= 0?
-1, 1
Let k(n) be the first derivative of -n**3/2 + 303*n**2/2 - 30603*n/2 + 402. Suppose k(x) = 0. What is x?
101
Let y(n) be the third derivative of -n**7/525 + 7*n**5/150 - n**4/10 - 2*n**2 - 137. Factor y(i).
-2*i*(i - 2)*(i - 1)*(i + 3)/5
Suppose -3*j + 30 = 3*j. Suppose -3*m + 4 = j*n - 1, 4*m - 12 = -4*n. Factor 0 + 0*i**4 + 0*i**2 - 4/3*i**3 + 2/3*i**m + 2/3*i.
2*i*(i - 1)**2*(i + 1)**2/3
Suppose -2*d = 4*u - 16, 0*u + u - 4*d + 5 = 0. Let o(c) = -c**3 - 18*c**2 + 21*c + 42. Let i be o(-19). Factor 0 + 10*l**i - 32/5*l**2 + 8/5*l + 2*l**u.
2*l*(l + 1)*(5*l - 2)**2/5
Factor -168*c + 28 + 212 + 23*c**3 - 30*c**3 + 4*c**3 - 14*c**2 + 53*c**2.
-3*(c - 5)*(c - 4)**2
Let k(i) be the third derivative of 0 + 0*i + 0*i**3 + 1/4*i**6 + 5/24*i**4 + 1/3*i**5 - 11*i**2 + 5/336*i**8 + 2/21*i**7. Factor k(n).
5*n*(n + 1)**4
Suppose -21 = -4*w + f, -2*f = -5*w - 5*f + 22. Let l(t) be the second derivative of 10/3*t**3 - 4*t**2 + 1/5*t**w - 4/3*t**4 + 0 + t. Factor l(r).
4*(r - 2)*(r - 1)**2
Let h be (-2)/(-10) - 154/(-55). Let a(o) be the third derivative of 0*o + 1/12*o**h - 1/16*o**4 - 9*o**2 - 1/30*o**5 + 0. Determine x, given that a(x) = 0.
-1, 1/4
Let h(d) be the second derivative of -d**4/3 - 41*d**3/6 + 33*d**2/2 + 57*d. Factor h(y).
-(y + 11)*(4*y - 3)
Let x(m) be the second derivative of 0*m**2 - 1/30*m**4 + 0 + 30*m + 0*m**3 + 1/50*m**5. Find y such that x(y) = 0.
0, 1
Factor 23*y - 15*y + 7*y**3 + y**3 - 10*y**3.
-2*y*(y - 2)*(y + 2)
Let a(c) be the second derivative of -c**6/105 - c**5/7 + 5*c - 6. Determine h, given that a(h) = 0.
-10, 0
Let a(p) = p**2 + 3*p + 2. Let n be a(-2). Suppose 10 + n = 2*b. Factor -2*g**3 - g + 6*g + 2*g**2 - b*g.
-2*g**2*(g - 1)
Let y = 32 + -32. Suppose -9*a + 4*a + 10 = y. Determine s so that 17 - 7*s - 5*s**3 - 25*s**a - 11*s + 3*s + 28 = 0.
-3, 1
Suppose 19*h + 40 = 14*h. Let i(a) = -a**2 + 17*a - 13. Let x(k) = -4*k**2 + 52*k - 40. Let g(q) = h*i(q) + 3*x(q). Find l such that g(l) = 0.
1, 4
Factor -31/5*g + 2/5*g**2 + 42/5.
(g - 14)*(2*g - 3)/5
Let l(o) = -o**4 + o**3 - o - 1. Suppose n + 2 - 20 = 0. Let c(d) = -21*d**4 + 24*d**3 + 9*d**2 - 18*d - 18. Let k(g) = n*l(g) - c(g). Factor k(z).
3*z**2*(z - 3)*(z + 1)
Let v be -4 - -5 - 1/1. Suppose -158 = i - 80*i. Factor v + 2/7*h**3 + 2/7*h**i + 0*h.
2*h**2*(h + 1)/7
Let k = -34 + 36. Let o(x) be the first derivative of 4/5*x**5 + 2*x**3 + x**2 - 5/2*x**4 - k*x + 4. Solve o(j) = 0 for j.
-1/2, 1
Let p(c) be the first derivative of -c**4 - 56*c**3 - 1176*c**2 - 10976*c + 33. Determine z so that p(z) = 0.
-14
Let c(r) = r**2 - 6*r - 11. Let u be c(-2). Suppose -u*z - 8 = -9*z. Factor -3/5*s**3 - 27/5 - 9/5*s + 3*s**z.
-3*(s - 3)**2*(s + 1)/5
Let i = -167163 + 1502840/9. Let n = i + 181. Factor -n*o**3 + 10/9*o - 2/3 - 2/9*o**2.
