/4*a**z - 1/2*a**m + 0*a**4 + 0.
a*(a - 1)**2*(a + 1)**2/4
Let y be -3*(5/3 - 2). Let w = 1 + y. Factor -3*d - d**3 + 2*d + 0*d**3 + w*d**2.
-d*(d - 1)**2
Let o(y) be the first derivative of 1/20*y**4 + 0*y**3 - 1/30*y**6 - 2 + 0*y + 0*y**5 + 0*y**2. What is z in o(z) = 0?
-1, 0, 1
Let q(l) = -1. Let i(s) = -s**2 + 2*s - 5. Let a(c) = -2*i(c) + 10*q(c). Factor a(g).
2*g*(g - 2)
Suppose -13*p + 8*p + 105 = 0. Let j be p/(-14)*(-4)/39. Factor 2/13*g**2 + j*g - 4/13.
2*(g - 1)*(g + 2)/13
Let s(c) be the second derivative of -9*c**7/14 + 3*c**6 - 111*c**5/20 + 5*c**4 - 2*c**3 - c. What is j in s(j) = 0?
0, 2/3, 1
Let y(c) = c + 1. Let w(j) = -j**3 - 2*j**2 - 2*j - 1. Suppose 4*o - 3*o = -6. Let v(l) = o*y(l) - 2*w(l). Factor v(x).
2*(x - 1)*(x + 1)*(x + 2)
Let g(j) be the second derivative of -1/3*j**4 + 0 + 2/5*j**5 - 2/15*j**6 + 0*j**2 + 7*j + 0*j**3. Factor g(f).
-4*f**2*(f - 1)**2
Let u be (2/15)/(336/60). Let t(k) be the second derivative of -1/6*k**3 + 1/10*k**5 + 0 + 0*k**4 + 3*k - u*k**7 + 0*k**6 + 0*k**2. Factor t(l).
-l*(l - 1)**2*(l + 1)**2
Determine l, given that 0*l**3 + 2/7*l**5 + 4/7*l**4 - 2/7*l - 4/7*l**2 + 0 = 0.
-1, 0, 1
Suppose 4*y - 4 + 4 = 0. Solve -2/3 + y*z**3 - 2/3*z**4 + 4/3*z**2 + 0*z = 0.
-1, 1
Let g(x) = 14*x**3 + 8*x**2 - 6*x. Suppose 3*a + 26 = -2*h + 3, 2*h = 4. Let f be (3/a)/((-2)/6). Let p(u) = u**2 + u. Let n(j) = f*g(j) + 2*p(j). Factor n(y).
2*y*(y + 1)*(7*y - 2)
Let g(j) = 15*j**3 + 6*j**2 - 12*j. Let h = -40 - -22. Let a(o) = -o**3 - o**2. Let f(c) = h*a(c) - g(c). Factor f(k).
3*k*(k + 2)**2
Let f(a) be the third derivative of 0*a**3 + 0*a - 1/96*a**4 - 1/240*a**5 - 8*a**2 + 0. Suppose f(u) = 0. What is u?
-1, 0
Let q(n) be the first derivative of -3 - 1/6*n**3 + 1/4*n**2 + n. Suppose q(t) = 0. Calculate t.
-1, 2
Let d(x) be the first derivative of x**6/6 - 3*x**4/16 - x**3/12 - 8. Determine n so that d(n) = 0.
-1/2, 0, 1
Let s = 499 + -3490/7. Determine a so that 9/7*a + s*a**2 + 6/7 = 0.
-2, -1
Let q(t) = -t**2 - 3*t + 2. Suppose 12 = -6*j + 2*j. Let f be q(j). Factor a + 4*a**2 + f*a - 1 + 0*a.
(a + 1)*(4*a - 1)
Let t(u) be the second derivative of u**4/3 + 8*u**3/3 + 6*u**2 - 12*u. Factor t(z).
4*(z + 1)*(z + 3)
Let v = 29 - 25. Determine r, given that -3*r**3 + v*r + 3*r**3 + 4*r**3 + 8*r**2 = 0.
-1, 0
Let i(j) be the third derivative of -j**8/80640 - j**5/60 + 5*j**2. Let q(x) be the third derivative of i(x). Factor q(b).
-b**2/4
Let p(j) be the second derivative of -j**8/672 + j**6/240 - 2*j**2 - 2*j. Let x(i) be the first derivative of p(i). Factor x(m).
-m**3*(m - 1)*(m + 1)/2
Let l(t) be the second derivative of 0 - t + 0*t**2 - 1/6*t**3 - 1/20*t**5 - 1/6*t**4. Find i such that l(i) = 0.
