What is w?
0, 1
Let g(l) be the third derivative of 0 + 5*l**2 + 0*l - 1/12*l**3 - 1/24*l**4 - 1/120*l**5. Find h, given that g(h) = 0.
-1
Let z(f) be the second derivative of -f**7/168 - 17*f**6/120 - 6*f**5/5 - 31*f**4/6 - 38*f**3/3 - 18*f**2 + 218*f. Factor z(n).
-(n + 2)**4*(n + 9)/4
Let t be 1*10*10/4. Suppose -4*w - 5 = -t. What is l in -10*l + 3 - 5 + w*l**2 + 2 = 0?
0, 2
Solve -4/3 + 4/3*c - 1/3*c**2 = 0.
2
Let r(t) be the third derivative of t**5/120 + t**4/6 + 4*t**3/3 - 83*t**2. Find s such that r(s) = 0.
-4
Let b(h) be the first derivative of 2*h**6/3 + 32*h**5/5 + 24*h**4 + 136*h**3/3 + 46*h**2 + 24*h + 175. Suppose b(f) = 0. Calculate f.
-3, -2, -1
Let t(w) be the first derivative of -2*w**3/15 - 86*w**2/5 - 3698*w/5 + 89. Factor t(m).
-2*(m + 43)**2/5
Let w(d) be the first derivative of -3*d**5/80 + 3*d**4/16 + d**3/8 - 9*d**2/8 + 2*d - 9. Let i(t) be the first derivative of w(t). Solve i(m) = 0 for m.
-1, 1, 3
Let y(h) = h**2 + 5*h - 1. Suppose d + 8 = -i, -d + 20 = -4*i + d. Let a(t) = -t**2 - 6*t + 1. Let c(b) = i*y(b) - 5*a(b). Factor c(n).
-(n - 1)*(n + 1)
Suppose 0*h + 5/3*h**4 - h**3 + 0 - 1/3*h**5 - 3*h**2 = 0. What is h?
-1, 0, 3
Let d be 0 - (-44)/55*(-20)/(-6). Factor -d*c - 4/3 - 1/3*c**3 - 5/3*c**2.
-(c + 1)*(c + 2)**2/3
Suppose -1156*h**3 + 205*h + 63*h + 2176*h**2 + 6 + 6 - 7 + 3 = 0. Calculate h.
-1/17, 2
Let u(d) = -32*d**3 + 64*d**2 - 52*d + 8. Let i(a) = -a**4 - a**3 - a + 2. Let c(b) = -4*i(b) + u(b). Determine n so that c(n) = 0.
0, 2, 3
Suppose -203*d + 487 + 122 = 0. Factor 3/8*k**2 - d - 21/8*k.
3*(k - 8)*(k + 1)/8
Let i(b) = -b - 8 - 2 - 2*b. Let t be i(-4). Let 9*s**2 + 9*s**t + 10*s**4 - 10*s**3 - 14*s**3 - 4*s = 0. What is s?
0, 2/5, 1
Factor -582 + 2*w**2 + 42 + 38*w + w**2 - 143*w - 8*w**2.
-5*(w + 9)*(w + 12)
Let w(l) be the third derivative of 2/1155*l**7 + 1/132*l**6 + 0*l + 0 - 2/165*l**5 - 1/44*l**4 - 6*l**2 + 0*l**3. Suppose w(d) = 0. What is d?
-3, -1/2, 0, 1
Suppose -7 = -3*w - 10. Let q(x) = -25*x**3 + x**2 + x. Let d be q(w). Factor d - 2*i**2 - i**2 - 25 + 9*i.
-3*i*(i - 3)
Find q such that -1/2*q**3 + 9/2*q + 0 + 3/2*q**4 - 27/2*q**2 = 0.
-3, 0, 1/3, 3
Let c(t) be the third derivative of -t**5/360 + t**4/18 - t**3/3 - 3*t**2 - 7. Solve c(m) = 0 for m.
2, 6
Let k be (144 - 152)/((-10)/4). Factor -24/5*h**3 - 48/5*h - 52/5*h**2 - 4/5*h**4 - k.
-4*(h + 1)**2*(h + 2)**2/5
Suppose m - 149 + 38 = 0. Factor -108 + 0*u**4 - 6*u**3 - 6*u**2 + m + 3*u + 3*u**5 + 3*u**4.
3*(u - 1)**2*(u + 1)**3
Let v = 1622/11 + -3211/22. Suppose -3/2*c**2 - 3/4*c**3 + 3/4*c + v = 0. What is c?
-2, -1, 1
Suppose 0 = f - 3*t - 18, 8 = 5*f + 2*t + 3. Let x be (-10)/(-25) - 4*4/(-60). Factor -2/3*y**2 - 2/9 + 2/9*y**f + x*y.
2*(y - 1)**3/9
Let n(c) = -10*c**3 - 4650*c**2 - 4775*c + 45. Let a(v) = -v**3 - 423*v**2 - 434*v + 4. Let y(p) = 45*a(p) - 4*n(p). Factor y(b).
