. What is h in u(h) = 0?
163
Let d(g) = g**2 - 19*g + 74. Let y be d(14). Let u(h) be the third derivative of -1/160*h**6 + 0*h**3 + h**2 + 0*h**5 + 0 + 0*h**y + 0*h. Factor u(j).
-3*j**3/4
Let p(j) be the second derivative of -j**6/450 - j**5/75 + 7*j**3/2 - 33*j. Let h(i) be the second derivative of p(i). Let h(q) = 0. Calculate q.
-2, 0
Let h(c) be the second derivative of 0*c**3 + 0 - 1/90*c**6 + 0*c**2 + 1/60*c**5 + 0*c**4 + 12*c. Factor h(x).
-x**3*(x - 1)/3
Let s be (-54)/24*160/15. Let x be (2/7)/(s/(-21)). Factor 1/2 - 1/4*m**4 - x*m**2 + 3/4*m**3 - 3/4*m.
-(m - 2)*(m - 1)**2*(m + 1)/4
Let l(q) = -q**3 + 21*q**2 + 46*q + 5. Let g be l(23). Suppose -g*p = -4*r - 0 - 10, 3*p - r - 6 = 0. Factor -1/5*y**p - 3/5*y + 0.
-y*(y + 3)/5
Let z(g) be the first derivative of -g**6/900 - g**5/600 + g**4/120 + g**3/3 - 11*g**2 - 35. Let d(t) be the third derivative of z(t). Factor d(w).
-(w + 1)*(2*w - 1)/5
Let x(k) be the first derivative of -k**6/39 - 2*k**5/5 - 24*k**4/13 - 136*k**3/39 - 32*k**2/13 + 186. Solve x(l) = 0 for l.
-8, -2, -1, 0
Let i(l) be the first derivative of 2/21*l**3 + 1 - 2/35*l**5 + 1/7*l**2 - 1/14*l**4 + 0*l. Factor i(y).
-2*y*(y - 1)*(y + 1)**2/7
Let g be 33/(-22)*4/(-3). Factor -8 + 6*m - 2*m**g + 4 + 1 - 1.
-2*(m - 2)*(m - 1)
Suppose -4*l + 19 = 11. Let 3 - 13*q**2 - 21*q**2 + 37*q**l + 6*q = 0. Calculate q.
-1
Let k(j) be the second derivative of j**5/120 - j**4/12 + j**3/4 - j**2/3 - 26*j + 2. Factor k(b).
(b - 4)*(b - 1)**2/6
Let i(l) be the third derivative of l**5/40 - 25*l**4 + 10000*l**3 - 45*l**2 + 5. Factor i(y).
3*(y - 200)**2/2
Let r(s) = -6*s**4 + 75*s**3 - 24*s**2 - 174*s + 129. Let q(y) = -y**4 + 15*y**3 - 5*y**2 - 35*y + 26. Let t(f) = -21*q(f) + 4*r(f). Factor t(w).
-3*(w - 1)**2*(w + 2)*(w + 5)
Let y be (-8)/44 - (2 + 1047/(-132)). Let q(n) be the first derivative of y*n**4 - 14/3*n**5 + 0*n + 25/18*n**6 + 2/3*n**2 + 1 - 28/9*n**3. Factor q(s).
s*(s - 1)**2*(5*s - 2)**2/3
Let b(j) = 7*j**3 - 259*j**2 + 7931*j + 8192. Let h(t) = 4*t**3 - 130*t**2 + 3965*t + 4096. Let w(r) = 6*b(r) - 10*h(r). Factor w(m).
2*(m - 64)**2*(m + 1)
Factor -11*y - y**2 + 6*y - 8*y.
-y*(y + 13)
Let b = 10/19 + -3281/6270. Let k(c) be the third derivative of 4/33*c**3 + 0*c + 5*c**2 - 5/132*c**4 + b*c**5 + 0. Factor k(z).
2*(z - 4)*(z - 1)/11
Factor -284/17*y**2 - 784/17 - 10/17*y**3 - 2072/17*y.
-2*(y + 14)**2*(5*y + 2)/17
Determine o so that 8/13 + 2/13*o**4 + 24/13*o + 2*o**2 + 12/13*o**3 = 0.