-1, 0
Let m be (-12)/16 + 3 - 2. Factor -m*a**2 - 1/4*a**3 + 1/4*a**4 + 1/4*a + 0.
a*(a - 1)**2*(a + 1)/4
Let d(o) = -o**4 - o**2 - o + 1. Let t(y) = -5*y**4 - 7*y**2 - 6*y + 6. Let k be 4 + (-2*2 - -1). Let i(u) = k*t(u) - 6*d(u). Factor i(q).
q**2*(q - 1)*(q + 1)
Let w(o) be the second derivative of o**4/54 - 2*o**3/27 + o**2/9 - o. Factor w(i).
2*(i - 1)**2/9
Let g be ((-8)/(-6) - (-32)/12) + 1. Solve 0 + 1/5*c**2 - 2/5*c**3 + 2/5*c**g - 1/5*c**4 + 0*c = 0 for c.
-1, 0, 1/2, 1
Factor -f**4 + 8*f**3 + 156*f**2 - 160*f**2 - f**4 - 2*f**4.
-4*f**2*(f - 1)**2
Let i = 19 + -15. Let n(g) = 2*g**3 + 6*g**2 - 2*g - 6. Let b(r) = 8*r**3 + 25*r**2 - 8*r - 25. Let x(l) = i*b(l) - 18*n(l). Let x(f) = 0. What is f?
-2, -1, 1
Suppose 4*b - 62 = 94. Let v = -36 + b. Factor -4/5*u**4 + 2/5*u + 0*u**v - 2/5*u**5 + 0 + 4/5*u**2.
-2*u*(u - 1)*(u + 1)**3/5
Let h(j) be the second derivative of j**4/12 + 12*j. Find l such that h(l) = 0.
0
Let u(j) be the second derivative of -j**6/10 + 3*j**5/20 + 3*j**4/4 - j**3/2 - 3*j**2 + 2*j. Find i, given that u(i) = 0.
-1, 1, 2
Let l be (-348)/(-5) + 12/30. Let s be 60/(-80) + l/72. Solve 0*z + 2/3*z**2 + 4/9*z**3 - s = 0.
-1, 1/2
Let k = -64 + 64. Let u(p) be the third derivative of -1/72*p**4 - 1/18*p**3 + 7/180*p**6 + 1/336*p**8 + k - p**2 + 0*p + 1/30*p**5 + 11/630*p**7. Factor u(s).
(s + 1)**4*(3*s - 1)/3
Let i = 12459823022/1795 - 6941408. Let o = -6/359 - i. Suppose 2/5*v**4 - o*v**3 + 26/5*v**2 + 8/5 - 24/5*v = 0. Calculate v.
1, 2
Let a(j) be the first derivative of 2/33*j**3 - 2 + 18/11*j - 6/11*j**2. Factor a(y).
2*(y - 3)**2/11
Let f(x) be the first derivative of x**4/26 - x**2/13 - 10. Let f(a) = 0. What is a?
-1, 0, 1
Factor -1/4 + 1/2*h**3 + 1/4*h**5 - 3/4*h + 3/4*h**4 - 1/2*h**2.
(h - 1)*(h + 1)**4/4
Solve -38*d**4 + 4 + 30*d**3 + 14*d**5 - 2*d**2 - 26*d + 22*d - 4 = 0.
-2/7, 0, 1
Let f(q) be the second derivative of -7*q**5/20 - 3*q**4/4 - 7*q**3/6 - q. Let v(n) = -3*n**3 - 4*n**2 - 3*n. Let a(z) = -6*f(z) + 15*v(z). Factor a(d).
-3*d*(d + 1)**2
Suppose 3*h = 8*h - 5. Let l be (-1)/h + 8/6. What is a in -2/3 - 1/3*a + l*a**2 = 0?
-1, 2
Let p be 6/(-36) + (-491)/(-30). Let f = 263/15 - p. Determine a, given that 2/3 - 2/3*a + 2/3*a**4 - f*a**2 + 4/3*a**3 - 2/3*a**5 = 0.
-1, 1
Suppose -6*m + m - 85 = 0. Let d = m + 17. Suppose -1/2*n**5 + n**3 + d + 0*n**4 + 0*n**2 - 1/2*n = 0. Calculate n.
-1, 0, 1
Let x(i) be the first derivative of -1/9*i**3 - 1/5*i**5 + 1/18*i**6 + 0*i**2 + 1 + 0*i + 1/4*i**4. Factor x(p).
p**2*(p - 1)**3/3
Let i(o) be the first derivative of o - 1 - 1/8*o**4 + 0*o**3 + 3/4*o**2. Factor i(u).
-(u - 2)*(u + 1)**2/2
Let u(x) = x**2 + x + 3. Let c(n) = n**2 + 2*n + 3. Let i(y) = -3*c(y) + 2*u(y). Determine q so that i(q) = 0.
-3, -1
Let s(c) be the third derivative of c**6/540 + c**5/135 - c**4/108 - 2*c**3/27 + 2*c**2. What is b in s(b) = 0?
