6*v**5 - 44*v**3 - 30*v + s*v**2 - 3*v + 8 - 16*v**4 = 0.
-2, 1/2, 1
Factor 35*y**4 + 11*y**4 - 54*y**4 + 4*y**5.
4*y**4*(y - 2)
Suppose 3*y - 2 = 2*y. Let f = y - 0. Factor 3*r**2 - 3*r**2 - 50*r - 3*r**f + 44*r.
-3*r*(r + 2)
Let f be 1/(51/(-68)*(-6)/45). Suppose -2*d + d = -2. Factor f*i**3 - 4 - 14*i**2 + d + 2 + 4*i.
2*i*(i - 1)*(5*i - 2)
Let i be (-6)/(-4) - ((3 - 11) + (-140)/(-15)). Factor 0 + 1/3*p**2 + 0*p**3 + i*p**5 - 1/3*p**4 - 1/6*p.
p*(p - 1)**3*(p + 1)/6
Let m(u) = -190*u**3 + 8370*u**2 - 8290*u - 55. Let l(z) = -7*z**3 + 310*z**2 - 307*z - 2. Let s(o) = 55*l(o) - 2*m(o). Factor s(g).
-5*g*(g - 61)*(g - 1)
Let t = 28 + -28. Suppose 3*r - 2*r = -t*r. Solve r - 1/4*y**3 - 1/4*y**4 + 1/2*y**2 + 0*y = 0.
-2, 0, 1
Let s be (1/36)/(9/72*4). Let a(w) be the second derivative of 0 + 2/3*w**2 - s*w**4 + 1/9*w**3 + 5*w. Suppose a(y) = 0. What is y?
-1, 2
Let f(s) = -50*s**2 - 60*s - 18. Let q be -7 + 3 + ((-15)/(-3) - 6). Let b(r) = 100*r**2 + 120*r + 36. Let y(n) = q*f(n) - 3*b(n). Factor y(k).
-2*(5*k + 3)**2
Let f(w) be the second derivative of -w**4/78 + 6*w**3/13 - 17*w**2/13 + 4*w - 2. Factor f(r).
-2*(r - 17)*(r - 1)/13
Let -7*a + 2*a**2 - 11*a - 65 + 33 + 32 = 0. Calculate a.
0, 9
Solve 16/5*f + 2/15*f**2 + 0 = 0.
-24, 0
Let a = 1412 + -1412. Let y(p) be the second derivative of 6*p + a*p**2 + 0 - 1/7*p**3 - 1/42*p**4. Solve y(q) = 0.
-3, 0
Let 1/6*u**2 + 1/3*u - 4/3 = 0. What is u?
-4, 2
Let p(x) = -4*x**2 + 3*x + 1. Let b = 54 + -57. Let c(r) = -9*r**2 + 6*r + 3. Let n(h) = b*c(h) + 7*p(h). Determine k, given that n(k) = 0.
1, 2
Let t(x) be the third derivative of -x**6/96 - 11*x**5/240 - 7*x**4/96 - x**3/24 - 76*x**2. Factor t(z).
-(z + 1)**2*(5*z + 1)/4
Factor 386/5*y**2 + 512/5 - 12*y**3 + 192*y + 2/5*y**4.
2*(y - 16)**2*(y + 1)**2/5
Let s = 8/29 - -5/87. Let v(h) be the second derivative of 4*h - s*h**2 + 1/30*h**5 - 1/6*h**4 + 0 + 1/3*h**3. Factor v(g).
2*(g - 1)**3/3
Let s(w) = -22*w**3 - 70*w**2 - 84*w + 3. Let u(n) = 46*n**3 + 138*n**2 + 168*n - 7. Let h(j) = -7*s(j) - 3*u(j). Solve h(g) = 0.
-3, -7/4, 0
Factor -296*k + 12 - 77*k**2 + 268*k - 15*k**2 - 52*k**3.
-4*(k + 1)**2*(13*k - 3)
Suppose -16/3*q**4 + 8*q**3 + 0 + 4/3*q + 4/3*q**5 - 16/3*q**2 = 0. What is q?
0, 1
Let m(a) be the third derivative of -a**5/12 - 5*a**4/12 - 422*a**2. Factor m(n).
-5*n*(n + 2)
Let a(u) be the first derivative of -u**4/2 + 218*u**3/3 - 215*u**2 + 214*u - 492. Find x, given that a(x) = 0.
1, 107
Solve -216*p + 1053/5*p**2 - 129/5*p**3 + 324/5 - 16/5*p**5 - 152/5*p**4 = 0.
-6, 3/4, 1
What is u in -179969*u**4 + 179972*u**4 + 291*u**2 - 57*u**3 - 514 - 135*u + 28 = 0?
-1, 2, 9
Let f(a) be the second derivative of -2/3*a**3 + 1/6*a**4 + 0 - 1/60*a**5 + 4/3*a**2 - 14*a. Find u, given that f(u) = 0.