-5*b*(b + 1)*(b + 86)
Let g(o) = -21*o**2 + 320*o - 600. Let i(b) = 4*b**2 - 64*b + 120. Let y(v) = -4*g(v) - 22*i(v). Find t such that y(t) = 0.
2, 30
Factor 0 + 10/3*d - 32/3*d**2 + 2/3*d**5 - 16/3*d**4 + 12*d**3.
2*d*(d - 5)*(d - 1)**3/3
Let g(y) = -5*y**2 + 1775*y - 27000. Let p(t) = t**2 - 296*t + 4500. Let u(a) = -4*g(a) - 25*p(a). Let u(w) = 0. Calculate w.
30
Let s(u) be the second derivative of 3*u**5/100 + 21*u**4/20 + 12*u**3 + 30*u**2 + 143*u. Factor s(g).
3*(g + 1)*(g + 10)**2/5
Let f be (((-195)/(-10))/13)/(2/4). Factor f*y + 2*y**2 + 3*y - 2*y**3 - 7*y + 5*y.
-2*y*(y - 2)*(y + 1)
Let z(p) be the second derivative of 0*p**2 + 1/30*p**6 + 0 - 7*p + 0*p**4 + 0*p**3 - 1/10*p**5. Factor z(f).
f**3*(f - 2)
Let y(m) be the first derivative of -4*m**2 - 2/3*m**3 + 4 - 8*m. Factor y(x).
-2*(x + 2)**2
Let u = -32 - -19. Let b = u - -16. Factor -2*z + z**b - z + 6 - 6*z**2 + 2*z**3.
3*(z - 2)*(z - 1)*(z + 1)
Suppose 0 = 2*m - 5*m. Suppose -2*p + 0*p + 3*o + 51 = m, 4*p - 82 = 2*o. Find x, given that p*x**3 + 0*x**5 + 3*x + 3*x**5 + 0*x - 24*x**3 = 0.
-1, 0, 1
Let d be (-4 - (3 + -2)) + 11 + -8. Let g be (12/(-144))/(19/(-9) - d). Factor -3*m**3 + 9/2*m**2 + 3/4*m**4 - 3*m + g.
3*(m - 1)**4/4
Let v(o) be the second derivative of 1/165*o**6 + 61/66*o**4 + 0 + 37*o + 28/11*o**3 + 36/11*o**2 + 7/55*o**5. Let v(q) = 0. Calculate q.
-6, -1
Suppose 0 = -2*k - 0*k. Suppose 12*x**2 - 4*x**3 - 9*x + k*x**2 + x = 0. What is x?
0, 1, 2
Let y(m) be the third derivative of 121*m**5/300 - 77*m**4/30 + 98*m**3/15 - 24*m**2. Factor y(z).
(11*z - 14)**2/5
Let a be (-822)/(-42) + -14 - (-1 - 0 - -6). Factor 10/7*f - a*f**2 + 6/7.
-2*(f - 3)*(2*f + 1)/7
Factor 0 + 0*w - 1/5*w**5 - w**3 + 4/5*w**4 + 2/5*w**2.
-w**2*(w - 2)*(w - 1)**2/5
Let n be (-5)/(-2)*(-2512)/(-2041). Solve -24/13 + 102/13*f**2 - n*f + 18/13*f**3 = 0.
-6, -1/3, 2/3
Suppose z = 2*g - 4*z - 43, 0 = 4*g - 2*z - 62. Factor -9*u**4 - 5 - 2*u**4 + 50*u**3 - 50*u**2 + 5*u**5 - g*u**4 + 25*u.
5*(u - 1)**5
Suppose -2*c + 6 - 2 = 0. Factor 33*f**3 - 20*f**c + 9*f**2 - 6 - 7*f**4 - 12 - 69*f.
-(f - 3)**2*(f + 1)*(7*f + 2)
Factor 20*r + 5*r**2 - 10*r**2 + 1472 - 1492.
-5*(r - 2)**2
Let g(m) = -m**2 + 6*m + 3. Let u be ((-90)/35)/(-3)*7. Let w be g(u). Factor 0 - 2/3*f + 10/3*f**w - 2/3*f**2 - 2*f**4.
-2*f*(f - 1)**2*(3*f + 1)/3
Let j = -6 - -8. Factor -2*s**3 - 18*s - 18*s + 28*s + 10*s**j.
-2*s*(s - 4)*(s - 1)
Find m such that 2/13*m**3 - 8*m**2 + 104*m + 0 = 0.
0, 26
Find y such that 6/5*y**2 - 2/3*y**3 + 4/15 + 2/15*y**4 - 14/15*y = 0.
1, 2
Let g(h) = -2*h - 10. Let c(b) = -b - 3. Let l(a) = 7*c(a) - 2*g(a). Let d be l(-2). Factor -5*y**3 + d*y - 5*y**2 + 0*y**2 + 0*y**2 + 5*y**4 + 0*y.
