tor d(w).
-2*(w - 1)*(w + 9)
Let v(x) be the first derivative of -1/2*x**2 + 2*x - 5 + 1/24*x**4 + 1/12*x**3. Let o(b) be the first derivative of v(b). Factor o(p).
(p - 1)*(p + 2)/2
Let p(f) be the second derivative of -f**6/120 + f**5/10 - 3*f**4/8 + 2*f**3/3 + 31*f**2/2 - 14*f. Let z(t) be the first derivative of p(t). Factor z(y).
-(y - 4)*(y - 1)**2
Let j be (-25)/20 - 1/(-4). Let l be j/((-15)/54) + (-4)/(-10). Let 11*h**2 + l*h + 12*h**3 + 1/2 + 9/2*h**4 = 0. What is h?
-1, -1/3
Let t = -25208 + 25211. Find o, given that 1/3*o**2 + 0 - 2/3*o + 1/3*o**t = 0.
-2, 0, 1
Factor -21/2*i + 3/2*i**2 + 15.
3*(i - 5)*(i - 2)/2
Suppose 12 - 4 = 2*d. Suppose y - d*y = -6. Factor 6*o**3 - 8*o**y - o + 0*o**2 - 3*o - 2*o**3 + 8.
4*(o - 2)*(o - 1)*(o + 1)
Suppose -5*v = -p + 5, 2*v + 6 = -2*p + 4. Suppose 5*i - i - 18 = -5*k, k - 8 = -3*i. Let p*q + 0 + 1/5*q**k = 0. What is q?
0
Let -188/9*n**3 + 64/9*n**5 - 224/9*n**2 - 8/9 + 32/9*n**4 - 76/9*n = 0. What is n?
-1, -1/4, 2
Factor 0 + 0*p - 4/5*p**4 - 84/5*p**3 + 184/5*p**2.
-4*p**2*(p - 2)*(p + 23)/5
Suppose 7*m + 100 = 2*m. Suppose -244 = 6*q - 256. Let j(o) = o**2 - o + 1. Let i(a) = 8*a**2 - 14*a + 16. Let y(w) = m*j(w) + q*i(w). Factor y(c).
-4*(c - 1)*(c + 3)
Let k(l) be the first derivative of -2*l**3/3 - 45*l**2 - 88*l - 228. Find f, given that k(f) = 0.
-44, -1
Let a be 2 + -2 + 6 - (7 + 75/(-63)). Factor 0 - 2/21*u**2 + a*u - 2/21*u**3.
-2*u*(u - 1)*(u + 2)/21
Let x(v) = 3*v**2 + 4*v + 5. Let d be x(-3). Factor -d*q**2 + 47*q**3 + 130*q**3 - 385*q**4 + 245*q**5 - 17*q**3.
5*q**2*(q - 1)*(7*q - 2)**2
Let j be 5 + (-145)/15 + (-2)/(-3). Let u be 0/(j + (5 - 0)). Factor 2/15*x**2 + 0*x + u.
2*x**2/15
Suppose -4/7*p**4 + 4/7*p**2 + 0 - 4/7*p**5 + 12/7*p**3 - 8/7*p = 0. What is p?
-2, -1, 0, 1
Let p(y) = 3*y**3 + 11*y**2 - 16. Let l(o) = 2*o**3 + 10*o**2 - 2*o - 16. Let b(x) = 4*l(x) - 3*p(x). Factor b(j).
-(j - 4)**2*(j + 1)
Let s(n) be the first derivative of n**4/2 - 8*n**3/3 + 4*n**2 + 37. Suppose s(c) = 0. Calculate c.
0, 2
Factor -432/11 + 2/11*r**3 - 72/11*r + 12/11*r**2.
2*(r - 6)*(r + 6)**2/11
Suppose -3*y + 3 = -54. Suppose 3*m + y = 46. Let g(f) = -13*f**2 + f. Let u(z) = -3*z**2. Let b(v) = m*u(v) - 2*g(v). Factor b(a).
-a*(a + 2)
Suppose 0 = -d, -7*c - 4 = -8*c - 4*d. Let n(b) be the third derivative of 0*b**3 - 1/240*b**5 + 0 + 0*b + 4*b**2 - 1/96*b**c. Determine s, given that n(s) = 0.
-1, 0
Let u(m) be the third derivative of m**7/147 - 38*m**6/105 + 52*m**5/7 - 200*m**4/3 + 2000*m**3/21 + 5*m**2 + 15. Let u(l) = 0. What is l?
2/5, 10
Let y(x) = -x**3 + 3*x**2 - 5*x - 12. Let n(r) = 4*r**2 - 4*r - 10. Let j(i) = 3*n(i) - 2*y(i). Factor j(u).
2*(u - 1)*(u + 1)*(u + 3)
Let x be 1/((-27)/18) - -1. Let l(k) be the third derivative of -1/30*k**5 - 7*k**2 + 0*k + 0 - k**3 - x*k**4. Find d such that l(d) = 0.
