t w = 8298 - 8296. Suppose 28/3*x - 2/3*x**w - 98/3 = 0. What is x?
7
Let f = -152 + 154. Let w(d) be the first derivative of 1/3*d**4 - d**f + 4/9*d**3 + 1/9*d**6 + 2 - 2/5*d**5 + 2/3*d. Factor w(h).
2*(h - 1)**4*(h + 1)/3
Let h(w) be the third derivative of w**4/12 - 7*w**3/3 + 23*w**2. Let b be h(7). Find p, given that b*p**2 + 3/2*p - 1 - 1/2*p**3 = 0.
-2, 1
Let z(h) be the first derivative of 13/6*h**2 + 2/3*h - 5/3*h**3 + 9. Let z(v) = 0. Calculate v.
-2/15, 1
Let j(i) be the third derivative of i**9/3024 + i**8/840 - i**6/180 - i**5/120 - 2*i**3/3 + 11*i**2. Let w(p) be the first derivative of j(p). Factor w(t).
t*(t - 1)*(t + 1)**3
Let b(k) be the first derivative of k**4 + 16*k**3/3 - 2*k**2 - 16*k - 187. Suppose b(d) = 0. What is d?
-4, -1, 1
Let q = -4 + 8. Factor -20 - 140*y - q*y**2 - 61*y**2 - 180*y**2.
-5*(7*y + 2)**2
Suppose -l = 5*p + 61 - 21, -p - 32 = 5*l. Let m = p + 11. What is z in z**m - z + 3*z**2 - 3*z**2 + z**3 - z**2 = 0?
-1, 0, 1
Let k(l) be the second derivative of 4/9*l**3 + 2/3*l**2 + 0 - 7*l + 1/9*l**4. Solve k(z) = 0 for z.
-1
Let u = 38 + -264/7. Let a = 14/703 + 4120/4921. Factor -u*p**2 + a*p - 4/7.
-2*(p - 2)*(p - 1)/7
Let t(m) be the second derivative of -m**4 + 63*m**3/2 + 24*m**2 + 326*m. Factor t(d).
-3*(d - 16)*(4*d + 1)
Let j = -2973 - -8921/3. Determine s, given that 16/3*s - j*s**3 + 4/3*s**2 + 0 = 0.
-2, 0, 4
Let m(f) be the third derivative of -f**5/20 + 41*f**4/8 + 21*f**3 + 45*f**2. Solve m(o) = 0.
-1, 42
Let m = -7 - -18. Suppose -10*x = -m*x + 3. Factor 8*z - x*z**2 - 4*z**2 + 3*z**2 + 4*z**4 - 8*z**3.
4*z*(z - 2)*(z - 1)*(z + 1)
Suppose 3*b**2 - 394*b - 394*b + 1185*b - 391*b = 0. What is b?
-2, 0
Let u be 4*(6 + (-76)/16 - 0). Let b(t) be the second derivative of -1/18*t**4 + 1/45*t**5 + 0 - 1/18*t**2 - 1/270*t**6 + 2/27*t**3 + u*t. Factor b(g).
-(g - 1)**4/9
Suppose 184*n + 212 - 331 = 433. Factor -49/5*z + 0 - 14/5*z**2 - 1/5*z**n.
-z*(z + 7)**2/5
Suppose 2*l + 7*p - 8 = 2*p, -5*l - 3*p + 20 = 0. Factor -2*r**l - 11*r**3 + r**3 - r**4 + 15*r**2 - 2*r**4.
-5*r**2*(r - 1)*(r + 3)
Let a(t) be the first derivative of 5*t**6/6 + 4*t**5 + 5*t**4/4 - 50*t**3/3 - 10*t**2 + 40*t + 314. Factor a(c).
5*(c - 1)**2*(c + 2)**3
Let p(d) = -d**2 - 16*d - 16. Let z(m) be the first derivative of 5*m**3/3 + 65*m**2/2 + 65*m - 16. Let n(c) = 15*p(c) + 4*z(c). Determine h so that n(h) = 0.
-2
Let l be (1/(6/24) - 6) + 5. Factor -2/3*b**2 + 0 - 2/3*b**l + 2/3*b**4 + 2/3*b.
2*b*(b - 1)**2*(b + 1)/3
Factor 0*q**2 + 0 + 0*q - 2/3*q**5 - 4*q**4 - 6*q**3.
-2*q**3*(q + 3)**2/3
Suppose 8*h = -3*h + 55. Factor -7*s**4 - 3*s**h + 3*s**5 + 10*s**4 + s**5 - 3*s**2 - s**3.
s**2*(s - 1)*(s + 1)*(s + 3)
Let s be (-14)/(-5) - 14/(-70). Let d(w) be the third derivative of 0*w**s + 0 + 1/60*w**4 + 1/300*w**5 - 2*w**2 + 0*w. What is k in d(k) = 0?
