0. Calculate l.
-4, 0, 1, 2
Factor -30/11*k - 2/11*k**2 - 28/11.
-2*(k + 1)*(k + 14)/11
Determine w so that -625/2 - 25*w - 1/2*w**2 = 0.
-25
Let n(w) be the first derivative of w**4/6 + 32*w**3/9 + 80*w**2/3 + 256*w/3 + 47. Determine d, given that n(d) = 0.
-8, -4
Let a(g) be the second derivative of g**4 + 9*g**3/2 + 3*g**2 - 28*g. Let a(s) = 0. Calculate s.
-2, -1/4
Let y = -561 - -36461/65. Let o = y - -6/13. Let -o + 0*n**2 + 4/5*n + 2/5*n**4 - 4/5*n**3 = 0. Calculate n.
-1, 1
Let l(b) be the first derivative of -b**7/2240 - b**6/960 + 2*b**3/3 - 7. Let u(d) be the third derivative of l(d). Suppose u(i) = 0. What is i?
-1, 0
Let d(k) be the third derivative of -k**8/84 - 2*k**7/35 + k**6/15 + 2*k**5/5 - k**4/6 - 2*k**3 - 197*k**2 - 1. Suppose d(i) = 0. What is i?
-3, -1, 1
Let m be (0 - 1)/((-98)/35 - -3). Let z(t) = 13*t + 65. Let g be z(m). Factor 3/2*q**3 - q**4 + q**2 + 0 + g*q.
-q**2*(q - 2)*(2*q + 1)/2
Let z = 0 + 5. Suppose p = -0*p + z*m, 0 = -4*p + 4*m. Factor 8/5*b**2 - 4/5*b + p.
4*b*(2*b - 1)/5
Let n(m) = 25*m - 1597. Let f be n(64). Let y = 0 - 0. Factor 0*u + 1/2*u**4 + y + 1/2*u**2 + u**f.
u**2*(u + 1)**2/2
Let l(v) be the third derivative of -v**7/490 + v**6/420 + v**5/420 - 98*v**2. Factor l(i).
-i**2*(i - 1)*(3*i + 1)/7
Let r(i) = -i**2 + 2*i - 4. Let m(w) = 16 - 2 - 2 - 6*w + 2*w**2. Let t = 4 + -7. Let n(y) = t*m(y) - 8*r(y). Factor n(d).
2*(d - 1)*(d + 2)
Let f(u) = 7*u + 4*u**2 + u**3 - 4*u + 32 - 36. Let p(h) = 2*h**3 + 9*h**2 + 7*h - 9. Let o(l) = -9*f(l) + 4*p(l). Factor o(y).
-y*(y - 1)*(y + 1)
Let t(i) be the second derivative of i**4/42 + 3*i**3/7 + 8*i**2/7 + 171*i. Determine f so that t(f) = 0.
-8, -1
Let k(u) = -u**3 + 6*u - 1. Let w be k(5). Let b = w - -99. Find n, given that 1/5*n**b + n - 2/5 - 4/5*n**2 = 0.
1, 2
Find f such that 0 + 33/5*f - 1/5*f**2 = 0.
0, 33
Let d(l) be the third derivative of 0 + 0*l + 4/15*l**4 + l**2 - 2/5*l**3 + 1/25*l**5. Factor d(p).
4*(p + 3)*(3*p - 1)/5
Let q(u) be the third derivative of -u**5/120 - u**4/8 - 5*u**3/12 + 2*u**2 - 34. Factor q(y).
-(y + 1)*(y + 5)/2
Let i(a) = -a**3 + 2*a**2 - 2*a + 52. Let n be i(0). Let o be n/10 - 2*4/2. Suppose 4/5*u + 4/5*u**2 - o*u**4 - 11/5*u**3 + 0 + 9/5*u**5 = 0. Calculate u.
-2/3, 0, 1
Let p(v) = -v**5 - v**4 - v**3 + v**2 + v. Let l(b) = -3*b**5 - 3*b**4 + 27*b**3 + 3*b**2 - 42*b + 20. Let w(r) = -l(r) - 2*p(r). Let w(d) = 0. What is d?
-2, 1
Let k(p) be the third derivative of -3/50*p**5 + 1/525*p**7 + 6*p**2 + 0*p**3 + 0 - 1/12*p**4 + 0*p - 1/100*p**6. Let k(s) = 0. Calculate s.
-1, 0, 5
Suppose -4*j + 21 = 3*o, 3*o - 4*j + 0*j = 21. Suppose -1 = o*k - 1. Factor 2/5*s + k + 4/5*s**2 + 2/5*s**3.
