 = 0.
1
Suppose 3*x = -14*p + 9*p - 5, 0 = -5*p + 3*x + 25. Let k**p + 3/2*k**3 + 0 - 1/2*k**5 + 0*k**4 + 0*k = 0. What is k?
-1, 0, 2
Let v(s) be the third derivative of s**5/180 + s**4/12 + 5*s**3/18 - 469*s**2. Factor v(j).
(j + 1)*(j + 5)/3
Let q(z) be the first derivative of 1/4*z**4 + 6 + 0*z**3 + 0*z**2 + 3/20*z**5 + 4*z. Let v(f) be the first derivative of q(f). Factor v(n).
3*n**2*(n + 1)
Let f(h) be the third derivative of -h**7/42 - 5*h**6/24 - 5*h**5/12 + 25*h**4/24 + 5*h**3 + 4*h**2 + 19*h. Find x, given that f(x) = 0.
-3, -2, -1, 1
Suppose -5*s = -2*n - 16, -106*n - 2 = -107*n. Find m such that -1/2*m**5 + 0 + 1/2*m**s - m + 3/2*m**3 - 1/2*m**2 = 0.
-1, 0, 1, 2
Let b(t) be the first derivative of -t**7/1050 - t**6/150 - 4*t**3/3 + 5. Let w(d) be the third derivative of b(d). Factor w(q).
-4*q**2*(q + 3)/5
Let g be 0 - (-197)/210 - 1/2. Let s = g + 2/15. Factor -s*f + 2/7 + 2/7*f**2.
2*(f - 1)**2/7
Let n(d) be the first derivative of -d**6/3 + 8*d**5/5 + 5*d**4/2 - 194. Determine b so that n(b) = 0.
-1, 0, 5
Let l = -8 + 16. Let n = -104 + 104. Factor 8*s**2 + s + 8*s**5 + n*s**2 + s + l*s**4 - 6*s**5 + 12*s**3.
2*s*(s + 1)**4
Suppose 20 = u - 5*r, u - r - 4 = 6*u. Let t(a) be the first derivative of -2/3*a**3 + u*a - 2/5*a**5 - a**4 + 0*a**2 + 4. Suppose t(g) = 0. What is g?
-1, 0
Let k(r) be the first derivative of -r**3/18 + 5*r**2/2 - 75*r/2 + 20. Factor k(s).
-(s - 15)**2/6
Let i be 78/8 + 95 + -103. Let m(k) be the second derivative of -i*k**3 + 1/2*k**4 + 0 + 3*k - 3/2*k**2. Factor m(z).
3*(z - 2)*(4*z + 1)/2
Let l(q) be the third derivative of q**8/5040 - q**6/180 - 13*q**5/60 - 9*q**2. Let c(x) be the third derivative of l(x). Let c(j) = 0. What is j?
-1, 1
Factor 0 + 3/5*o**5 - 6/5*o - 3/5*o**4 - 9/5*o**3 + 3*o**2.
3*o*(o - 1)**3*(o + 2)/5
Let c be 6 + (-196)/32 + 5/((-1400)/(-91)). Factor -36/5*l + 11/5*l**3 - c*l**4 - 24/5*l**2 + 0.
-l*(l - 6)**2*(l + 1)/5
Solve 9 - 1/3*g**3 - 9*g + 3*g**2 = 0.
3
Suppose -22*g = -20*g - 6. Factor -12*d + 5*d**g + 11*d**2 - 7 - 8*d - d**2 - 33.
5*(d - 2)*(d + 2)**2
Suppose 72*z**4 + 11*z**3 - 34*z**4 - 35*z**4 + 0*z**5 + 9*z**2 - 3*z**5 + 4*z**3 = 0. What is z?
-1, 0, 3
Solve -72/7*z**3 + 20*z**2 - 4/7 - 64/7*z = 0.
-1/18, 1
Let p(c) = 55*c**3 + 55*c**2 - 190*c - 20. Let w(t) = 8*t**3 + 7*t**2 - 27*t - 3. Let v(l) = -3*p(l) + 20*w(l). Solve v(z) = 0 for z.
-6, 0, 1
Let t(x) be the first derivative of -3*x**4/4 + 2*x**3 - 229. Factor t(j).
-3*j**2*(j - 2)
Let x(d) be the second derivative of d**6/165 - d**5/55 - 5*d**4/22 + 537*d. Factor x(h).
2*h**2*(h - 5)*(h + 3)/11
Factor -316/5*u**2 - 638/5*u + 2/5*u**3 - 64.
2*(u - 160)*(u + 1)**2/5
Let k(q) be the first derivative of -q**3 + 153*q**2 - 7803*q - 276. What is a in k(a) = 0?