-3, -1
Let p(h) be the third derivative of 0 - 50*h**3 - 31*h**2 - 1/20*h**5 + 0*h - 5/2*h**4. Find k, given that p(k) = 0.
-10
Suppose 2*b = -p - p - 6, 0 = -5*p - 2*b. Let f be (-2 + p + 0)/(28/7). Solve 2/3*c**4 + f*c**2 + 2/3*c**3 + 0 + 0*c = 0.
-1, 0
Let n = 202 + -217. Let d be 1 + (-40)/n + -3. Suppose d*r - 1 + 1/3*r**2 = 0. What is r?
-3, 1
Suppose -g = -m - 12 - 28, 194 = 5*g - 2*m. Suppose 37*s + 2 = g*s. Solve 2*l**s + 8/3*l - 8/9 - 14/9*l**3 = 0.
-1, 2/7, 2
Let l(t) be the first derivative of t**4/32 + 3*t**3/8 + 5*t**2/4 + 292. Find q such that l(q) = 0.
-5, -4, 0
Suppose 70 + 26 = -7*x + 55*x. Find v such that 0*v + 0 + 1/4*v**3 + 1/2*v**x - 1/4*v**4 = 0.
-1, 0, 2
Solve 3*a**3 - 66*a**2 + 18*a**2 + 36*a + 17*a**2 + 13*a**2 - 24 = 0.
2
Suppose 20 = 2*g + 3*g. Suppose -6 = -g*m + 6. What is s in -2*s + 0*s - m*s**2 + 3*s**2 - 2*s**2 = 0?
-1, 0
Suppose 40 = -8*k + 296. Suppose -28*z = -k*z. Find d, given that -2/7*d**2 + 8/7*d + z = 0.
0, 4
Let r(n) be the second derivative of -n**5/4 + 25*n**4/12 - 35*n**3/6 + 15*n**2/2 + 112*n. Factor r(p).
-5*(p - 3)*(p - 1)**2
Let l(q) be the first derivative of 17 - 1/8*q - 1/40*q**5 - 1/8*q**4 + 1/8*q**2 + 1/24*q**6 + 1/12*q**3. Find z, given that l(z) = 0.
-1, 1/2, 1
Let v be ((-3)/(-5))/((-54)/(-1320)*11). Factor -16/9*f + 0 - 8/3*f**2 - 2/9*f**4 - v*f**3.
-2*f*(f + 2)**3/9
Let l(a) be the third derivative of a**7/630 - a**6/36 + 17*a**5/180 - a**4/9 + 2*a**2 + 58*a. Factor l(x).
x*(x - 8)*(x - 1)**2/3
Let a be (-1548)/(-420) - (-144)/(-112). Factor -3/5*j**2 + 12/5*j + a - 3/5*j**3.
-3*(j - 2)*(j + 1)*(j + 2)/5
Let v(l) = l + 9. Let n be v(-9). Suppose 3*z**2 + n*z + z**3 - 3*z**4 - z**5 + 2*z**5 + 4*z - 6*z = 0. What is z?
-1, 0, 1, 2
Let i(p) = -10*p**2 + 262*p. Let k(j) = 7*j**2 - 264*j. Let f(z) = 3*i(z) + 4*k(z). Suppose f(x) = 0. What is x?
-135, 0
Let o = 50 - 50. Let a be 2/(o - 8) - (-4)/16. Solve -6/5*u**2 + 2/5*u**3 + a + 4/5*u = 0.
0, 1, 2
Suppose 4*m - 20 = 4*k, -m + 5*k = 3*m - 23. Suppose -25 = -m*p - 3*p. Suppose 2*a**2 - 3 - 3 - p*a**2 + 9*a = 0. Calculate a.
1, 2
Let c(t) be the first derivative of -t**4/18 + 28*t**3/27 - 32*t**2/9 - 256*t/9 + 293. Factor c(z).
-2*(z - 8)**2*(z + 2)/9
Suppose -2*b + 3*y = -11, b + 120*y = 124*y + 8. Let r = -2 + 5. Determine g so that -4/3*g**b - 2/3*g**5 + 0 + 0*g + 0*g**2 - 2/3*g**r = 0.
-1, 0
Let x(n) be the first derivative of 4/9*n**3 + 13*n - 2/15*n**5 + 1/3*n**2 - 1/18*n**4 - 7. Let s(h) be the first derivative of x(h). Factor s(q).
-2*(q - 1)*(q + 1)*(4*q + 1)/3
Let c(v) be the third derivative of 7*v**6/300 - 16*v**5/25 + 7*v**4/3 + 16*v**3/5 - 2*v**2 - 166*v. Factor c(j).
