**2 + 0 + 2/9*m.
-2*m*(4*m - 1)/9
Let h(m) = -m**3 - 10*m**2 - 9*m + 5. Let k be h(-9). Let 3*n**3 - k*n**5 - 5*n**3 + n + 6*n**5 = 0. Calculate n.
-1, 0, 1
Let i = 873561/140 - 6240. Let s = 1/140 - i. Let -s*b**2 - 2/7*b + 0 = 0. Calculate b.
-1, 0
Let a(w) be the third derivative of -3*w**2 + 1/60*w**6 + 0*w**4 + 0*w**3 + 0*w**5 + 0*w - 1/70*w**7 + 0 - 5/336*w**8. Factor a(d).
-d**3*(d + 1)*(5*d - 2)
Let a(u) be the second derivative of 2*u**7/105 + 14*u**6/75 + 18*u**5/25 + 22*u**4/15 + 26*u**3/15 + 6*u**2/5 - u - 18. Factor a(y).
4*(y + 1)**4*(y + 3)/5
Suppose -4/5*c**3 - 4/5*c**4 + 4/5*c + 0 + 4/5*c**2 = 0. What is c?
-1, 0, 1
Factor -5*z**4 - 90*z**2 - 100*z + 65*z**3 - 26 - 100*z**3 - 14.
-5*(z + 1)*(z + 2)**3
Let y(i) = -14*i**2 - 12*i - 14. Let m(h) = 9*h**2 + 8*h + 9. Let x(k) = -8*m(k) - 5*y(k). Factor x(g).
-2*(g + 1)**2
Factor -1/9*p + 1/9*p**3 - 2/9*p**2 + 2/9.
(p - 2)*(p - 1)*(p + 1)/9
Let f(t) = -14*t - 2. Let j be f(-1). Let a be (9/10)/(j/10). Find v such that -a*v**2 - 1/2 - 5/4*v = 0.
-1, -2/3
Let x be -1 + 4 + 10/5. Let o(z) be the third derivative of 1/6*z**4 + 7/30*z**x + z**2 + 0*z**3 + 0 + 0*z. Suppose o(u) = 0. Calculate u.
-2/7, 0
What is p in -2*p**4 + 480 - 480 = 0?
0
Suppose -4*p = -2*p - 4*p. Let v(m) be the first derivative of -4 + p*m**2 + 0*m - 2/5*m**5 + 2/3*m**3 + 0*m**4. Factor v(t).
-2*t**2*(t - 1)*(t + 1)
Factor -3*u + 66*u**3 - 64*u**3 - 4*u + 5*u.
2*u*(u - 1)*(u + 1)
Let z(n) be the first derivative of 125*n**6/33 + 70*n**5/11 - 5*n**4/11 - 92*n**3/33 + 13*n**2/11 - 2*n/11 + 6. Solve z(i) = 0 for i.
-1, 1/5
What is m in -8*m - 5*m**2 + 2*m - 3 - 17 - 19*m = 0?
-4, -1
Let f(b) = -9*b**2 + 27*b + 36. Let g(z) = 5*z**2 - 13*z - 18. Let l(t) = 3*f(t) + 5*g(t). Solve l(o) = 0 for o.
-1, 9
Let c(h) be the first derivative of 3*h**5/5 - 3*h**4/2 - 7*h**3 - 6*h**2 - 19. Factor c(n).
3*n*(n - 4)*(n + 1)**2
Let i(f) be the second derivative of 0*f**5 + 0*f**3 + 1/36*f**4 - 1/90*f**6 + 0*f**2 + 3*f + 0. Suppose i(h) = 0. What is h?
-1, 0, 1
Let h(f) be the first derivative of -4*f**5/5 + 5*f**4 - 32*f**3/3 + 8*f**2 + 21. Determine d, given that h(d) = 0.
0, 1, 2
Let d(g) be the first derivative of g**4/24 - 2*g**3/9 + g**2/3 - 3. Factor d(n).
n*(n - 2)**2/6
What is h in -1/2*h**4 + 0*h**3 + 0 + 0*h + 1/2*h**2 = 0?
-1, 0, 1
Let z(g) = -2*g - 1. Let q be z(-2). Suppose -3 = -2*k + q. Factor 3*v**2 + v - 5*v**2 + k*v - 2*v**3.
-2*v*(v - 1)*(v + 2)
Let t(n) be the first derivative of 4*n**5/35 + 4*n**4/7 + 8*n**3/7 + 8*n**2/7 + 4*n/7 - 11. Suppose t(r) = 0. Calculate r.
-1
Let k(q) be the second derivative of 0*q**2 + 1/105*q**6 + 5*q + 0*q**3 - 1/147*q**7 + 1/70*q**5 - 1/42*q**4 + 0. Factor k(w).
