e the first derivative of x**5/25 + x**4/10 - 7*x**3/15 + 2*x**2/5 + 134. Factor z(g).
g*(g - 1)**2*(g + 4)/5
Let x(n) = n**3 - n**2 + 3*n + 1. Let r = 169 + -170. Let u(h) = -2*h**2 + 5*h**2 - 2*h**2. Let k(s) = r*x(s) - 4*u(s). Suppose k(m) = 0. Calculate m.
-1
Let x(o) = -3*o - 70. Let q be x(-24). Suppose -d - q*d + 20 = 5*c, -16 = 4*d - 4*c. Factor -2/7*s**5 + 0*s - 2/7*s**4 + d + 2/7*s**3 + 2/7*s**2.
-2*s**2*(s - 1)*(s + 1)**2/7
What is k in 6*k**2 - 3*k**2 + 174 - 1413*k + 1590*k = 0?
-58, -1
Let u(a) be the second derivative of -a**7/336 + 17*a**6/60 - 611*a**5/80 + 187*a**4/8 - 363*a**3/16 + 2*a - 421. Find x, given that u(x) = 0.
0, 1, 33
Let k = 911/3676 - -2/919. Let l(i) be the second derivative of -5*i - k*i**3 + 0 + 1/4*i**2 + 1/8*i**4 - 1/40*i**5. Determine z so that l(z) = 0.
1
Let y(c) be the second derivative of -3*c**5/20 + c**4 - 2*c**3 - 32*c + 1. Find o, given that y(o) = 0.
0, 2
Let b(w) be the second derivative of -1/10*w**5 + 4*w - 4/3*w**3 + 0*w**2 + 0 + 2/3*w**4. What is l in b(l) = 0?
0, 2
Let x(c) be the third derivative of -5*c**6/24 - c**5/3 + 25*c**4/24 + 10*c**3/3 - 105*c**2. Factor x(g).
-5*(g - 1)*(g + 1)*(5*g + 4)
Suppose -17 = 2*s + 4*h - 57, 4*s + 4*h - 68 = 0. Suppose 8*q - s = 10. What is m in -10/11*m**q + 4/11*m**2 - 4/11 + 10/11*m = 0?
-1, 2/5, 1
Let l = -27 - -30. Solve 22 - 22 - 8*p**l - 4*p + 5*p**2 + 7*p**3 = 0 for p.
0, 1, 4
Let a(u) be the second derivative of -u**5/120 + 5*u**4/8 + 4*u**3/3 - 23*u**2/3 - 396*u. Suppose a(z) = 0. Calculate z.
-2, 1, 46
Let i(b) be the third derivative of -b**9/80640 - b**8/3360 - b**7/420 + b**5/15 - 6*b**2. Let h(f) be the third derivative of i(f). Factor h(m).
-3*m*(m + 4)**2/4
Suppose -32*m + 6163 = -1965. Let o = -501/2 + m. Solve -o*t - 1 + 5/8*t**4 - 9/4*t**2 + 7/8*t**3 = 0 for t.
-2, -1, -2/5, 2
Let g(s) be the first derivative of 3*s**5 - 5*s**4/2 - 5*s**3 + 5*s**2 - 133. Find n, given that g(n) = 0.
-1, 0, 2/3, 1
Let k(b) = -11*b**2 - 52*b - 71. Let u(d) = -4*d**2 - 18*d - 22. Let w(i) = -2*k(i) + 7*u(i). Suppose w(f) = 0. Calculate f.
-3, -2/3
Determine p so that 68/3*p + 0 + 4/3*p**2 = 0.
-17, 0
Let r = 22327 - 111632/5. Factor r*i**3 + 3/5*i**2 + 0 - 6/5*i.
3*i*(i - 1)*(i + 2)/5
Let k(x) be the third derivative of x**8/336 - 3*x**7/70 + x**6/4 - 23*x**5/30 + 11*x**4/8 - 3*x**3/2 - 7*x**2 - 11*x. Factor k(z).
(z - 3)**2*(z - 1)**3
Let r(t) be the second derivative of 5*t**7/14 - 10*t**6/3 + 51*t**5/4 - 155*t**4/6 + 30*t**3 - 20*t**2 - 4*t + 2. Let r(d) = 0. What is d?
2/3, 1, 2
Let g(t) be the third derivative of t**6/840 - t**5/70 + t**4/21 - 2*t**2 + 71*t. Factor g(v).
v*(v - 4)*(v - 2)/7
Let q(v) = v**2 + 28*v + 55. Let z be q(-26). Let a(c) be the first derivative of -1/14*c**2 + 1/21*c**z + 0*c + 3. Factor a(u).
u*(u - 1)/7
Suppose 24 = 420*u - 408*u. Factor 4/5*s - 3/5 - 1/5*s**u.