51
Let q(t) = -t**3 - t - 1. Let k(n) = 17*n**2 + 5*n**3 + 9 + 2*n**5 - 13*n**2 - 2 - 2*n**4 + 11*n. Let z(g) = 2*k(g) + 18*q(g). Factor z(y).
4*(y - 1)**3*(y + 1)**2
Let q be (-135)/(-60)*(-1 + 148/(-6)). Let h = 58 + q. Factor h*b**3 + 0*b - 1/4*b**4 + 0*b**2 + 0.
-b**3*(b - 1)/4
Factor -1/3*d**3 - 1/3*d**2 + 0 + 2/3*d.
-d*(d - 1)*(d + 2)/3
Let o be -131*5/125 + 5. Let z = o - -21/25. Factor 3/5*f + 6/5 - z*f**3 - 6/5*f**2.
-3*(f - 1)*(f + 1)*(f + 2)/5
Let a(p) be the third derivative of p**8/11200 + p**7/1050 + p**6/300 - p**4/4 + 7*p**2. Let f(v) be the second derivative of a(v). Factor f(x).
3*x*(x + 2)**2/5
Let u be (-4)/((-1176)/(-590)) + 2. Let y = u + 197/147. Factor 0 - 2*h**2 - 1/6*h**4 + h**3 + y*h.
-h*(h - 2)**3/6
Suppose 0*k = -2*k. Suppose k = q - 4*w - 130, 3*q + 2*q - 5*w - 695 = 0. Factor 231*y**2 + 96*y - 1 + q*y**3 + 5 + 5*y**3 + 8.
3*(y + 1)*(7*y + 2)**2
Let a(n) = -3*n - 1. Let x be a(-5). Let g = x - 8. Factor -6*v**2 + g*v**2 - 4*v**3 - v - 5*v**2.
-v*(v + 1)*(4*v + 1)
Let c(t) = t**5 + 7*t**4 + 18*t**3 + 20*t**2 + 8*t - 3. Let n(w) = 1. Suppose -28*h + 23*h = 15. Let a(b) = h*n(b) - c(b). Factor a(m).
-m*(m + 1)*(m + 2)**3
Let s be (-18)/(-8) + (1 - (9 - 6)). Let p(v) be the first derivative of -2 + 1/8*v**4 + s*v**2 + 0*v + 1/3*v**3. Factor p(l).
l*(l + 1)**2/2
Suppose -3 = -3*b + 6. Let f be (0 - 676/(-9)) + (-40)/360. Determine q so that -34*q**4 - 66*q**2 - b*q - 27 + f*q + 24*q**3 + 31*q**4 = 0.
1, 3
Let o(z) = 3*z**2 - 10*z + 12. Let k(d) be the third derivative of 4*d**5/5 - 53*d**4/8 + 32*d**3 - 7*d**2. Let j(p) = 2*k(p) - 33*o(p). Factor j(q).
-3*(q - 2)**2
Factor 50 - 2*v**2 + 10*v - 2/5*v**3.
-2*(v - 5)*(v + 5)**2/5
Let o(n) be the first derivative of -n**5/25 + n**4/10 - n**3/15 - 97. Find c, given that o(c) = 0.
0, 1
Suppose 5*s + 3*s = -2*s. Let q(y) be the second derivative of 0*y**3 + 5*y + s + 0*y**4 - 1/10*y**5 + 0*y**2. Factor q(i).
-2*i**3
Let a(k) = 5*k + 3. Let y be a(1). Find x, given that 7*x**4 - 26*x**2 - 24*x + 2*x**4 - y*x**4 - 3*x**4 - 12*x**3 - 8 = 0.
-2, -1
Suppose 0 = -j - 8 + 63. Factor -20*v**4 - 75*v - 94*v**3 - 16*v**3 + 10 + 185*v**2 + 65*v**4 - j*v**3.
5*(v - 2)*(v - 1)*(3*v - 1)**2
Let p be 246/(-10) + 1 - (-3)/5. Let w be p/(-69) - (-1)/15. Factor 2/5*d - w*d**3 - 2/5*d**2 + 2/5.
-2*(d - 1)*(d + 1)**2/5
Factor -5476 - 1/4*i**2 - 74*i.
-(i + 148)**2/4
Let a(f) = f + 1. Let o(r) = 2 - 6 - 7*r + r**2 - 5*r**2. Let t(h) = 3*a(h) + o(h). Factor t(g).
-(2*g + 1)**2
Let n(o) be the first derivative of -11*o**3/6 + 13*o**2/4 - o - 502. Determine k, given that n(k) = 0.
2/11, 1
Suppose -10 = -3*y - 1. What is s in -s + 0*s**2 - y*s - s - 5*s**2 = 0?
