w + 2)/4
Let -8/3 - 244/9*c + 76/9*c**3 - 16*c**2 = 0. What is c?
-1, -2/19, 3
Let g = -490 - -495. Let p(r) be the third derivative of 0*r + 0 + 0*r**3 - 8*r**2 + 1/18*r**4 - 1/90*r**g. What is y in p(y) = 0?
0, 2
Suppose 15 = s + 2*s + 5*j, -5*j = 0. Let d(z) be the second derivative of -1/5*z**s - 4/3*z**3 - 3*z - z**4 + 0*z**2 + 0. Factor d(c).
-4*c*(c + 1)*(c + 2)
Let r = 306/127 + -3112/1397. Determine v, given that -2/11*v**4 + r*v**2 - 4/11*v + 0 + 4/11*v**3 = 0.
-1, 0, 1, 2
Suppose -42 = -4*m - 2*z, 4*z - 3*z - 31 = -3*m. Let l be (-114)/(-30) - 8/m. Factor l*a**2 + 1 - 3*a - 1 + 1 - 7.
3*(a - 2)*(a + 1)
Let b(f) be the third derivative of f**10/604800 - f**9/34560 + f**8/5376 - f**7/2240 + f**5/60 - 9*f**2. Let v(w) be the third derivative of b(w). Factor v(m).
m*(m - 3)**2*(m - 1)/4
Let l(f) be the third derivative of -f**8/1176 + 2*f**7/735 - f**5/105 + f**4/84 - 19*f**2. Factor l(z).
-2*z*(z - 1)**3*(z + 1)/7
Let v(j) = 2*j + 18. Let o be v(-6). Let w(p) be the first derivative of -6 - 1/8*p**4 + 1/4*p**o + 0*p**2 - 1/3*p**3 + 2/5*p**5 + 0*p. Factor w(s).
s**2*(s + 1)**2*(3*s - 2)/2
Let p(l) be the second derivative of 5*l**3/6 + 57*l**2/2 + 2*l - 16. Let j be p(-11). Solve -6/11*q + 2/11*q**j + 4/11 = 0 for q.
1, 2
Let s be (-11)/(-6) - (-78)/468. Let i(b) be the third derivative of 0*b**3 + 9*b**s + 1/105*b**7 + 0*b**6 + 0 + 0*b - 1/30*b**5 + 0*b**4. Factor i(a).
2*a**2*(a - 1)*(a + 1)
Suppose 28 = -5*v + 4*z, -5*v + v + 4*z = 24. Let s be v - 0 - 44/(-11). Find a such that -1/4*a**3 + 1/2*a**4 + 0*a - 1/4*a**2 + s = 0.
-1/2, 0, 1
Let y(d) be the first derivative of -d**4/8 - 4*d**3/3 - 5*d**2 - 8*d + 98. Solve y(h) = 0.
-4, -2
Suppose 23 = 3*k + 11. Factor 11*r**2 - 20*r - k*r - 7*r**2 - 28.
4*(r - 7)*(r + 1)
Suppose 0*g + 5*g - 65 = 0. Let r = g + -13. Determine s so that 1 + 5*s + r + 1 - 7*s**2 = 0.
-2/7, 1
Let t(j) be the second derivative of j**4/12 + 8*j**3/3 + 32*j**2 - 3*j - 12. Solve t(c) = 0.
-8
Let q be 1 - 8/2 - (235 - 240). Find r such that -1/2*r**3 + 0*r + 0 - 1/6*r**q - 1/6*r**5 - 1/2*r**4 = 0.
-1, 0
Let b(z) be the second derivative of -z**7/105 - 7*z**6/150 + 4*z**5/25 + z**4/30 - 7*z**3/15 + z**2/2 + 2*z + 53. Suppose b(a) = 0. Calculate a.
-5, -1, 1/2, 1
Suppose -3*i - 2*i = t - 25, 0 = -4*t - 3*i + 15. Let j(x) be the third derivative of 0*x - 1/4*x**4 + t*x**3 + x**2 - 1/20*x**5 + 0. Solve j(k) = 0.
-2, 0
Let o = 56/531 + 2431/2124. Factor -o*j**2 - 65/2*j - 845/4.
-5*(j + 13)**2/4
Let d be (5/4)/(4 - (-114)/(-36)). Let u(m) be the second derivative of 0 - 2*m + 3/10*m**5 - 1/10*m**6 + 0*m**4 - m**3 + d*m**2. Suppose u(z) = 0. What is z?
-1, 1
Let p(a) be the first derivative of 0*a + 5 - 1/3*a**2 - 2/9*a**3. Factor p(m).
-2*m*(m + 1)/3
Let n(l) = 14*l**2 - 90*l - 4. Let v(w) = 11*w**2 - 90*w - 3. Let m(z) = -3*n(z) + 4*v(z). Factor m(a).