2*s*(s + 1)**2/5
Let i be 2/(2/2) + 22 + 16. Let 45*k - 7*k**2 - i*k + 25 - 23*k**2 = 0. Calculate k.
-5/6, 1
Let p(r) = r**3 - 3*r**2 + 4*r - 2. Let b = 2 + 0. Let k be p(b). Factor 2*t**k - 127 + 127.
2*t**2
Let m = -18 - -20. Let s = 8 - 8. Suppose s + 0 - 4*d - 2*d - m*d**2 - 4 = 0. What is d?
-2, -1
Let -4/13 - 2/13*t + 2/13*t**3 + 4/13*t**2 = 0. What is t?
-2, -1, 1
Factor 99 + 1191/4*o + 9/4*o**2.
3*(o + 132)*(3*o + 1)/4
Let i(w) be the third derivative of 0*w - 1/6*w**3 - 1/120*w**6 - 1/20*w**5 - 1/8*w**4 - 19*w**2 + 0. Find c, given that i(c) = 0.
-1
Let f(j) be the first derivative of 0*j**2 + 2/15*j**3 - 2/25*j**5 - 11 + 0*j + 0*j**4. Let f(b) = 0. What is b?
-1, 0, 1
Let k = 8613 - 25838/3. What is h in -1/3*h + k*h**3 + 1/3*h**2 - 1/3 = 0?
-1, 1
Suppose 3 = 4*w + 59. Let x = 16 + w. Factor -3*u**2 - 3 - 4*u - 7*u - 3 + x*u.
-3*(u + 1)*(u + 2)
Let c(p) be the second derivative of 3*p**6/20 - 3*p**5/10 - 9*p**4/4 + p**3 + 45*p**2/4 + p + 17. Find j, given that c(j) = 0.
-5/3, -1, 1, 3
Let u be (2 - (-4)/(16/(-12))) + 8. Suppose -10*k = -u*k. Suppose 6/7*p + 3/7*p**2 + k - 9/7*p**3 = 0. What is p?
-2/3, 0, 1
Suppose y - 20 = -6. Suppose 0*d + 3*d - 5*g = -y, g - 4 = 0. Let 3*t**d + 2 + t**2 - t**2 - 5 = 0. Calculate t.
-1, 1
Let m be -1 - 8/(-20) - (-36)/10. Factor 2*d**4 + 24*d**m + 60*d**2 + 15 - 5 + 56*d + 3 + 5.
2*(d + 1)**3*(d + 9)
Let q = -40 + 18. Let m = q - -41. Factor -16 + 3*g - m*g + 8*g**2 + 4*g**2.
4*(g - 2)*(3*g + 2)
Factor -1/2*v**2 - 3/2 + 2*v.
-(v - 3)*(v - 1)/2
Let t(u) be the first derivative of -u**3/18 + u**2 - 6*u - 396. Find x such that t(x) = 0.
6
Let l(a) be the third derivative of 1/150*a**5 + 0*a - 1/60*a**4 + 3 - 6*a**2 - 2/15*a**3. Determine p so that l(p) = 0.
-1, 2
Let t(c) = 6*c**3 - 4*c**2 + 2*c + 2. Let z(w) = 5*w**3 - 5*w**2 + 3*w + 3. Suppose 18*d - 22*d + 12 = 0. Let p(f) = d*t(f) - 2*z(f). Factor p(m).
2*m**2*(4*m - 1)
Suppose i + 8 - 10 = 0. Factor -10*t**3 + 4*t + 14*t - 66*t**i + 10*t.
-2*t*(t + 7)*(5*t - 2)
Let y(s) be the first derivative of -s**8/1344 - s**7/840 + 8*s**2 - 5. Let x(j) be the second derivative of y(j). Let x(g) = 0. Calculate g.
-1, 0
Let d = 445 + -438. Let u(q) be the first derivative of 2/3*q**3 + 0*q + d + 1/3*q**6 - 1/2*q**4 - 2/5*q**5 + 0*q**2. Factor u(b).
2*b**2*(b - 1)**2*(b + 1)
Let l(m) be the first derivative of m**4/14 + 156*m**3/7 + 18252*m**2/7 + 949104*m/7 - 75. Suppose l(p) = 0. Calculate p.
-78
Let m be -21 + 22 + 4/2 + 0. Factor v**2 + 7/2*v**m - 14*v - 4.
(v - 2)*(v + 2)*(7*v + 2)/2
Let g(r) be the first derivative of r**5/30 + r**4/6 - r**2/2 + 18. Let m(o) be the second derivative of g(o). Let m(h) = 0. What is h?
-2, 0
Let j(p) = 7*p**4 + 3*p**3 - 8*p**2 + 6*p - 8. Let t(x) = -20*x**4 - 8*x**3 + 23*x**2 - 19*x + 24. Let a(c) = -17*j(c) - 6*t(c). Factor a(v).