-2, -1, 1
Let z(x) be the second derivative of -3*x + 2/15*x**6 + 0*x**5 - 1/3*x**4 + 0*x**2 + 1/21*x**7 - 1/3*x**3 + 0. What is p in z(p) = 0?
-1, 0, 1
What is q in -2/9*q**2 - 8/9*q - 8/9 = 0?
-2
Let j(h) = 1911*h**2 - 831*h + 96. Let p(z) = 239*z**2 - 104*z + 12. Let t be -1 + 0 + (-3)/1. Let v(r) = t*j(r) + 33*p(r). Factor v(q).
3*(9*q - 2)**2
Let r(d) = 4*d + 16. Let g be r(-7). Let i = g + 16. Factor i*s**2 + 26/3*s**3 + 8*s**4 + 8/3*s**5 + 0 + 2/3*s.
2*s*(s + 1)**2*(2*s + 1)**2/3
Let x(l) be the second derivative of l**5/5 - l**4/3 - 9*l. Factor x(o).
4*o**2*(o - 1)
Factor 0 + 2/5*x**2 - 2/5*x**3 + 12/5*x.
-2*x*(x - 3)*(x + 2)/5
Let l be (6/(-9))/(25 - 28). Solve -l*n**2 - 2/3*n + 8/9 = 0.
-4, 1
Suppose 8 = 5*p - 12. Factor 5*a**4 + a**3 - a**5 - a**3 - p*a**4.
-a**4*(a - 1)
Suppose 0 = c - 4*c - 2*i + 9, 2*c - 6 = 5*i. Factor -51*p**2 - 3*p**4 + 51*p**2 + 6*p**3 - 6*p + c.
-3*(p - 1)**3*(p + 1)
Let s be 100/15 - 4/6. Let c(h) be the second derivative of 0*h**3 + h**2 + 0*h**5 + 1/15*h**s + 0 - 1/3*h**4 + h. Factor c(t).
2*(t - 1)**2*(t + 1)**2
Let l(g) be the second derivative of -2/15*g**3 + 0 - 8*g - 1/30*g**4 + 0*g**2. Factor l(j).
-2*j*(j + 2)/5
Let i(n) = n - 2. Let g be i(6). Suppose m - 3*m + 8 = g*p, -3*m - p = -7. Factor 4*r - 2*r - 2 + m*r - 2*r**2.
-2*(r - 1)**2
Let q = 5785/6 + -964. Suppose 1/6*p**4 + 0 + 0*p**3 + 0*p - q*p**5 + 0*p**2 = 0. Calculate p.
0, 1
Let m(w) = -36*w**3 - 7*w**2 + 20*w + 16. Let g(f) = -12*f**3 - 2*f**2 + 7*f + 5. Let x(n) = -7*g(n) + 2*m(n). Factor x(u).
3*(u - 1)*(2*u + 1)**2
Suppose -5*j + 6 = -2*j. Determine r so that 2*r**3 + j*r**5 - 2*r**3 - 7*r + 5*r - 4*r**4 + 4*r**2 = 0.
-1, 0, 1
Let y(o) be the first derivative of o**8/42 + 4*o**7/35 + 13*o**6/60 + o**5/5 + o**4/12 - 7*o**2/2 + 4. Let d(t) be the second derivative of y(t). Factor d(f).
2*f*(f + 1)**2*(2*f + 1)**2
Let c be (6/20)/((-27)/(-15)). Let y(i) be the first derivative of 7/5*i**5 + 8*i**2 + c*i**6 + 19/4*i**4 + 4*i - 2 + 25/3*i**3. Find h, given that y(h) = 0.
-2, -1
Let n = -110 - -113. Factor -2/5*b**n + 2/5*b**2 + 0*b + 0.
-2*b**2*(b - 1)/5
Suppose -n = -4*n. Let w = 5 - 3. Factor n*f - 2*f**2 + 8*f**3 + 0*f**3 - 4*f - w*f**3.
2*f*(f - 1)*(3*f + 2)
Factor 10*s**3 + 15*s - 115*s**2 + 90*s**2 - 5*s**3 + 45.
5*(s - 3)**2*(s + 1)
Let a be -1 - (4/(-30) + 58/(-15)). Let -4*m + a*m**3 + 11/3*m**4 - 7/3*m**2 + m**5 - 4/3 = 0. Calculate m.
-2, -1, -2/3, 1
Suppose 0 = -4*v - 49 + 9. Let m be 0 + (v/4)/(-5). Suppose -m*y**2 + 0 + 1/4*y**3 + 1/4*y = 0. What is y?
0, 1
Let g = 12 + -24. Let m be 16/(-9) + g/(-6). Factor 0*y + m - 2/9*y**2.
-2*(y - 1)*(y + 1)/9
Suppose 0 = -5*x - 5*h + 2*h + 25, 4*x - 3*h - 47 = 