*u + 0*u**2 + 1/20*u**5 - 1/12*u**4. Suppose s(h) = 0. What is h?
-1, 0, 1
Let m = 46/231 + -5/33. Let p(k) be the third derivative of -m*k**3 + 1/210*k**5 + 0*k + 0 + k**2 + 0*k**4. Factor p(n).
2*(n - 1)*(n + 1)/7
Let p = -4 - -6. Let v(i) = i - 5. Let m be v(8). Let 7*t**3 + 2*t + t**p + t**5 - t**4 + 0*t - 10*t**m = 0. Calculate t.
-1, 0, 1, 2
Let c be (12/(-4))/(-3) - -1. Suppose z = -j + 7, 4*z - j - 5 = -2. Let -u**2 - 3*u**z + 3*u**c - u = 0. Calculate u.
-1, 0
Let w(g) be the second derivative of -g**6/15 + 7*g**5/50 + g**4/10 - 7*g**3/15 + 2*g**2/5 - 8*g. Suppose w(b) = 0. What is b?
-1, 2/5, 1
Factor 1/6*n**2 - 1/3 + 1/6*n.
(n - 1)*(n + 2)/6
Let w(k) be the second derivative of -k**6/6 + k**5 - 5*k**4/3 + 11*k. Let w(j) = 0. What is j?
0, 2
Let o(c) be the third derivative of -c**9/1512 + c**8/840 + c**7/420 - c**6/180 + c**3/2 + 3*c**2. Let j(i) be the first derivative of o(i). Solve j(g) = 0.
-1, 0, 1
Let y(r) = r**2. Suppose 0 = j + 2 - 3. Let w(d) = 2*d - 1. Let b(f) = j*w(f) - y(f). Determine m so that b(m) = 0.
1
Let x(b) be the second derivative of 7*b**6/120 - 19*b**5/60 + b**4/3 + 2*b**3/3 - b**2/2 + 10*b. Let c(i) be the first derivative of x(i). Factor c(s).
(s - 2)*(s - 1)*(7*s + 2)
Let c(g) = -g**3 + 10*g**2 - 11*g + 22. Let r be c(9). Let i be 2*(-1)/3*-3. Suppose 3/4*v + 3/4*v**i - 27/4*v**3 + 0 - 3*v**5 + 33/4*v**r = 0. What is v?
-1/4, 0, 1
Let x = 18 - 13. Let z(y) be the third derivative of -y**2 - 1/40*y**x + 1/6*y**3 + 0 + 0*y + 5/48*y**4. Determine u so that z(u) = 0.
-1/3, 2
Factor 36*b**2 + 39/2*b + 3 + 27/2*b**3.
3*(b + 2)*(3*b + 1)**2/2
Let c(y) be the first derivative of -1/2*y**2 - 1/6*y**3 + 0*y - 6. Find b such that c(b) = 0.
-2, 0
Suppose -m = -1 - 1. What is b in -3*b + m - 3*b - b**3 - b**3 + 6*b**2 = 0?
1
Let j be -1 + (-3)/(1/(-1)). Let s(w) be the first derivative of -4*w - 5*w**3 - j + 9/8*w**4 + 7*w**2. Factor s(i).
(i - 2)*(3*i - 2)**2/2
Suppose 0 = 3*c + 5*j + 20, -j + 4*j = -2*c - 12. Suppose 2 = 4*y - 4*n + 6, c = 4*y + 5*n - 23. Factor 2*v - 1 - 4*v**y + 0*v + 3*v**2.
-(v - 1)**2
Factor 3*v + 5*v - 5*v**2 + 4*v**2 - 3*v**2.
-4*v*(v - 2)
Suppose -2*a = -0*a - 2*g - 14, 5*a = 3*g + 31. Factor c**a - 4*c**3 + c**3 + c**3 + 4*c**4 - 3*c**5.
-2*c**3*(c - 1)**2
Let n(s) be the first derivative of 3/2*s**2 + 1/4*s**4 - s - s**3 + 2. Let n(r) = 0. Calculate r.
1
Factor -1/2*u**2 + 1/2*u**3 - 1/2*u**5 + 0 + 1/2*u**4 + 0*u.
-u**2*(u - 1)**2*(u + 1)/2
Let g(m) be the second derivative of -1/360*m**6 + 3*m + m**2 + 1/180*m**5 + 0 + 0*m**3 + 0*m**4. Let h(r) be the first derivative of g(r). Solve h(a) = 0.