-2*w**2*(w - 1)**2*(w + 1)/7
Let o(w) be the second derivative of -w**7/1680 + w**6/240 - w**5/80 + w**4/48 - w**3/2 - 2*w. Let f(i) be the second derivative of o(i). What is n in f(n) = 0?
1
Let t(i) be the second derivative of -i**7/42 - i**6/6 - 9*i**5/20 - 7*i**4/12 - i**3/3 - i. Find h, given that t(h) = 0.
-2, -1, 0
Find v, given that -15/7*v + 3/7*v**2 + 3/7*v**3 + 9/7 = 0.
-3, 1
Suppose 0 = -0*c - 2*c. Suppose -2/7*y**2 - 4/7*y + c = 0. What is y?
-2, 0
Suppose 0*t = -3*t + 18. Let -t*i**3 + i**3 + i**4 + 0*i**3 + 2*i**2 + 2*i**3 = 0. Calculate i.
0, 1, 2
Suppose 0 = -5*d + 2*d + 12. Let q = 2/5 - -2/45. Factor 0 + 2/3*u**2 - q*u + 14/9*u**d + 8/3*u**3.
2*u*(u + 1)**2*(7*u - 2)/9
Let o = 72 + -214/3. Let f(l) be the first derivative of -o*l**3 - 2*l**2 - 2 - 2*l. What is y in f(y) = 0?
-1
Let k be 494/190 - (-7)/(-5). Determine q, given that k*q - 8/5*q**2 + 2/5 = 0.
-1/4, 1
Suppose -5 = 5*c + 5*f, -2*c = -3*f - 14 - 9. Suppose l**3 + 4*l**4 - l**c + l**4 - 5*l**4 + l**2 - l = 0. Calculate l.
-1, 0, 1
Let -x**2 + 2/3*x - 1/3*x**3 - 1/3*x**5 + x**4 + 0 = 0. What is x?
-1, 0, 1, 2
Suppose 5*p - 4*p = -3*p. Suppose -1/5*a**4 + p*a**2 + 2/5*a**3 - 2/5*a + 1/5 = 0. What is a?
-1, 1
Let n(d) = -11*d**5 + 17*d**4 - 9*d**3 - d**2 - 2*d + 2. Let y(x) = -x**5 + x**4 - x**3 - x**2 - x + 1. Let c(r) = 3*n(r) - 6*y(r). Factor c(l).
-3*l**2*(l - 1)*(3*l - 1)**2
Let b(w) be the first derivative of w**4/6 - 14*w**3/9 + 16*w**2/3 - 8*w - 26. Let b(c) = 0. Calculate c.
2, 3
Let s(o) be the third derivative of o**5/15 + o**4/4 - 2*o**3/3 - 20*o**2. Factor s(c).
2*(c + 2)*(2*c - 1)
Let l = 50 - 46. Let g(s) be the second derivative of 0*s**2 + 0 - 2/9*s**3 - 5/63*s**7 - 3*s - 17/45*s**6 - 11/18*s**l - 7/10*s**5. Factor g(p).
-2*p*(p + 1)**3*(5*p + 2)/3
Let w(l) be the first derivative of 2*l**3/3 + 8*l**2 + 32*l - 17. What is a in w(a) = 0?
-4
Let 0*b - 14*b**4 - 46*b**3 - 40*b**2 - 13*b - 14*b**2 - 4 - 13*b = 0. Calculate b.
-1, -2/7
Let o(m) be the second derivative of 0 + 4*m + 1/21*m**3 + 2/7*m**2 - 1/42*m**4. Factor o(n).
-2*(n - 2)*(n + 1)/7
Factor 24/5*l**2 - 8/5*l**4 - 2/5*l**5 - 18/5*l + 0 + 4/5*l**3.
-2*l*(l - 1)**2*(l + 3)**2/5
Let d(a) be the first derivative of a**8/5040 - a**7/1260 + a**5/180 - a**4/72 - 2*a**3/3 - 1. Let u(f) be the third derivative of d(f). Factor u(g).
(g - 1)**3*(g + 1)/3
Let t(f) be the first derivative of f**6/6 + 2*f**5/5 + f**4/4 + 6. Find x such that t(x) = 0.
-1, 0
Let c(k) be the third derivative of -k**6/120 - k**5/12 - k**4/3 - 2*k**3/3 - 5*k**2. Suppose c(f) = 0. What is f?
-2, -1
Factor 3/5*f**4 + 1/5*f**5 + 0*f**2 + 2/5*f**3 + 0 + 0*f.
f**3*(f + 1)*(f + 2)/5
Let x(i) be the third derivative of 0*i**7 + 1/112*i**8 + 0*i - 1/40*i**6 + 0*i**3 + 0 - 2*i**2 + 0*i**5 + 0*i**4. Factor x(t).