2*a*(a - 45)
Suppose -5 = -9*w + 11*w + z, -4*w = -4*z - 20. What is k in -3/7*k**5 - 3/7*k**2 - 5/7*k**4 + w*k + 0 + 11/7*k**3 = 0?
-3, 0, 1/3, 1
Let r be (-60)/(-33) - (-2)/11. Let s be r + (1 + -1 - -3). Let -5*h - 2*h + 1 + 4*h + h**2 + s*h = 0. Calculate h.
-1
Let h(y) = 193*y - 8104. Let o be h(42). Factor -96/5*j**o + 0 - 4/5*j**3 - 576/5*j.
-4*j*(j + 12)**2/5
Suppose 4*n = w + 100 - 104, 0 = -w - 2*n - 2. Solve w + 3/5*o**5 + 0*o**2 - 6/5*o**3 + 3/5*o + 0*o**4 = 0 for o.
-1, 0, 1
Let d(s) = -s**2 + 102*s + 3026. Let y be d(-24). Factor -4 + 1/2*w**3 + w**2 - y*w.
(w - 2)*(w + 2)**2/2
Let m = -241/2 + 121. Let k(d) be the second derivative of -1/4*d**4 - m*d**3 + 0 + 3*d**2 + d. Factor k(b).
-3*(b - 1)*(b + 2)
Let z = 25886/5 - 1630624/315. Let a = -6/35 + z. Let 2/9 + 2/9*k - a*k**2 = 0. Calculate k.
-1/2, 1
Suppose -3*l = i + 2 + 1, -l - 9 = 3*i. Let w(r) be the second derivative of 2*r + 3/4*r**3 + 1/8*r**4 + 3/2*r**2 + l. Factor w(a).
3*(a + 1)*(a + 2)/2
Find z such that -2/3*z**2 + 48*z - 864 = 0.
36
Let c(u) be the second derivative of u**5/5 - 28*u**4/3 + 200*u**3/3 - 192*u**2 - 428*u. Suppose c(t) = 0. What is t?
2, 24
Let h(c) be the first derivative of -15842*c**3/21 - 356*c**2/7 - 8*c/7 - 63. Solve h(u) = 0 for u.
-2/89
Let k = -39 - -48. Suppose b + 0*b = -4*z + 22, -z + k = 2*b. Factor 2/13*d**3 - 2/13*d - 2/13 + 2/13*d**b.
2*(d - 1)*(d + 1)**2/13
Let i(n) = n + 2. Let r be i(-6). Let a be 1 + 34/10 + r. What is h in -a + 3/5*h + 0*h**2 - 1/5*h**3 = 0?
-2, 1
Let s(w) be the third derivative of -w**6/24 - w**5/2 - 5*w**4/3 - 49*w**2. Find g, given that s(g) = 0.
-4, -2, 0
Let m(x) = x**2 - x + 2. Let u(w) = -5*w**2 + 5*w - 12. Let j(y) = -22*m(y) - 4*u(y). Factor j(t).
-2*(t - 2)*(t + 1)
Solve 36/5 - 33/5*v + 6/5*v**2 = 0 for v.
3/2, 4
Suppose 5*j - 20 = 5. Suppose -j*z + 10 = -2*x - 3*x, 4*z = 16. Factor t - 2*t**3 + t**2 + 0*t**x + 0*t**3.
-t*(t - 1)*(2*t + 1)
Let h(u) be the first derivative of -u**6/900 + u**5/300 + u**4/30 + 13*u**3/3 + 29. Let j(k) be the third derivative of h(k). Let j(b) = 0. What is b?
-1, 2
Solve -22/5*p - 1/5*p**2 - 17 = 0.
-17, -5
Find i such that -18*i**4 - 52*i**3 + 8 - 2*i**4 - 136*i**2 + 4*i + 100*i**2 = 0.
-1, 2/5
Let k(b) be the second derivative of b**6/6 - 13*b**5/20 + 14*b**4/15 - 8*b**3/15 - 21*b + 2. Factor k(y).
y*(y - 1)*(5*y - 4)**2/5
Let i(x) be the first derivative of 2*x**3/33 + 332*x**2/11 + 55112*x/11 - 219. Factor i(p).
2*(p + 166)**2/11
Factor -325/2*j - 5/6*j**3 - 2125/6 - 45/2*j**2.
-5*(j + 5)**2*(j + 17)/6
Let b be 3657/(-21) - (-10 - -4 - -3). Let o = 172 + b. Factor -2/7*z + o*z**2 + 0.
2*z*(3*z - 1)/7
Factor 7*n + 135 - 2*n**2 - 153 + 13*n - n**3 - 7*n + 8*n.