(v - 2)**2*(v - 1)*(v + 2)
Let p(k) be the third derivative of k**9/272160 - 11*k**5/60 - 8*k**2. Let o(u) be the third derivative of p(u). Find a such that o(a) = 0.
0
Factor 8/9*i**3 + 0 + 2*i**2 - 26/9*i.
2*i*(i - 1)*(4*i + 13)/9
Let j = -9998/63 + 1436/9. Factor -j*f + 3/7*f**2 + 3/7.
3*(f - 1)**2/7
Let d(a) be the second derivative of -a**4/60 + 8*a**3/15 + 3*a + 70. Factor d(r).
-r*(r - 16)/5
Let x(d) be the third derivative of 5*d**8/336 - 9*d**7/70 + 5*d**6/12 - 3*d**5/5 + d**4/3 + 132*d**2. Solve x(i) = 0 for i.
0, 2/5, 1, 2
Solve 2/3*v**2 - 32/3*v**3 - 2/3 + 32/3*v = 0 for v.
-1, 1/16, 1
Let d(q) be the first derivative of -q**4 - 68*q**3 - 1350*q**2 - 2500*q - 231. Factor d(i).
-4*(i + 1)*(i + 25)**2
Suppose -2/11*u**3 + 170/11*u**2 - 336*u + 3528/11 = 0. Calculate u.
1, 42
Let q(a) be the first derivative of -a**5/20 + a**4/4 - a**3/4 - a**2/2 + a + 40. Solve q(s) = 0.
-1, 1, 2
Let o(a) be the second derivative of a**6/10 - a**5/10 - a**4/4 + a**3/3 - 604*a. Let o(g) = 0. What is g?
-1, 0, 2/3, 1
Let d(n) be the second derivative of n**6/30 + n**5/4 + 7*n**4/12 + n**3/2 + 3*n - 18. Suppose d(u) = 0. Calculate u.
-3, -1, 0
Let f be -4 + 7 - 2 - -13. Factor -3*u**4 + f*u**3 - u**3 + 9*u**2 - 19*u**3.
-3*u**2*(u - 1)*(u + 3)
Let h = 306/7 + -290/7. Let y be 46764/2142 - 16 - (-8)/(-68). Determine n so that 0 + y*n**2 + h*n - 52/7*n**3 + 2*n**4 = 0.
-2/7, 0, 2
Let r(c) = 170*c**3 + 190*c**2 + 20*c - 11. Let y(d) = 34*d**3 + 38*d**2 + 4*d - 2. Suppose -8*t + 12 = -5*t. Let n(p) = t*r(p) - 22*y(p). Factor n(o).
-4*o*(o + 1)*(17*o + 2)
Let o be 1 + 7/(-4) + 36/48. Solve o*f**2 + 14*f**3 - 4*f - 13*f**3 + f**2 - 4 = 0.
-2, -1, 2
Let v = -35 + 37. Find a such that -3*a**4 + 11*a**v - 12*a**4 + 35*a**3 + 0*a**4 - 21*a**2 = 0.
0, 1/3, 2
Let p(q) = q + 3. Let z be p(9). Suppose 4*i - z = 24. Factor 0 - 2*t**4 - 12*t + 4*t**4 - 5*t**4 + 12*t**3 + 12 - i*t**2.
-3*(t - 2)**2*(t - 1)*(t + 1)
Let j(k) be the third derivative of -5/24*k**4 + 0*k**3 + 0 - 1/24*k**5 - 47*k**2 - k + 1/8*k**6. Determine p, given that j(p) = 0.
-1/2, 0, 2/3
Let y(v) be the third derivative of v**10/226800 - v**9/45360 + v**8/30240 + 13*v**5/60 - 15*v**2. Let k(a) be the third derivative of y(a). Factor k(h).
2*h**2*(h - 1)**2/3
Suppose 0 = -5*g - s + 23, 0 = g - 4*g - 3*s + 9. Let u be 2*9/(9/4). Factor -g - 12*a - a**2 + 14*a - u*a.
-(a + 1)*(a + 5)
Let y(m) be the second derivative of m**9/37800 + m**8/5600 + m**7/3150 + 7*m**4/12 - 13*m. Let z(i) be the third derivative of y(i). Let z(n) = 0. Calculate n.
-2, -1, 0
Let c = -2127/8 - -266. Let l(h) be the second derivative of 1/56*h**7 - 5*h - 1/4*h**2 - 7/24*h**3 - c*h**4 + 1/20*h**5 + 1/15*h**6 + 0. What is p in l(p) = 0?
-1, -2/3, 1
Let b(o) be the first derivat