2
Suppose -2*j + 2 - 4 = 2*a, -4*a - 16 = 0. Let c be ((-26)/j + 6)*(-3)/2. Determine l so that -2/7*l**2 - 2/7*l**c + 0 - 4/7*l**3 + 0*l = 0.
-1, 0
Let u(a) be the first derivative of a**7/105 - 3*a**6/40 + a**5/6 - a**4/8 - 15*a**2 - 3. Let i(d) be the second derivative of u(d). Factor i(b).
b*(b - 3)*(b - 1)*(2*b - 1)
Let a be 2/5 - 36/90. What is s in a*s - 20*s + 8 + 3*s**2 - 13 + 2*s**2 + 20*s**3 = 0?
-1, -1/4, 1
Let h(c) be the third derivative of 2*c**7/945 - c**6/15 + 7*c**5/9 - 116*c**4/27 + 32*c**3/3 - 25*c**2. Determine s, given that h(s) = 0.
1, 4, 9
Let t = 36 - 107/3. Let j = -640 + 640. Find h, given that -t*h + j - 1/6*h**2 = 0.
-2, 0
Suppose 4 = 2*w - 0*w. Factor -8*c**3 + 2 - 4*c**5 + 8*c**2 - 10*c**4 + 2 - w*c**4 + 12*c.
-4*(c - 1)*(c + 1)**4
Let o(v) be the first derivative of v**6/30 - 3*v**5/25 - 7*v**4/20 + v**3 + 9*v**2/5 - 407. Let o(u) = 0. Calculate u.
-2, -1, 0, 3
Let z(i) = -i**2 - 8*i - 3. Let y be z(-9). Let o(k) = -2*k - 24. Let m be o(y). Factor l**2 + 0*l + 7/2*l**3 + m - 2*l**4.
-l**2*(l - 2)*(4*l + 1)/2
Let w(b) be the third derivative of b**7/2100 - b**6/100 + 9*b**5/100 - 9*b**4/20 + 5*b**3/2 + 5*b**2. Let f(h) be the first derivative of w(h). Factor f(o).
2*(o - 3)**3/5
Let q(c) = c**3 + 9*c**2 + 14*c - 4. Let z be q(-7). Let p be (-9)/z + (-48)/64. Find o such that 0*o + 0 + 3/2*o**2 - p*o**3 + 3/2*o**5 - 3/2*o**4 = 0.
-1, 0, 1
Let i(p) be the second derivative of 1/2*p**2 + 1/90*p**6 + 0 - 1/10*p**5 + 1/3*p**4 - 5/9*p**3 - 16*p. Solve i(m) = 0.
1, 3
Let m be (2 + 1)/((-15)/10). Let z(f) = -16*f**2 - 153*f - 41. Let q(h) = 8*h**2 + 76*h + 20. Let w(p) = m*z(p) - 5*q(p). Factor w(y).
-2*(y + 9)*(4*y + 1)
Let g = 3533 + -3533. What is t in -2*t**3 + 4/3*t**2 + g - 1/3*t - 1/3*t**5 + 4/3*t**4 = 0?
0, 1
Suppose -19 = -5*x - 9. Factor -9*z + 4*z**x + 0*z**2 - z**2.
3*z*(z - 3)
Let b(s) = s**2 + 13*s - 11. Let o be b(-14). Determine j so that -4*j**4 + 4*j**2 + 6*j - 4*j**3 + 0*j**o - 2*j = 0.
-1, 0, 1
Let r = -470/17 + 5204/187. Suppose -6/11 - r*l**2 - 8/11*l = 0. Calculate l.
-3, -1
Let a be 20/24 - (-60)/90. Factor 1/4*w**3 + 0 + a*w**2 + 0*w.
w**2*(w + 6)/4
Suppose 25*c + 4 = 26*c. Let x(k) be the third derivative of -1/6*k**c + 1/105*k**7 + 0*k + 0*k**5 + 0 - 1/3*k**3 - 4*k**2 + 1/30*k**6. Let x(l) = 0. What is l?
-1, 1
Factor -9*n**5 + 84*n**3 - 90*n**3 + 11*n**5 - 10*n**2 + 2*n**4 - 4*n.
2*n*(n - 2)*(n + 1)**3
Factor 34*f**3 + 37*f**3 + 51*f + 30*f**2 + 24 + 30*f**3 - 98*f**3.
3*(f + 1)**2*(f + 8)
Suppose -16/7*l**2 + 2/7*l**4 + 0 + 4/7*l**3 + 0*l = 0. Calculate l.
-4, 0, 2
Let r(p) be the third derivative of p**9/15120 - p**8/1680 + p**7/504 - p**6/360 + 3*p**4/4 - 13*p**2. Let w(t) be the second derivative of r(t). Factor w(u).
u*(u - 2)*(u - 1)**2
Let k(c) be the third derivative of -c**6/360 - 4*c**5/45 + 19*c**4/18 - 40*c**3/9 + c**2 + 17. Factor k(i).