-2, 0
Suppose 19*q - 17*q = -6. Let i(g) = 35*g**3 + 13*g**2 - 17*g. Let k(s) = 18*s**3 + 6*s**2 - 9*s. Let w(m) = q*i(m) + 5*k(m). Factor w(l).
-3*l*(l + 1)*(5*l - 2)
Let v be (-3 - (-24)/9)*3. Let g be (-1)/45 + ((-7)/9 - v). Factor -g*j**5 + 0*j**4 + 0 + 0*j**2 + 1/5*j**3 + 0*j.
-j**3*(j - 1)*(j + 1)/5
Let a(x) be the first derivative of -3/2*x**4 + 4*x**2 - 1/4*x**5 - 2*x**3 + 10*x + 7. Let r(h) be the first derivative of a(h). Factor r(z).
-(z + 2)**2*(5*z - 2)
Let f = 247 + -242. Let t(z) be the second derivative of 1/36*z**4 + 0*z**2 + 1/30*z**f + 5*z + 0*z**3 + 1/90*z**6 + 0. Factor t(a).
a**2*(a + 1)**2/3
Let c = 721/2 + -360. Let s(i) be the third derivative of -c*i**4 - 7*i**2 + 0 + 0*i - 2/3*i**3 + 7/60*i**5. Factor s(o).
(o - 2)*(7*o + 2)
Let z = -2814 + 2814. Factor -1/4*n**3 + z*n**2 + n + 0.
-n*(n - 2)*(n + 2)/4
Let k(f) be the third derivative of -f**8/1008 - 2*f**7/63 - 2*f**6/45 + 31*f**5/90 + 97*f**4/72 + 19*f**3/9 - 95*f**2 + 2. Find b such that k(b) = 0.
-19, -1, 2
Let g(v) = v**3 - v + 1. Let t be g(1). Let s be (-1 + 5 + 0)*t. Find b such that 0*b - 4*b - 9*b**3 + 3*b**s + b + 9*b**2 = 0.
0, 1
Let q(w) be the first derivative of -w**6/120 - 7*w**5/40 - 3*w**4/4 - 29*w**3/3 - 5. Let v(a) be the third derivative of q(a). Factor v(f).
-3*(f + 1)*(f + 6)
Let c(r) be the third derivative of r**8/504 + 11*r**7/105 + 53*r**6/30 + 383*r**5/45 + 235*r**4/12 + 25*r**3 + 22*r**2. What is d in c(d) = 0?
-15, -1
Let y(i) be the second derivative of -i**7/252 + 2*i**6/45 - 7*i**5/40 + i**4/4 - 159*i. What is v in y(v) = 0?
0, 2, 3
Let l(q) be the second derivative of q**7/21 + 11*q**6/60 + 3*q**5/20 - 7*q + 23. Factor l(j).
j**3*(j + 2)*(4*j + 3)/2
Let h(a) be the first derivative of -2*a**5/25 - a**4/15 - 75. Let h(t) = 0. What is t?
-2/3, 0
Factor 0 + 0*b + 3/2*b**3 - b**2 - 1/2*b**4.
-b**2*(b - 2)*(b - 1)/2
Let x(g) = 6*g**3 + 11*g**2 - 6*g - 11. Let d be 4*2*(-1)/2. Let c(y) = y**3 + 2*y**2 - y - 2. Let f(o) = d*x(o) + 22*c(o). Factor f(b).
-2*b*(b - 1)*(b + 1)
Let m(i) = 7*i + 10. Let v be m(5). Let t = 45 - v. Suppose -1/2*b**4 - 2*b**3 - 2*b**2 + 0 + t*b = 0. What is b?
-2, 0
Suppose -10*f + 6*f**2 - 2/3*f**3 - 50/3 = 0. Calculate f.
-1, 5
Let s(o) be the second derivative of 3*o**5/4 - 95*o**4/3 - 130*o**3/3 - 10*o + 3. Factor s(f).
5*f*(f - 26)*(3*f + 2)
Suppose -14 = 9*q + 13. Let y be 0/(-1 + 3/q). Factor 0*o + 1/7*o**3 + 0*o**2 + 1/7*o**5 + 2/7*o**4 + y.
o**3*(o + 1)**2/7
Let m(v) be the second derivative of 2*v**2 + 1/2*v**4 + 0 - 5/3*v**3 + 6*v. Factor m(b).
2*(b - 1)*(3*b - 2)
Let z(m) = 3*m**3 - 81*m**2 + 165*m - 63. Let s(d) = -d**3 + 32*d**2 - 66*d + 25. Let a(f) = 12*s(f) + 5*z(f). Find r, given that a(r) = 0.