0, 1
Let i be (-1)/5 - 136/20. Let p be ((-1)/i)/(4/14). Determine q, given that -1/4*q**3 + 1/2 - p*q**2 + 1/4*q = 0.
-2, -1, 1
Let c(o) be the third derivative of o**7/420 - o**6/240 - o**5/120 + o**4/48 - 4*o**2. Determine d so that c(d) = 0.
-1, 0, 1
Let f be 56/360 + 2/(-9). Let b = 2/5 + f. Factor -b*g - 1/3*g**2 + 1/3*g**3 + 1/3*g**4 + 0.
g*(g - 1)*(g + 1)**2/3
Let a(t) be the third derivative of t**7/420 - t**6/120 - t**5/30 + t**4/6 + 4*t**2. Factor a(z).
z*(z - 2)**2*(z + 2)/2
Let s = -1 - -1. Suppose -15 = -s*p - 5*p. Factor -4*u**2 + 3*u**2 - 3*u**2 - 2*u - 2*u**p.
-2*u*(u + 1)**2
Let v(d) be the first derivative of d**6/18 + 2*d**5/15 - 2*d**3/9 - d**2/6 + 5. Let v(s) = 0. Calculate s.
-1, 0, 1
Factor 7*l**2 + 4*l**3 - l**2 + 4*l**4 - 4*l**2 - 10*l**2.
4*l**2*(l - 1)*(l + 2)
Let l(w) be the second derivative of -w**6/60 + 3*w**5/40 - w**4/12 + 9*w. Suppose l(k) = 0. Calculate k.
0, 1, 2
Let v(g) be the first derivative of -g**3/4 - 3*g**2/8 + 3*g/2 - 3. Factor v(p).
-3*(p - 1)*(p + 2)/4
Suppose 4*r + 1 = -4*i - 11, 0 = -4*r + 2*i + 18. Let j(c) be the first derivative of 0*c**2 + 0*c + 1/4*c**4 - r + 0*c**3. Factor j(w).
w**3
Let g = -2327/5 + 467. Factor 2/5 + 12/5*m**2 - 8/5*m**3 + 2/5*m**4 - g*m.
2*(m - 1)**4/5
Suppose -5*d + 22 + 18 = 0. Suppose 0 = 5*c - d - 2. Suppose h**3 + h**3 - 5*h**3 - 2*h - 5*h**3 + 10*h**c = 0. What is h?
0, 1/4, 1
Solve -132 - 5*n**2 + 7 - 17*n + 67*n = 0 for n.
5
Suppose 4*p - 32 = -20. Let u(h) be the first derivative of -1 + 0*h + 2/9*h**p - 2/3*h**2. Factor u(r).
2*r*(r - 2)/3
Factor 216*z**5 - 55*z**4 + 530*z**2 + 50*z**3 + 245 - 102*z + 767*z - 211*z**5.
5*(z - 7)**2*(z + 1)**3
Let m(p) = p + 5. Let u be m(-3). Determine h so that 8*h**2 - 4*h + 2*h + 6*h**3 - u - 5 + 3 = 0.
-1, 2/3
Suppose 8*o - 28 = 3*o + 2*r, 12 = -3*r. Let f = 6 - o. Factor 4 - f - m**3 + 8*m - 5*m.
-(m - 2)*(m + 1)**2
Let r = -4936 + 1776961/360. Let q(d) be the third derivative of r*d**6 + 0 - 1/90*d**5 + 0*d**3 - d**2 + 0*d + 1/72*d**4. Factor q(c).
c*(c - 1)**2/3
Let x(a) be the third derivative of -2*a**7/105 + a**6/20 + 2*a**5/15 - a**4/4 - 2*a**3/3 - 8*a**2. Suppose x(l) = 0. What is l?
-1, -1/2, 1, 2
Suppose -2*c = -2*f - 8 - 0, 40 = -4*f - 2*c. Let p = -6 - f. Suppose 5*x**2 - 2*x**2 - 3*x**p - x**3 = 0. Calculate x.
0
Let h(u) be the second derivative of -u**9/75600 + u**8/16800 - 5*u**4/12 + 3*u. Let y(x) be the third derivative of h(x). Factor y(q).
-q**3*(q - 2)/5
Determine q, given that -10*q**2 - 5*q**2 + 11*q**2 = 0.
0
Let p(