-2*(o - 1)**2*(o + 3)/9
Let u be 28/(-4060)*-29 - (-103)/10. Factor u*w**3 + 12*w**2 + 27/4*w + 9/2*w**4 + 3/4*w**5 + 3/2.
3*(w + 1)**4*(w + 2)/4
Suppose 4*z = -0 + 84. Let m(s) = -s**2 - 8*s - 7. Let j(h) = h + 1. Let t(k) = z*j(k) + 3*m(k). Determine c so that t(c) = 0.
-1, 0
Let w(v) be the second derivative of -v**6/75 - 11*v**5/25 - 157*v**4/30 - 132*v**3/5 - 324*v**2/5 + 85*v. Determine g, given that w(g) = 0.
-9, -2
Suppose 3*c - 15 = -5*f, 4*c - 6 = 2*f - 12. Let h(t) be the first derivative of -1/5*t**2 + 8 + 1/10*t**4 + 2/15*t**f - 2/5*t. Factor h(g).
2*(g - 1)*(g + 1)**2/5
Let b(z) = -z**3 + 15*z**2 - z + 19. Let l be b(15). What is k in 7*k**l - 372 + 160*k + 452 + 40*k**3 + 120*k**2 - 2*k**4 = 0?
-2
Let b(c) be the first derivative of 1/4*c**2 - 1/30*c**5 + 0*c + 1/18*c**3 + 20 - 1/8*c**4. Suppose b(p) = 0. Calculate p.
-3, -1, 0, 1
Suppose -3*y + 12 = 2*y - 4*o, -3*y + 3*o + 9 = 0. Suppose s + 1 = 4, -2*p + s + 5 = y. Find t such that 2/11*t + 4/11*t**2 + 8/11*t**p - 14/11*t**3 + 0 = 0.
-1/4, 0, 1
Let h(t) = -5*t**4 + 3*t**3 - 3*t**2 + 5*t + 5. Let g(y) = 5*y**4 - 3*y**3 + 4*y**2 - 6*y - 6. Let r(q) = 5*g(q) + 6*h(q). Factor r(p).
-p**2*(p - 1)*(5*p + 2)
Let c = -718/3 + 240. Let a(w) be the first derivative of -c*w**3 + 6 + 0*w**2 + 0*w. Solve a(i) = 0.
0
Solve -3399 - 184*s + 3*s**2 - 3639 - 7*s**2 - 256*s - 5062 = 0 for s.
-55
Let w be 3 - (-12)/(-4 - -7). Find o such that -33*o**3 - w*o**2 - 9*o**2 + 37*o**3 + 12*o = 0.
0, 1, 3
Suppose 3*f = v - 12, -5*v + 35 = -4*f - 25. Suppose -v*o = 3*o. Solve -1/4*i + o + 1/4*i**2 = 0.
0, 1
Let v(t) = 28*t**4 - 2016*t**3 + 48364*t**2 - 387052*t. Let m(h) = 4*h**4 - 288*h**3 + 6909*h**2 - 55293*h. Let j(x) = 20*m(x) - 3*v(x). Factor j(q).
-4*q*(q - 24)**3
Let u(z) be the third derivative of 0*z + 7/4*z**4 - 1/20*z**5 - 49/2*z**3 + 0 - 4*z**2. Factor u(w).
-3*(w - 7)**2
Let v(r) be the first derivative of 0*r - 5/8*r**4 + 0*r**3 + 0*r**2 + 1. Find u, given that v(u) = 0.
0
Suppose -4*i = a - 1 - 8, 3*a - i + 12 = 0. Let b(h) = -h**2 - 2*h + 5. Let v be b(a). Solve -13*g**2 + 9*g**3 + 13*g**2 - 12*g**4 + 27*g**v + 6*g = 0 for g.
-1, -1/4, 0, 2
Suppose 32 = -176*t + 172*t. Let c(z) = 17*z**2 + 11*z. Let f(p) = -26*p**2 - 17*p. Let j(v) = t*c(v) - 5*f(v). Determine d so that j(d) = 0.
-1/2, 0
Suppose 4*d - 5*r - 4765 = -1084, 3*r - 2754 = -3*d. Factor 5*l + 14*l**3 + 916*l**4 - d*l**4 - 19*l**2 - l + 4.
-(l - 2)**2*(l - 1)*(3*l + 1)
Let d(q) = 7*q**3 - 4*q**2 + 5*q + 2. Let v(f) = -f**3 - f**2 - f + 1. Let s(u) = -d(u) - 6*v(u). Let g be s(10). Factor -g*h + h - 2*h**3 + 0*h**3 + 3*h**3.
h*(h - 1)*(h + 1)
Let m = -275/3 + -1. Let g = 95 + m. Factor 4/3*r**4 + 0 - 1/3*r + g*r**3 + 2/3*r**2.
r*(r + 1)**2*(4*r - 1)/3
Let a(l) be the first derivative of 5/4*l**3 - 3/2*l - 9/8*l**2 - 6. Factor a(h).