3*t**3*(t - 1)*(t + 1)
Let w(u) be the first derivative of u**2/2 - u - 2. Let s be w(3). Suppose 3*v - 3*v**s + 2*v**3 - v**2 - v = 0. What is v?
0, 1
Suppose 5*o + 2*g - 4 = 0, -4*o + 6*g - 2*g + 20 = 0. Let z = 163/220 + 1/110. Factor 0*p - 1/4*p**3 + 1 - z*p**o.
-(p - 1)*(p + 2)**2/4
Let n(k) be the third derivative of -k**7/945 - k**6/270 - k**5/270 - 11*k**2. Let n(v) = 0. What is v?
-1, 0
Factor -63*h**4 - 4*h**5 - 9*h**4 + 31*h**5 + 66*h**3 - 24*h**2 + 3*h + 0*h.
3*h*(h - 1)**2*(3*h - 1)**2
Let r(t) be the second derivative of -1/5*t**5 - 3*t + 1/3*t**4 + 2/3*t**3 + 0 + 0*t**2 - 2/15*t**6. Factor r(q).
-4*q*(q - 1)*(q + 1)**2
Let z(o) = -2*o**2 - 3*o + 2. Let j be z(0). Factor 1/3*c - 1/3*c**j - 1/3*c**3 + 1/3.
-(c - 1)*(c + 1)**2/3
Let j(w) be the third derivative of -5*w**8/1848 - 13*w**7/1155 - 3*w**6/220 + w**5/330 + w**4/66 + 22*w**2. Suppose j(p) = 0. Calculate p.
-1, 0, 2/5
Let i(b) = -60*b**4 - 86*b**3 - 38*b**2 - 4. Let r(w) = -179*w**4 - 258*w**3 - 113*w**2 - w - 11. Let f(l) = 11*i(l) - 4*r(l). Find d, given that f(d) = 0.
-1, -2/7, -1/4, 0
Let b(w) be the first derivative of 3*w**4/28 - 5*w**3/7 + 12*w**2/7 - 12*w/7 + 31. Factor b(z).
3*(z - 2)**2*(z - 1)/7
Let u = 20 + -15. Let r be 6*2/u + -2. Factor 0 - r*b**2 - 2/5*b.
-2*b*(b + 1)/5
Let g = -41 + 43. Let d(b) = 2*b**2 - 6*b + 6. Let l be d(g). Factor -4/5*z**l + 0 + 2/5*z**3 + 0*z.
2*z**2*(z - 2)/5
Let i be 0 - 0 - (-5 - -2). Factor 2*h**5 - 3*h**i + 0*h**3 - 3*h**5 + 4*h**3.
-h**3*(h - 1)*(h + 1)
Let i = -1 - -3. Solve -7*k**2 - 5*k**4 + 4*k**3 + i*k + k**5 + 6*k**3 - k**3 = 0 for k.
0, 1, 2
Suppose 0 = -5*l + 4*p - 38, 4*p = -2*l + p - 6. Let q = -2 - l. Let -4*j**q - 4*j**2 + 3*j**2 + 2*j**3 + 3*j**4 = 0. Calculate j.
0, 1
Let t(r) be the third derivative of 1/24*r**6 + 0*r + 2/15*r**5 - 1/6*r**4 - 5*r**2 + 0*r**3 + 0. Factor t(h).
h*(h + 2)*(5*h - 2)
Find l such that 10/3*l**2 + 2/3*l**3 + 2*l + 0 - 2/3*l**4 = 0.
-1, 0, 3
Let g(j) be the first derivative of -j**4/12 + j**3/3 - j**2/2 + j - 3. Let i(x) be the first derivative of g(x). What is b in i(b) = 0?
1
Let y(z) be the second derivative of -z**6/720 - z**5/240 - z**3/2 + 2*z. Let t(s) be the second derivative of y(s). Suppose t(x) = 0. What is x?
-1, 0
Let x(w) = w - 11. Let k be x(13). Factor 3*u + 6 - 4*u**k - 4*u**2 + 0*u**2 - 4*u**2 - 9*u**3.
-3*(u + 1)**2*(3*u - 2)
Let r(j) be the third derivative of 0*j**3 - 1/105*j**7 - 1/6*j**4 + 0*j + 1/30*j**6 + 1/30*j**5 + 0 + j**2. Determine l so that r(l) = 0.
-1, 0, 1, 2
Let x(i) be the first derivative of i**3/7 + 6*i**2/7 + 12*i/7 + 23. Factor x(d).
3*(d + 2)**2/7
Suppose 6 = 7*w - 5*w. Let l(o) be the second derivative of -1/3*o**w + 2*o**2 - 1/6*o**4 + 4*o + 0. Suppose l(c) = 0. Calculate c.
-2, 1
Let z(b) = -b**3 + 2*b**