 1
Suppose -3*g - 13 = w - 2, -3*g = -w + 19. Suppose 0 = 4*b + 4 - 12. Factor -4*p**3 + 3*p**3 + p**5 + p**b + 2*p**w - 3*p**4.
p**2*(p - 1)**2*(p + 1)
Let o(y) be the third derivative of -y**8/1680 - 2*y**7/525 - y**6/150 + y**5/150 + y**4/24 + y**3/15 + 7*y**2. Find h such that o(h) = 0.
-2, -1, 1
Let k(o) = o**3 - 8*o**2 + 10*o - 10. Let y be k(7). Let i(p) = -4*p**3 + 2. Let u(v) = 21*v**3 + v**2 - 11. Let l(f) = y*i(f) + 2*u(f). Factor l(t).
-2*t**2*(t - 1)
Factor 171/7*r**2 + 3249/7*r + 20577/7 + 3/7*r**3.
3*(r + 19)**3/7
Let m(t) = t**2 - 8*t. Let j(r) = r**3 - r**2 + 3*r - 2. Let i be j(2). Let q be m(i). Find u, given that q + 2/7*u**2 + 4/7*u = 0.
-2, 0
Let s = 73 + -130. Let c = -397/7 - s. Suppose 4/7*a + 2/7*a**2 + c = 0. Calculate a.
-1
Let u be (0 + -5)*3/(-5). Factor -1 + 4*n**u + 3 + 4 - n**3 - 9*n.
3*(n - 1)**2*(n + 2)
Suppose 6*j - 3*j = -90. Let o be j/(-7) - (-2)/(-7). Let -6*h**2 + 0 - 2 + 6*h + o*h**2 - 2*h = 0. Calculate h.
1
Suppose 4*t + 8 = -0*t. Let u be t/3*(0 - 3). Find p such that 2*p**3 - 3*p**4 - 5*p**u - 2*p + p**4 + 3*p**2 + 4*p**4 = 0.
-1, 0, 1
Factor -3/2 + 0*i**3 - 27*i**2 + 81/2*i**4 - 12*i.
3*(i - 1)*(3*i + 1)**3/2
Determine o, given that -2/11*o**2 + 2/11*o**4 - 2/11*o + 2/11*o**3 + 0 = 0.
-1, 0, 1
Let w(r) = 3*r**2 - 10*r + 1 + 4*r + 2*r. Let n(l) = -5*l + 2*l**2 + 1 - 3*l + 5*l. Let s(d) = 4*n(d) - 3*w(d). Suppose s(q) = 0. Calculate q.
-1, 1
Let c = 33 - 27. Let s(o) be the third derivative of 0 - 2/9*o**3 + 1/315*o**7 + 3*o**2 + 0*o - 1/30*o**5 + 1/180*o**c - 5/36*o**4. Factor s(j).
2*(j - 2)*(j + 1)**3/3
Let k be (-3 - (-1 - -1)) + 1. Let s be (-33)/(-27) + 2/k. Factor -s*m**2 + 0 + 2/9*m**3 + 0*m.
2*m**2*(m - 1)/9
Let z be (22/77)/(-2 + 92/42). Determine x so that -2 - z*x**2 - 1/4*x**3 - 3*x = 0.
-2
Let p(t) = t - 2. Let n be p(3). Let h be (0 - n) + (-27)/(-9). Suppose -3/2*d**4 - 1/2*d**3 + 0*d + 0*d**h + 0 = 0. Calculate d.
-1/3, 0
Suppose -268 + 24*m**3 + 9*m**4 + 6*m + 268 + 3*m**2 + 18*m**2 = 0. Calculate m.
-1, -2/3, 0
Let p(m) be the first derivative of -4*m**3/3 + 12*m**2 - 72. Find j, given that p(j) = 0.
0, 6
Let x be -5*3/(-105)*(6 + -4). Factor x*d**2 + 4/7*d + 0.
2*d*(d + 2)/7
Suppose 4/3*t + 0 - t**3 + 4/3*t**4 - 1/3*t**5 - 4/3*t**2 = 0. What is t?
-1, 0, 1, 2
Let m(r) be the first derivative of -1/4*r**4 + 1/6*r**6 + 0*r + 1/5*r**5 + 0*r**2 - 1/3*r**3 + 4. Factor m(s).
s**2*(s - 1)*(s + 1)**2
Let x(c) be the first derivative of 3*c**5/25 - 2*c**4/5 + 4*c**3/15 + 9. Find l such that x(l) = 0.
0, 2/3, 2
Let c = 18 + -12. Let p = c + -17/3. What is f in -p*f**2 + 1/3*f**3 + 0 + 0*f = 0?
0, 1
Let i(h) = h - 4. Let p be i(5). Suppose l**2 - p - 1 - 4*l**2 + 5*l**2 = 0. What is l?
-1, 1
Let y = 1615/2 - 806. Factor -y*c**3 - 3/2*c + 3*c**2 + 0.