3*(h - 1)*(5*h + 2)/4
Determine s so that 32/5 - 4/5*s**2 - 8/5*s = 0.
-4, 2
Let r(b) = -2*b**2 + 8*b + 17. Let x(n) = 2*n**2 - 8*n - 18. Let p(c) = -6*r(c) - 7*x(c). Factor p(k).
-2*(k - 6)*(k + 2)
Let x = 5 - 1. Let v be (1/3)/(x/36). Factor 11 - 3*y**2 - 11 + v*y + 0*y.
-3*y*(y - 1)
Suppose 11 = 3*h + 53. Let d = h - -16. Factor -11 + 11 - 3*s**d + 3*s.
-3*s*(s - 1)
Let b(c) be the third derivative of c**6/300 - c**5/25 + 3*c**4/20 - 114*c**2. Let b(j) = 0. Calculate j.
0, 3
Find y such that 1864 - 179*y - 1998 - 3*y**2 + 135*y - 289*y + 8*y**2 = 0.
-2/5, 67
Let u be (-1 - 25/(-24)) + 0. Let z(x) be the second derivative of -u*x**4 + 0 + 0*x**3 - 1/16*x**5 + 5*x + 0*x**2. Solve z(g) = 0 for g.
-2/5, 0
Suppose -1 = -2*j + 2*i - 17, -2*j = -4*i + 24. Let o = 0 - j. Let 12*a**2 + o*a - a**4 - 3*a**4 - 8 - 6*a**3 + 2*a**3 = 0. What is a?
-2, -1, 1
Factor -36 - 3/5*k**2 - 69/5*k.
-3*(k + 3)*(k + 20)/5
Let o = 2/103 - -1582/3399. Let j(u) be the third derivative of 0*u + 5*u**2 - 1/330*u**5 + 0 - 2/33*u**4 - o*u**3. Factor j(i).
-2*(i + 4)**2/11
Solve -37/4*t**2 - 9 + 15*t + 5/2*t**3 - 1/4*t**4 = 0 for t.
2, 3
Let g(w) = w**2 + 12*w - 25. Let l be g(-14). Factor 1/3*n**4 - 1/3*n**2 + 0 + 0*n + 0*n**l.
n**2*(n - 1)*(n + 1)/3
Let a(u) be the first derivative of u**5/70 - u**4/42 - 2*u**3/21 + 22*u - 20. Let v(s) be the first derivative of a(s). Factor v(p).
2*p*(p - 2)*(p + 1)/7
Let k(c) be the first derivative of 5*c**6/6 + c**5 - 15*c**4/2 + 10*c**3/3 + 25*c**2/2 - 15*c + 177. Suppose k(g) = 0. What is g?
-3, -1, 1
Let q(g) be the second derivative of g**4/3 + 14*g**3 - 92*g**2 + 344*g. Suppose q(y) = 0. Calculate y.
-23, 2
Let p(t) = t**2 - 29*t - 294. Let y be p(-8). Factor -2/5 + 2/15*l**y + 4/15*l.
2*(l - 1)*(l + 3)/15
Factor -675 - 1/3*h**2 + 30*h.
-(h - 45)**2/3
Let p be (474/39 - 16/104) + -10. Solve -22/9*l + 10/9*l**p + 4/9 = 0.
1/5, 2
Factor 18*l**3 - 13*l**3 - 24*l**2 - 13*l**3 + 2*l**4 + 0*l**4.
2*l**2*(l - 6)*(l + 2)
Let p = 13 + -13. Suppose -k = -p*k. Factor 3 + 3 - 6*i**2 + 17*i**3 + 4*i**3 - 21*i + k.
3*(i - 1)*(i + 1)*(7*i - 2)
Suppose -5*b + 26 - 6 = 0. Suppose 2*m - 5*w - 33 = 0, -b*m - 5*w - 12 = -3. Factor -64*h**3 + 26*h**m + 2*h**4 + 44*h**2 + 7*h - 15*h.
4*h*(h - 1)**2*(7*h - 2)
Factor -3*f**3 + 8*f**2 - 6*f**2 - f**2 - 31*f**2.
-3*f**2*(f + 10)
Suppose 0 = 2*j - 2 + 6. Let p be (2 - 1 - 107)/j. Solve -p*c**2 + c + 38*c**2 + 2*c = 0.
0, 1/5
Let g(o) be the second derivative of -o**6/25 + 33*o**5/100 - 3*o**4/20 - 11*o**3/10 + 3*o**2/2 - 2*o + 21. Find p such that g(p) = 0.
-1, 1/2, 1, 5
Let i(x) = x**2 + 5*x + 6. Let u be i(-4). Let d be -31 - (0 + (-6174)/198). S