1, 5
Factor 11/7 + 4/7*a**2 - 45/7*a.
(a - 11)*(4*a - 1)/7
Let g(s) be the third derivative of 0*s + 0 - 1/70*s**5 + 13*s**2 + 1/84*s**4 + 0*s**3. Factor g(z).
-2*z*(3*z - 1)/7
Let r(n) = -9*n**3 - 25*n**2 - 31*n - 11. Let q be (50/8*2)/(8/16). Let x(k) = 55*k**3 + 150*k**2 + 185*k + 65. Let g(c) = q*r(c) + 4*x(c). Factor g(l).
-5*(l + 1)**2*(l + 3)
Let o(j) be the first derivative of j**4/10 - 6*j**3/5 - 8. Find p such that o(p) = 0.
0, 9
What is d in -15*d - 3*d**2 + 2 + 1 + 21*d + 2 + 4 = 0?
-1, 3
Let y(n) = -n**2 + 5. Let i be y(0). Suppose 2*u - 5*u**i - 10*u**2 - 8*u**3 - 5 + 15*u**4 - 2*u**3 + 13*u = 0. What is u?
-1, 1
Let m be (9 + -3)/(-4 + 14 - (22 - 14)). Solve 0 + 12/5*s + 3/5*s**m - 12/5*s**2 = 0.
0, 2
Let l(s) = 7*s**4 - 13*s**3 + 4*s**2 + 16*s. Let w(i) = -6*i**4 + 12*i**3 - 3*i**2 - 15*i. Let u = -20 - -16. Let r(a) = u*w(a) - 3*l(a). Factor r(k).
3*k*(k - 2)**2*(k + 1)
Let r(m) be the first derivative of 7*m**3/3 + 127*m**2 + 72*m + 34. Factor r(q).
(q + 36)*(7*q + 2)
Let p be (-26 + 16575/637)/(9/42). Factor p*b**2 + 10/7*b - 32/21.
2*(b - 1)*(b + 16)/21
Let i be 58/10 + (-4)/(-20). Suppose -5*l - 6 = -i*l. Find s such that -6*s**2 + l + 4*s**3 + 0 - s**3 - 3*s = 0.
-1, 1, 2
Let w(d) be the first derivative of 11*d**6/27 + 4*d**5/45 - 11*d**4/18 - 4*d**3/27 - 76. Find a, given that w(a) = 0.
-1, -2/11, 0, 1
Suppose -3*x - 3*g - 6 = -2*x, g = -4*x + 9. Solve 115*s**x + 25*s**4 + 20 - 142*s**2 + 20*s - 23*s**5 - 3*s**2 - 12*s**5 = 0.
-2, -2/7, 1
Suppose 4*c + 16 = -k, -4*k + 3*c + 31 = -0*k. Factor 2*v**3 - v**3 - k*v**3 - 2*v**2 + 9 + 5*v**2 + 15*v.
-3*(v - 3)*(v + 1)**2
Let t(c) be the third derivative of -c**8/4800 + c**7/420 - c**6/100 + c**5/75 - 13*c**4/24 - 4*c**2. Let s(k) be the second derivative of t(k). Factor s(g).
-(g - 2)**2*(7*g - 2)/5
Let j(h) be the first derivative of -3*h**5/20 - h**4/4 + h**3/2 + 3*h**2/2 + 4*h - 6. Let q(l) be the first derivative of j(l). Suppose q(v) = 0. What is v?
-1, 1
Let c be (1/(-38))/(35/(-28)). Let y = c + 374/285. Factor -2*w + 2/3*w**2 + y.
2*(w - 2)*(w - 1)/3
Let t = 18 - 0. Let b be 4/t - 559/(-117). Factor 0 - b + 3 + 3*h**2 - h**2.
2*(h - 1)*(h + 1)
Let x = 36/569 + 109637/2845. Factor -104/5*m**3 - 78/5*m - x*m**2 - 16/5*m**4 - 9/5.
-(m + 3)**2*(4*m + 1)**2/5
Suppose -2*u - 2700 = -12*u. Let n be (0 + 3)*3/u*6. Suppose 0 - n*m**5 + 0*m**3 + 1/5*m + 2/5*m**2 - 2/5*m**4 = 0. Calculate m.
-1, 0, 1
Let c(w) be the first derivative of -7*w**6/480 - w**5/48 + w**4/48 - 4*w**2 - 24. Let i(y) be the second derivative of c(y). Factor i(a).
-a*(a + 1)*(7*a - 2)/4
Let z = -8733 + 131027/15. Factor 2/15*c**4 + 4/3*c**3 + 22/5*c**2 + z + 16/3*c.
2*(c + 1)**2*(c + 4)**2/15
Let n(k) be the 