-3*c*(c - 1)**2/2
Let r be 90/81*((-18)/10)/(-3). Solve 0 + r*b**2 - 2/3*b = 0.
0, 1
Let d(x) = 2*x**2 + 2*x + 2. Let t be d(-4). Let c = t + -77/3. Factor -1/3*i**3 + c - i + i**2.
-(i - 1)**3/3
Let j(y) = 2*y**2 + 8*y + 2. Let k(h) = -4*h**2 - 15*h - 4. Let f = -6 - -13. Let t(b) = f*j(b) + 4*k(b). Factor t(v).
-2*(v + 1)**2
Let o(w) be the first derivative of -w**5/40 - w**4/24 + w**3/6 + 3*w - 3. Let n(f) be the first derivative of o(f). Factor n(z).
-z*(z - 1)*(z + 2)/2
Let u(o) be the third derivative of -o**8/840 - o**7/525 + o**6/100 + o**5/150 - o**4/30 + 5*o**2. Solve u(s) = 0.
-2, -1, 0, 1
Suppose 2*d - 5*v + 11 = 0, -2*d - 3*v - 2*v = -19. Factor -4/9*r**4 + 4/9*r**d - 2/9*r**5 + 0*r**3 + 2/9*r + 0.
-2*r*(r - 1)*(r + 1)**3/9
Solve 4*u**2 + 9*u - 13*u**2 - 11*u**2 + 16 + 23*u = 0.
-2/5, 2
Let i be (-3)/7 - (-160)/14. Suppose 2*z - 5*z = 4*l - i, -3*l = -2*z + 13. Factor 2/11*a**4 - 2/11*a**2 + 2/11*a**3 - 2/11*a**z + 0 + 0*a.
-2*a**2*(a - 1)**2*(a + 1)/11
Let o(r) be the second derivative of -r**6/60 + 3*r**5/20 - 13*r**4/24 + r**3 - r**2 - 3*r. Factor o(y).
-(y - 2)**2*(y - 1)**2/2
Let u(k) = 2*k**2 + 20*k + 12. Let h be u(-11). Let w = 69/2 - h. Let 0*o**2 - 3/4*o**3 + 0 - w*o**4 + 1/4*o = 0. Calculate o.
-1, 0, 1/2
Let j be (-32)/54*9/(-6). Suppose 2/3*d**5 + j*d**2 - 8/9*d**4 + 0 - 4/9*d**3 - 2/9*d = 0. Calculate d.
-1, 0, 1/3, 1
Let h = -53 + 55. Determine w so that h*w + 2/3*w**2 + 4/3 = 0.
-2, -1
Let m(b) = -b**2 - b + 1. Let v(t) = t**3 + 8*t**2 + 9*t + 2. Let a(p) = -3*m(p) - v(p). Let i be a(-4). Solve -2*l**2 - 5 + 6 - i - 4*l = 0 for l.
-1
Suppose -2*g - 2*t + 37 = g, 2*g + t - 23 = 0. Let y = g + -9. Solve y + 0*z + 0*z**2 - 2/5*z**3 = 0.
0
Let i(u) be the first derivative of 5*u**8/1008 - u**7/42 + u**6/24 - u**5/36 - 3*u**2 - 8. Let r(j) be the second derivative of i(j). Factor r(b).
5*b**2*(b - 1)**3/3
Let a = 35/69 - 4/23. Find v, given that 2/3*v**2 + 1/3*v**5 - 1/3 - 2/3*v**3 + 1/3*v - a*v**4 = 0.
-1, 1
Suppose 0 = -0*n + n - 3*l + 8, -5*l + 32 = 3*n. Suppose n*f - 7 - 1 = 0. Find w, given that 2*w + f + w**3 - 2*w**2 - 3*w**3 + 0 = 0.
-1, 1
Let v(g) = 33*g - 1. Let n be v(1). Let k be (2/(-7))/(n/(-56)). Determine f, given that k*f**2 + 0 + 0*f = 0.
0
Let q be ((-24)/28)/(2/(-7)). Let p(w) be the second derivative of 1/35*w**5 + 1/35*w**6 - 1/21*w**4 + 1/147*w**7 + 0 - 1/7*w**2 + 2*w - 1/7*w**q. Factor p(z).
2*(z - 1)*(z + 1)**4/7
Suppose -4*o + 12 = 4. Suppose -49*l**4 + 52*l**o - 24*l**3 - 9*l**3 - 21*l**3 - 16*l**3 - 8*l = 0. Calculate l.
-2, 0, 2/7
Factor 9 - 48*x**3 - 6 + 0*x + 6 + 120*x**2 + 69*x.
-3*(x - 3)*(4*x + 1)**2
Let r = -47 + 143/3. Factor 0*s**2 + 0 + 4/3*s**5 - r*s**3 + 2/3*s**4 + 0*s.