5*y*(y - 1)**2*(y + 1)
Let c(x) = -x - 25*x**3 - x**4 + 25*x**3. Let k(s) = 9*s**4 - 3*s**2 + 6*s. Let t(i) = -6*c(i) - k(i). Determine n so that t(n) = 0.
-1, 0, 1
Let n be (15 - (-1 - 1)) + 0. Suppose -1 = -2*q + 3. Suppose -4 + 8*g + 22*g**3 - 47*g**q + 8*g + n*g**2 - 6*g**4 + 2*g = 0. Calculate g.
2/3, 1
Suppose 2*w - 16 = -4*u, 5*w = w + 8. Factor 16*g - u*g - 11*g - 2*g**2.
-2*g*(g - 1)
Let b = -32 + 32. Suppose 2*l = 10, 0 = 4*a - l - b*l - 123. Factor -1 + 3 + 29*h - a*h + h**2.
(h - 2)*(h - 1)
Let b = -205 - -99. Let y be (-2 + 2/((-16)/b))*3. Factor -35*m**3 + y*m + 10*m**4 + 45/2*m**2 - 135/4.
5*(m + 1)*(2*m - 3)**3/4
Let k be 1/(1 - (-21)/(-24)). Let h = k - 6. Solve -7*g - 3*g**3 - 37 + 34 - h*g - 9*g**2 = 0.
-1
Suppose -5*c + 290 = 280. Determine p, given that -48/7*p**c - 27/7*p**3 + 0 + 12/7*p = 0.
-2, 0, 2/9
Suppose 3*t + u = 10, 2*u = 5*t + u - 14. Let c(k) be the second derivative of 1/36*k**4 + 1/30*k**5 + 0*k**t + 0 - k + 0*k**2 + 1/90*k**6. Factor c(y).
y**2*(y + 1)**2/3
Let l(a) be the second derivative of 0*a**4 + 0 + 1/126*a**7 + 0*a**2 + 2/45*a**6 + 12*a + 1/20*a**5 + 0*a**3. Solve l(n) = 0 for n.
-3, -1, 0
Let v(t) = 2*t - 6. Let i be v(-5). Let r = 19 + i. Suppose -6*d**2 + 2*d + r*d**5 - 5*d - d**4 + 7*d**4 = 0. What is d?
-1, 0, 1
Let g = 18 - 46. Let k be (24/g)/(32/(-28)). Factor k*y**4 + 1/4*y**5 + 0 - 1/2*y - 3/4*y**2 + 1/4*y**3.
y*(y - 1)*(y + 1)**2*(y + 2)/4
Let j(b) = 3*b**3 + 3*b**2. Suppose 10*m - 5*m + 20 = 0. Let z(s) = -s**2 + 1. Let p(q) = m*z(q) + j(q). Factor p(d).
(d + 1)*(d + 2)*(3*d - 2)
Let n(q) be the first derivative of -13 - 1/5*q**5 + 0*q + q**4 - 5/3*q**3 + q**2. Factor n(k).
-k*(k - 2)*(k - 1)**2
Let k = 10945/3 - 3648. Factor 0 + 2/3*u + k*u**2.
u*(u + 2)/3
Let h(z) be the second derivative of z**4/20 + 9*z**3/5 + 231*z**2/10 - 186*z. Factor h(j).
3*(j + 7)*(j + 11)/5
Let s = -282 - -282. Factor s + 8/7*d - 4/7*d**2.
-4*d*(d - 2)/7
Suppose 3*w = 3*a - 3 - 6, 4*a - 5*w - 8 = 0. Suppose 4*s - 22 = a*v - 5*v, s = -2*v - 2. Factor -3/5*p - 3/5*p**s - 3/5 + 6/5*p**2 + 6/5*p**3 - 3/5*p**5.
-3*(p - 1)**2*(p + 1)**3/5
Let w be (2/(-4))/(21/84) + (-19)/(-3). Suppose 0 + 5/2*l**2 + 14/3*l**5 - w*l**3 - 1/3*l - 5/2*l**4 = 0. What is l?
-1, 0, 1/4, 2/7, 1
Let s be ((-20)/6)/(98 - 100). Factor s*b**2 - 5*b + 10/3.
5*(b - 2)*(b - 1)/3
Let r(j) be the second derivative of -j**4/24 - j**3/3 + 3*j**2 + 213*j. Factor r(y).
-(y - 2)*(y + 6)/2
Let u(z) = -155*z**3 + 630*z**2 + 170. Let d(h) = -11*h**3 + 45*h**2 + 12. Let t(s) = 85*d(s) - 6*u(s). Determine p, given that t(p) = 0.
0, 9
Let h be 2 - 24/(-28)*(-42)/45. Suppose 3/5*v**2 + 3/5 - h*v = 0. What is v?
1
Let i(x) be the first deriv