-(s - 3)*(s - 1)/5
Factor -3*w**2 + 0 + 1/4*w**3 - 13/4*w.
w*(w - 13)*(w + 1)/4
Let o(q) be the first derivative of q**7/168 - q**6/72 - q**5/3 + 5*q**4/2 - 19*q**3/3 + 20. Let w(g) be the third derivative of o(g). Factor w(i).
5*(i - 2)**2*(i + 3)
Let r be ((-5)/6)/5*(-357 - -354). Suppose t**4 + 0*t**2 + 0*t + r*t**5 + 1/2*t**3 + 0 = 0. Calculate t.
-1, 0
Factor -45*m - 3*m**3 - 9*m**2 - 43*m + 152*m + 0*m**3 - 52*m.
-3*m*(m - 1)*(m + 4)
Let l(n) be the first derivative of -n**5/40 + 5*n**4/24 - n**3/2 - 5*n + 11. Let q(i) be the first derivative of l(i). Factor q(v).
-v*(v - 3)*(v - 2)/2
Let f = -7 + 9. Let k be (-3)/f*8/(-21). Factor -2/7*u**5 + k*u**4 + 6/7*u**3 - 8/7*u + 0 - 8/7*u**2.
-2*u*(u - 2)**2*(u + 1)**2/7
Suppose -7496*h = -7502*h. What is n in 0 + h*n**3 + 2/7*n**4 + 4/7*n - 6/7*n**2 = 0?
-2, 0, 1
Let v be (1216/80 - 16)/(-1 + -1). Let u(i) be the first derivative of 0*i**2 - 1/10*i**4 + v*i**3 + 3 - 8/5*i. What is p in u(p) = 0?
-1, 2
Let y = 437/339 + 507617/8136. Let h = -536/9 + y. Let -15/8*b**3 - 3/4*b + 0 + h*b**2 = 0. Calculate b.
0, 1/5, 2
Let k = -1 - -3. Determine t so that -13*t + 4*t**2 + 16 + 5*t - 3*t**k = 0.
4
Let i(o) = 10*o**4 + 330*o**3 + 90*o**2 - 1255*o - 65. Let n(x) = x**4 + 30*x**3 + 8*x**2 - 114*x - 6. Let g(u) = 6*i(u) - 65*n(u). Factor g(r).
-5*r*(r - 6)*(r - 2)*(r + 2)
Let h(o) be the third derivative of 10*o**2 + 1/105*o**6 + 0*o**3 + 0*o + 0*o**4 - 2/105*o**5 + 0 - 1/735*o**7. Suppose h(s) = 0. What is s?
0, 2
Let y be 200/(-8)*4/(-20). Let z(a) be the third derivative of 0 + 1/120*a**6 + 2/45*a**y + 0*a - a**2 - 1/24*a**4 + 0*a**3. Find w such that z(w) = 0.
-3, 0, 1/3
Let -22/3*i**2 + 20/3 + 2*i**3 - 2*i + 2/3*i**4 = 0. What is i?
-5, -1, 1, 2
Let m = 52 - 49. Suppose -8 - 1 = -m*i. Determine o, given that -6/7*o**2 - 4/7*o + 2/7*o**4 + 0*o**i + 0 = 0.
-1, 0, 2
Let y(b) be the first derivative of 4*b**3 - 26 - 3/4*b**4 - 18*b - 3/2*b**2. Factor y(t).
-3*(t - 3)*(t - 2)*(t + 1)
What is d in 180/7 - 564/7*d**3 + 9*d**4 + 1437/7*d**2 - 996/7*d = 0?
2/7, 2/3, 3, 5
Suppose -4*i = 3*v - 8, -i = -52*v + 50*v - 2. Factor 0 - 1/9*u**i + 0*u.
-u**2/9
Suppose -4*h = -229 + 93. Factor 0*o**3 - 15*o - 5*o**3 - h + 2*o**3 - 12*o**2 + 28.
-3*(o + 1)**2*(o + 2)
Factor 46*n + 160/3 - 2/3*n**3 - 8*n**2.
-2*(n - 5)*(n + 1)*(n + 16)/3
Let n be 4/(-12) - (-3)/9. Let c = -5 + 10. Factor n*p**4 + p**c - 2*p**5 + p**2 + 3*p**4 - 3*p**3.
-p**2*(p - 1)**3
Let h(v) be the first derivative of v**4/72 - v**2/12 - 3*v - 12. Let g(p) be the first derivative of h(p). Factor g(n).