-(i - 2)**2*(i + 20)/3
Let b(j) = j**2 - 8*j + 4. Let m be b(8). Factor -8*c + m*c**3 + 11*c**5 - 7*c**5 + 3*c**2 + 3*c**4 + 9*c**2 - 15*c**4.
4*c*(c - 2)*(c - 1)**2*(c + 1)
Determine n so that 2/7*n**5 - 16/7*n + 8/7 + 2/7*n**2 - 10/7*n**4 + 2*n**3 = 0.
-1, 1, 2
Suppose 5*p + 25 = 0, 2*x + 110*p = 107*p - 15. Let 0 - 2/11*s**2 + 8/11*s**5 - 8/11*s**3 + 2/11*s**4 + x*s = 0. Calculate s.
-1, -1/4, 0, 1
Let g(s) = -s**3 + 14*s**2 - 13*s + 4. Let o = -4 - -2. Suppose -9*h - 18 = -3*h. Let y(w) = -15*w**2 + 12*w - 3. Let z(p) = h*g(p) + o*y(p). Factor z(j).
3*(j - 2)*(j - 1)**2
Let m(t) = -12*t - 136. Let b be m(-12). Let c(w) be the first derivative of 2/5*w**5 - 6*w - b*w**2 + 0*w**4 - 4*w**3 + 4. Factor c(u).
2*(u - 3)*(u + 1)**3
Suppose -3/4*x**2 - 15/2*x + 0 = 0. Calculate x.
-10, 0
Let d = 7 - 23. Let i = 19 + d. What is o in 3*o**i + 4*o**2 - o**3 + 2*o**3 + 19*o**4 - 4*o - 23*o**4 = 0?
-1, 0, 1
Let y(f) = -f**3 - f - 1. Let n(c) = c**4 - 2*c**3 - 9*c - 5. Let j = -2 + 5. Let s be 4 + j*(-8)/12. Let w(l) = s*n(l) - 10*y(l). Find m, given that w(m) = 0.
-2, 0, 1
Let t(w) be the third derivative of -60*w**5 - 7*w**2 - 100/3*w**6 + 0 - 45*w**4 + 0*w - 18*w**3. Let t(v) = 0. Calculate v.
-3/10
Let x(b) be the second derivative of -8/15*b**3 + 3*b**6 + 0 - 2/15*b**4 + 9*b + 13/5*b**5 + 0*b**2. Factor x(p).
2*p*(5*p + 2)**2*(9*p - 2)/5
Let d(u) be the first derivative of 5*u**4/32 + 11*u**3/3 - 131*u**2/16 + 19*u/4 - 282. Factor d(r).
(r - 1)*(r + 19)*(5*r - 2)/8
Let v = 7427 + -51977/7. Let -2/7*o**2 + v*o - 18/7 = 0. What is o?
3
Factor -7*n**2 - 4*n**2 + 88 - 36*n + 7*n**2.
-4*(n - 2)*(n + 11)
Suppose 16 = 10*d - 2*d. Let h(p) be the third derivative of 0*p**3 + 0*p**6 - 1/420*p**7 + 0 + 0*p**4 + 0*p - 7*p**d + 0*p**5. Factor h(b).
-b**4/2
Suppose -15 = 4*y - 27. Factor -9 + 28*m - 4*m**4 + 17*m**3 + 6*m**3 - y*m**3 + 1 - 36*m**2.
-4*(m - 2)*(m - 1)**3
Let z(j) be the third derivative of -1/6*j**3 - 1/12*j**4 - 1/540*j**6 + 0*j + 0 + 3*j**2 + 1/45*j**5. Let u(n) be the first derivative of z(n). Factor u(i).
-2*(i - 3)*(i - 1)/3
Determine d, given that -9*d + 0 + 1/3*d**2 = 0.
0, 27
Let i(a) be the second derivative of -a**6/30 - 3*a**5/20 + a**4/2 + 14*a**3/3 + 12*a**2 - 218*a. Find q, given that i(q) = 0.
-2, 3
Let f = -106 + 108. Suppose 4*x + c - 1 + f = 0, -3*x = -3*c - 3. Find u, given that 1/8*u**4 + 0*u + 0*u**2 + 1/8*u**5 + x*u**3 + 0 = 0.
-1, 0
Suppose -56 = -11*y - 17*y. Suppose 16*k = -y*k - 3*k. Factor k - 5/2*w**2 + 1/2*w**3 + 1/2*w**4 + 3/2*w.
w*(w - 1)**2*(w + 3)/2
Let b(g) = -4*g**5 + 3*g**3 - 3*g - 3. Suppose 82*i + 12 = 79*i. Let