2*s**3*(s + 1)*(2*s - 1)/3
Determine k so that 3*k**5 + 5*k**4 - 4*k**4 - k**5 - 2*k**3 - 5*k**4 + 4*k**2 = 0.
-1, 0, 1, 2
Factor 8*b**2 - 80*b**2 + 47*b - 28 + 16*b**3 + 45*b + 4*b**4 - 12*b.
4*(b - 1)**3*(b + 7)
Let d(o) be the third derivative of -o**6/480 - o**5/120 - o**4/96 + 2*o**2. Factor d(u).
-u*(u + 1)**2/4
Let d(x) be the third derivative of -x**5/210 - x**4/28 - 6*x**2. Factor d(h).
-2*h*(h + 3)/7
Let t(u) be the second derivative of u**7/14 + u**6/10 - 3*u**5/4 - u**4/4 + 4*u**3 - 6*u**2 - 3*u. Suppose t(y) = 0. Calculate y.
-2, 1
Factor -24/5*u**2 + 12/5 + 2*u**3 - 22/5*u.
2*(u - 3)*(u + 1)*(5*u - 2)/5
Let r = 36 - 44. Let g = r - -10. Suppose 8/5*c - 2/5 - 6/5*c**g = 0. What is c?
1/3, 1
Let c(a) be the second derivative of 11*a**4/30 + 13*a**3/15 + 2*a**2/5 - 7*a. Factor c(k).
2*(k + 1)*(11*k + 2)/5
Suppose 2 - 8 = -3*v. Let f = -433/5 + 87. Determine k so that f*k**4 + 2/5 - 4/5*k**v + 0*k + 0*k**3 = 0.
-1, 1
Let b(v) = 3*v**2 - 2*v - 3. Let s = 11 - 13. Let t be b(s). Let 2*m + 0*m**3 + 12*m**5 - 2*m**3 + 2*m**2 + 5*m**2 - 6*m**3 - t*m**4 = 0. Calculate m.
-2/3, -1/4, 0, 1
Let x(m) be the second derivative of m**8/13440 - m**7/1008 + 7*m**6/1440 - m**5/80 + 3*m**4/4 - m. Let t(u) be the third derivative of x(u). Factor t(h).
(h - 3)*(h - 1)**2/2
Let o(z) be the third derivative of -1/60*z**5 + 2/3*z**3 + 9*z**2 + 0 + 0*z + 0*z**4. Suppose o(l) = 0. Calculate l.
-2, 2
Suppose -4*g - g + 25 = 0. Suppose -3 = a + 3*y, -3*y - 2*y - g = 5*a. Factor 0*n**3 - 2/3*n**2 + a*n + 2/3*n**4 + 0.
2*n**2*(n - 1)*(n + 1)/3
Let v(y) be the third derivative of y**5/90 + y**4/6 + 8*y**3/9 - 24*y**2. Determine q so that v(q) = 0.
-4, -2
Determine n, given that 36*n - 3*n**2 - 48*n + 7*n**2 = 0.
0, 3
Let r(c) = -3*c**4 + 2*c**3 + c**2 + 4*c + 2. Let p(j) = j**4 - j**3 + j**2 - j - 1. Let w(q) = -2*p(q) - r(q). Factor w(d).
d*(d - 2)*(d + 1)**2
Let n(w) = -w**3 + 4*w - 3. Let k be n(2). Let p = k - -7. Factor 6*z - 4*z - z**p - 2*z**3 + 1 + 0*z**4.
-(z - 1)*(z + 1)**3
Determine a so that -6*a + a**3 + 10*a - 3*a**3 + 2*a**2 = 0.
-1, 0, 2
Let j = 1513/36 + -42. Let y(u) be the second derivative of j*u**4 + 0 + 1/18*u**3 + 0*u**2 + 4*u. Factor y(h).
h*(h + 1)/3
Let s(z) = z**5 - z**2 - z. Let w(v) = -6*v**5 + 5*v**4 + 7*v**3 + 10*v**2 + 7*v. Let u(c) = -28*s(c) - 4*w(c). Factor u(r).
-4*r**2*(r + 1)**2*(r + 3)
Let -2/7*p**4 + 0*p**3 - 1/7*p + 0 + 2/7*p**2 + 1/7*p**5 = 0. Calculate p.
-1, 0, 1
Let s be (-12 - -7) + (-51)/(-5) + -5. Let -3/5*n**3 + 3/5*n - 2/5 + 1/5*n**2 + s*n**4 = 0. What is n?
-1, 1, 2
Factor 8*k**2 + 0 - 2/3*k**4 - 2/3*k**5 + 16/3*k**3 + 0*k.
-2*k**2*(k - 3)*(k + 2)**2/3
Let t(q) be the second derivative of q**4/48 - q**3/8 + q**2/4 - 4*q. What is k in t(k) = 0?
1, 2
Factor 6*h**2 + 0 + 10/3*h**4 - 