-1, 0
Let z = -21412562/31486233 - 2/70439. Let s = -2/149 - z. Suppose -s*r + 4/3*r**2 + 0 - 2/3*r**3 = 0. Calculate r.
0, 1
Let z(l) be the first derivative of -75/4*l**4 - 70/3*l**3 + 40*l - 8 + 30*l**2 + 9*l**5. Determine n, given that z(n) = 0.
-2/3, 1, 2
Let p(i) be the third derivative of i**9/45360 + i**8/5040 + i**7/1890 + i**4/3 + 2*i**2. Let q(u) be the second derivative of p(u). Factor q(b).
b**2*(b + 2)**2/3
Let t(c) = 26*c**3 + 34*c**2 + 22*c - 22. Let n(d) = -d**3 + 3*d**2 - d + 1. Let z(q) = -6*n(q) - t(q). Find j, given that z(j) = 0.
-2, -1, 2/5
Let l be (16 - (-13461)/(-840))/(4/(-32)). Find s, given that l*s**2 + 144/5 + 24/5*s = 0.
-12
Let s(u) be the second derivative of u**4/12 - u**3/3 - 15*u**2/2 - 4*u + 10. Factor s(i).
(i - 5)*(i + 3)
Let v be (-6*1)/(((-28)/7)/2). Suppose -k + 18 = -v*a, 4 = 5*a + 29. Factor 0*w**k - 2/3*w**2 + 0 + 0*w + 2/3*w**4.
2*w**2*(w - 1)*(w + 1)/3
Let j be ((-4)/(-5))/((-9)/(-90)). Let s be j/(-60) - (-3 + 129/45). Suppose s*g - 1/3*g**2 + 0 = 0. Calculate g.
0
Let q(n) = -n**4 - n**3 - 1. Let i(k) = -5 - 4*k**3 + 194*k**4 + k**3 + 4*k**2 - 199*k**4. Let g(w) = -i(w) + 3*q(w). Let g(c) = 0. What is c?
-1, 1
Let w(b) = -b**3 + b + 1. Let r(z) = -5*z**4 - 191*z**3 - 2535*z**2 - 10989*z - 4. Let x(s) = r(s) + 4*w(s). Solve x(m) = 0 for m.
-13, 0
Let x(m) be the second derivative of m**7/18900 - m**5/900 - 2*m**4 - 17*m. Let v(g) be the third derivative of x(g). Factor v(h).
2*(h - 1)*(h + 1)/15
Determine z so that -3/2*z**2 + 7/2 + 10*z = 0.
-1/3, 7
Factor 11 - 11*i + i**2 + 17*i - 18*i.
(i - 11)*(i - 1)
Let k(m) be the second derivative of -m**5/50 + 7*m**4/30 - 14*m**3/15 + 8*m**2/5 + 87*m. Factor k(a).
-2*(a - 4)*(a - 2)*(a - 1)/5
Let c(k) be the first derivative of -k**5 + 25*k**4 - 590*k**3/3 + 450*k**2 - 405*k - 410. Factor c(b).
-5*(b - 9)**2*(b - 1)**2
Let -1/4*a**3 + 7*a + a**2 + 8 = 0. Calculate a.
-2, 8
Let i = -4/745 + 161/2235. Let p(b) be the second derivative of -3/100*b**5 - 1/60*b**4 + 1/210*b**7 + i*b**3 + 0*b**2 + 1/150*b**6 + 0 - 4*b. Factor p(g).
g*(g - 1)**2*(g + 1)*(g + 2)/5
Factor 0 - 102/5*g + 2/5*g**2.
2*g*(g - 51)/5
Suppose 0 = -5*d + 3*b + 78, 2*d + 0*d + 3*b - 27 = 0. Let i be d/3*(6/(-10) - -1). Suppose -21/4*j + 27/4*j**i - 3/2 = 0. What is j?
-2/9, 1
Suppose 0*b - 20 = 3*f - 4*b, 4*f = 3*b - 15. Let a = -2/127 - -131/254. Factor f*o + 3/2*o**3 + a*o**4 + o**2 + 0.
o**2*(o + 1)*(o + 2)/2
Let k(a) = -a - 8. Let x be k(-4). Let y be 0 - (6/3 + x). Factor -8*t - 3*t**3 + 4*t**y + 7*t - t**2 + t**4.
t*(t - 1)**3
Let z(u) be the first derivative of -2*u**6/3 + 44*u**5/5 - 36*u**4 + 64*u**3/3 + 128*u**2 - 212. Factor z(l).
-4*l*(l - 4)**3*(l + 1)
Find b such that -64*b**3 + 78*b**2 + 48*b + 29 - 55*b - 153*b + 23 + 4*b**4 + 90*b**2 = 0.
1, 13
Let m(o) = -2*o**4 + 4*o**3 - 5*o**2 + 3. 