-(n - 3)*(n - 1)*(n + 6)
Let g = 163 - 161. Let x(a) be the third derivative of 4/15*a**5 + 0 + 4/3*a**4 + 0*a + 0*a**3 + 5*a**g + 1/60*a**6. Factor x(i).
2*i*(i + 4)**2
Let q(v) be the third derivative of v**5/15 - 5*v**4 + 21*v**2 + v. Find m such that q(m) = 0.
0, 30
Suppose -7*f + 20 = -2*f. Suppose f*s + 19 - 5 = j, -3*s = -3*j + 15. Factor 2 - 2*x**5 - 16*x**3 + 9*x**j + 6*x**2 - 4*x**3 - 10*x + 10*x**4 + 5*x**2.
-2*(x - 1)**5
Suppose 20 - 10 = 5*y. Suppose -y*b - 3 + 0 = 3*q, b - 4*q - 4 = 0. Factor 6/5*f**4 + b*f + 2/5*f**2 - 6/5*f**3 + 0 - 2/5*f**5.
-2*f**2*(f - 1)**3/5
Let u be (2*(-24)/12)/(-15). Find b such that -u - 2/15*b + 2/15*b**2 = 0.
-1, 2
Let n(v) be the third derivative of 0*v**3 + 0 - 1/24*v**6 + 9*v**2 + 0*v - 1/36*v**5 + 0*v**4 - 1/42*v**7 - 5/1008*v**8. Solve n(l) = 0 for l.
-1, 0
What is t in 6/7*t**3 + 320/7 + 2/7*t**4 + 192/7*t - 124/7*t**2 = 0?
-10, -1, 4
Let l(w) = w**2 + 7*w + 14. Let g be l(-3). Let b be ((-14)/35)/(g/(-10)). Factor 1/4*a**b + 0 - 1/4*a**3 + 0*a.
-a**2*(a - 1)/4
Let y(t) be the first derivative of t**6/39 - 16*t**5/65 - 5*t**4/13 + 16*t**3/39 + 9*t**2/13 - 90. Solve y(c) = 0.
-1, 0, 1, 9
Let r be (0 + 2)*(6/12 + 1). Factor -9*d**r - 18*d + 3/2*d**4 + 6 + 39/2*d**2.
3*(d - 2)**2*(d - 1)**2/2
Let -1013*j**4 + 1018*j**4 - 120*j**3 + 6*j**2 - 11*j**2 + 120*j = 0. What is j?
-1, 0, 1, 24
Let o be (4/6)/(259/(-111)) + (-198)/(-56). Factor o*v + 5/4*v**2 - 1/4*v**3 + 7/4.
-(v - 7)*(v + 1)**2/4
Let c(l) = -5*l - 145. Let r be c(-29). Let h(v) be the third derivative of r - 1/180*v**5 - 2*v**2 + 0*v - 1/72*v**4 + 1/9*v**3. Factor h(k).
-(k - 1)*(k + 2)/3
Let c(m) be the second derivative of -2*m**6/15 - 6*m**5/5 - 13*m**4/3 - 8*m**3 - 8*m**2 - 92*m + 1. Solve c(o) = 0.
-2, -1
Let n(g) be the first derivative of 4*g**5/5 + 4*g**4 + 4*g**3 - 8*g**2 - 16*g + 52. Factor n(c).
4*(c - 1)*(c + 1)*(c + 2)**2
Suppose -r - 3*t + 8 = 0, -11*r + t - 8 = -14*r. Factor -b**r + 5 + b**2 - 21*b**3 + 11*b**3 + 10*b - 5*b**4.
-5*(b - 1)*(b + 1)**3
Let -3/4*q**3 + 0 - 6*q**2 + 27/4*q = 0. What is q?
-9, 0, 1
Let j(f) = 2*f**2 - 6*f + 10. Let w be j(2). Let 6*u**2 + 25*u + w*u - 6 - 11*u**2 = 0. What is u?
1/5, 6
Suppose -4*z = d - 34, -4*d - 30 = -5*z + d. Let p be (z/(-5))/(2/(-5)). Factor -1 + 1/2*b**2 + 3/2*b - 3/2*b**3 + 1/2*b**p.
(b - 2)*(b - 1)**2*(b + 1)/2
Let g(n) be the second derivative of 0 - 1/2*n**3 + 3/20*n**5 + 1/4*n**4 + 0*n**2 - 11*n - 1/10*n**6. Suppose g(a) = 0. What is a?
-1, 0, 1
Let n = -259/150 - -3/50. Let h = n + 47/21. Factor 0*q**2 - 8/7*q**3 + h - 4/7*q**4 + 8/7*q.
-4*(q - 1)*(q + 1)**3/7
Let k(s) = 2*s**5 - 18*s**4 - 93*s**3 - 270*s**2 - 405*s - 243. Let q(h) = h**5 - h**4 - h**3. Let u(v)