(n - 1)*(n + 1)/6
Let b(h) = -h**2 - 2*h + 2. Let k be b(1). Let y be (3 - 3) + 4 + k. Factor y*l**2 - 6*l - 1/2*l**3 + 4.
-(l - 2)**3/2
Let l(y) = y**3 + 5*y**2 + 3. Let b be l(-5). Suppose -b*j = 2*x, -5*x = -x - j. Solve 2/9*g - 2/9*g**2 + x = 0 for g.
0, 1
Let l(g) be the second derivative of g**4/16 + 45*g**3/8 - 323*g. Factor l(d).
3*d*(d + 45)/4
Let w(b) be the second derivative of b**5/20 + 9*b**4/8 + 4*b**3 - 8*b**2 - 13*b. Let g(o) be the first derivative of w(o). Factor g(r).
3*(r + 1)*(r + 8)
Let b(x) be the third derivative of -x**5/270 - x**4/12 - 20*x**3/27 + 316*x**2. Factor b(d).
-2*(d + 4)*(d + 5)/9
Let q = 964 - 961. Let b(p) be the second derivative of 0 - 1/48*p**4 - 1/6*p**q + 10*p - 1/2*p**2. Suppose b(j) = 0. What is j?
-2
Let n(v) be the first derivative of 15/2*v**4 - 6/5*v**5 + 4*v**3 - 6*v - 5/2*v**6 + 10 - 15/2*v**2. Determine u, given that n(u) = 0.
-1, -2/5, 1
Let j(c) be the second derivative of -c**6/30 - 61*c**5/20 - 119*c**4/12 - 59*c**3/6 + 8*c + 12. Let j(x) = 0. Calculate x.
-59, -1, 0
Let w(b) be the first derivative of -b**3/12 + 3*b**2/4 - 70. Solve w(j) = 0 for j.
0, 6
Let o(t) be the second derivative of -t**6/480 - t**5/48 - t**4/32 + 7*t**3/6 + 20*t. Let b(l) be the second derivative of o(l). Factor b(f).
-(f + 3)*(3*f + 1)/4
Let h be 418/225 - (-414)/(-5175). Suppose -16/9 - h*d**4 + 4/9*d + 4/9*d**5 + 32/9*d**2 - 8/9*d**3 = 0. What is d?
-1, 1, 4
Let i(m) be the first derivative of 1/270*m**6 + 0*m - 1/45*m**5 + 2 - 2/3*m**3 + 0*m**2 + 0*m**4. Let h(n) be the third derivative of i(n). Factor h(z).
4*z*(z - 2)/3
Let g(u) = 2*u**2 + 11*u - 25. Let o be g(3). Let p(i) = -5*i + 135. Let v be p(o). Factor -1/5*t**3 + 0*t**4 + 0*t + 0 + 0*t**2 + 1/5*t**v.
t**3*(t - 1)*(t + 1)/5
Suppose 0*t + 44 = 11*t. Let q be (t - (-50)/(-20)) + 2/4. Solve -6/5 - 2/5*d**3 - 14/5*d - q*d**2 = 0.
-3, -1
Let x(m) be the first derivative of -5*m**6/24 + 17*m**5 - 335*m**4/16 - 211. Factor x(c).
-5*c**3*(c - 67)*(c - 1)/4
What is u in 14*u**2 - 152*u - 31023*u**4 + 31019*u**4 + 84 + 34*u**2 + 24*u**3 = 0?
-3, 1, 7
Let k(y) be the second derivative of -3/40*y**5 + 0 - 18*y - 1/24*y**4 + 1/2*y**2 - 1/60*y**6 + 1/4*y**3. Suppose k(f) = 0. Calculate f.
-2, -1, 1
Let j(i) = i**3 - 2*i**2 - i + 2. Let o be j(1). Suppose 0 - 1 = l - z, -4*l + 3*z - 1 = o. Solve 0 + 2/3*f**l - 2*f = 0.
0, 3
Solve 18/13*l + 0 - 12/13*l**2 + 2/13*l**3 = 0 for l.
0, 3
Let q be 2 + 1*6/9*-3. Let u(z) be the second derivative of q - 1/3*z**3 - 1/2*z**2 - 4*z - 1/12*z**4. Factor u(w).
-(w + 1)**2
Let k(m) be the second derivative of -m**6/30 - 3*m**5/5 - 35*m**4/12 + 2*m**3 + 18*m**2 - 19*m - 2. Factor k(g).
-(g - 1)*(g + 1)*(g + 6)**2
Let l(f) = 2*f**3 + f**2 + f + 1. Let v(w) = 4*w**4 - 20*w**3 + 82*w**2 - 42*w + 6. Let i(a) = 6*l(a) - v(a). Find d such that i(d) = 0.
0, 1, 3, 4
L