2*(j - 12)*(j - 2)*(7*j + 2)/5
Let l = -2639 + 7928/3. Factor 4/3*x**3 + 0 - x - l*x**2.
x*(x - 3)*(4*x + 1)/3
Let w(a) = a - 1. Suppose 2*r = -r + 3. Let t(u) = 15*u**4 + 2 - 7 + 3*u**2 + 6*u + 9*u**3 - 1 - 9*u**4. Let f(v) = r*t(v) - 6*w(v). Factor f(s).
3*s**2*(s + 1)*(2*s + 1)
Let q be 1/(4/(-3))*16/(-4). Let p be -2 + q + -3*3/9. Factor 4/7*d**5 + 4/7*d**2 + 0 + 12/7*d**3 + 12/7*d**4 + p*d.
4*d**2*(d + 1)**3/7
Suppose 2*j - 12 = -3*r, 5*j + 5*r + 0*r - 25 = 0. Suppose -7 = -4*x + 1. Suppose -16*g**3 - 12 + 72*g + 32*g**j + 29*g**3 - 123*g**x = 0. Calculate g.
1/3, 2/5, 2
Let c(k) be the third derivative of 20 + 1/10*k**6 - 2*k**2 - 1/20*k**5 - 3/4*k**4 - 1/70*k**7 + 0*k + 0*k**3. Factor c(v).
-3*v*(v - 3)*(v - 2)*(v + 1)
Let w(x) be the first derivative of -2*x**3/9 - 3*x**2 - 28*x/3 - 133. Factor w(i).
-2*(i + 2)*(i + 7)/3
Let n = 426 + -422. Let k(c) be the second derivative of -2/15*c**3 - 1/50*c**5 + 4/25*c**6 + 0*c**2 + 0 - 3/10*c**n + 5*c. Find t, given that k(t) = 0.
-2/3, -1/4, 0, 1
Let y(m) be the second derivative of -m**6/120 + m**5/16 - 3*m**4/16 + 7*m**3/24 - m**2/4 + 39*m - 2. Find l such that y(l) = 0.
1, 2
Let v = 1627/88 + -202/11. Let c(b) be the first derivative of 1/4*b**4 + 1/24*b**6 + 1/12*b**3 - 1/8*b + 9 + 7/40*b**5 - v*b**2. Factor c(m).
(m + 1)**4*(2*m - 1)/8
Let t = 4423/3 - 21863/15. Let 12/5 + 219/5*s**3 + 111/5*s**4 + 21/5*s**5 + t*s + 201/5*s**2 = 0. Calculate s.
-2, -1, -2/7
Let r(s) be the first derivative of 4/5*s + 8/25*s**5 + 2/5*s**2 + 8 - 4/5*s**3 - 1/5*s**4. Let r(v) = 0. Calculate v.
-1, -1/2, 1
Suppose -1 = 8*u + 7. Let p be (u - (-8)/7)*4. Factor 0*y + 0*y**2 - p*y**3 + 0.
-4*y**3/7
Suppose 36 - 148 = -29*b - 25. Factor 1/4*i**4 + 3/4*i**b - 1/8*i**5 - 13/8*i - 3/4 - 1/2*i**2.
-(i - 3)*(i - 2)*(i + 1)**3/8
Suppose -m - 60 = 2*z - 56, -2*m = -4*z + 32. Factor -3/7*t**5 - 135/7*t**4 + 0 - 10125/7*t**2 + 0*t - 2025/7*t**z.
-3*t**2*(t + 15)**3/7
Let r = 643/560 + -3/560. What is v in 2/7*v**3 - 12/7 + r*v**2 + 2/7*v = 0?
-3, -2, 1
Let v(w) be the third derivative of w**6/200 - 3*w**5/50 + 9*w**4/40 + 4*w**2 + 40*w. Factor v(h).
3*h*(h - 3)**2/5
Let d(k) = -2*k**3 - 2*k**2 + k - 4. Let u be d(-3). Suppose -v + 5*g = 23, -6*g + u = 2*v - g. Determine x, given that -2 + 0*x - 2*x + 3*x + 3*x - v*x**2 = 0.
1
Suppose -12 = -2*b + 8. Suppose -8*q = -b*q + 6. Factor -2/3*h + 1/2*h**q + 0*h**2 + 0 + 1/6*h**4.
h*(h - 1)*(h + 2)**2/6
Let m be 5*(54/(-45))/(-3). Factor 0 - 24/7*l**m - 4/7*l.
-4*l*(6*l + 1)/7
Suppose 32 = 38*x + 63 - 31. Solve 20/3*j**2 + x - 5/6*j - 40/3*j**3 = 0 for j.
0, 1/4
Let o(k) be the first derivative of k**4/20 + 3*k**3/5 + 2*k**2 + 12*k/5 + 43. Factor o(p).
(p + 1)*(p + 2)*(p + 6)/5
Let h(t) be the first derivative of t**3 + 6*t**2 + 81.