-2, -1
Let g(k) = -k**3 - 17*k**2 - 15*k + 19. Let j be g(-16). Let c be 90/105*14/j. Let 5/2*s**3 + 1/2*s**4 + 2*s + 0 + c*s**2 = 0. Calculate s.
-2, -1, 0
Let s(r) = -2*r. Let w(x) = x + 6. Let m be w(-8). Let p be s(m). Determine b, given that 3*b - p*b**2 + 4*b**2 + b**2 + 0*b**2 = 0.
-3, 0
Let b(j) = 9*j**3 - 3*j**2 + 2*j + 7. Let w(f) = -8*f**3 + 2*f**2 - 2*f - 6. Let y(o) = -6*b(o) - 7*w(o). Factor y(t).
2*t*(t + 1)**2
Let x = 343/1881 - -31/171. Solve 2*f**3 - 8/11*f + 0 + x*f**5 - 18/11*f**4 + 0*f**2 = 0 for f.
-1/2, 0, 1, 2
Let q(b) be the second derivative of b**6/6 - 7*b**5/2 + 10*b**4 + 133*b. Suppose q(x) = 0. Calculate x.
0, 2, 12
Let t(h) = -28*h**4 + 29*h**3 + 114*h**2 + 32*h - 22. Let z(q) = -q**5 - q**4 + q**3 - q + 1. Let b(w) = 2*t(w) - 6*z(w). Suppose b(v) = 0. Calculate v.
-1, 1/3, 5
Let s(t) be the first derivative of 0*t - 1/5*t**5 - 2*t**2 - 5/4*t**4 - 8/3*t**3 + 16. Factor s(z).
-z*(z + 1)*(z + 2)**2
Let i(x) = -x**3 + 3*x**2 + 2*x - 1. Let j be i(3). Let c(d) be the third derivative of -1/28*d**4 - 3*d**2 + 0*d - 2/21*d**3 + 0 - 1/210*d**j. Factor c(m).
-2*(m + 1)*(m + 2)/7
Let n be 5/60 - 253/(-420) - 6/21. Find k, given that 0 + 1/5*k**3 - n*k**4 + 0*k + 2/5*k**2 - 1/5*k**5 = 0.
-2, -1, 0, 1
Factor -2/11*g**3 - 4/11*g - 16/11 + 10/11*g**2.
-2*(g - 4)*(g - 2)*(g + 1)/11
Let j(b) be the second derivative of 0 + 1/15*b**3 + 1/10*b**2 + 10*b + 1/60*b**4. Factor j(d).
(d + 1)**2/5
Let x = -11/6 - -25/12. Let u = -56 + 227/4. Factor -u*n - 1/2 - x*n**2.
-(n + 1)*(n + 2)/4
Let x = 55 + -45. Factor 48*t**2 - x + 5*t**3 - 38 - 2 + 105*t.
(t + 5)**2*(5*t - 2)
Let i(b) be the first derivative of -2/11*b + 29 + 0*b**3 + 2/55*b**5 - 2/11*b**2 + 1/11*b**4. Suppose i(r) = 0. What is r?
-1, 1
Let c = -1033 + 1033. Let h(o) be the second derivative of 1/10*o**4 + 1/50*o**5 + 0 + 7*o + c*o**2 + 2/15*o**3. Suppose h(v) = 0. What is v?
-2, -1, 0
Let z(h) = -h**3 + 71*h**2 - 68*h - 136. Let g be z(70). Suppose 8/13*v**2 + 4/13*v**3 - 2/13*v - 2/13*v**5 - 4/13*v**g - 4/13 = 0. Calculate v.
-2, -1, 1
Let k(a) be the first derivative of -7*a**6/9 - 32*a**5/15 - 2*a**4/3 - 83. Factor k(v).
-2*v**3*(v + 2)*(7*v + 2)/3
Find k such that 13*k**3 - 4*k - 3*k**3 + 15*k - 27*k - 6*k**4 + 6 + k**5 + 5*k = 0.
-1, 1, 2, 3
Let y(d) be the third derivative of d**6/24 + d**5/3 + 5*d**4/8 + 8*d**2 - 4. What is l in y(l) = 0?
-3, -1, 0
Factor 21*d**2 + 15*d**3 - 96*d**4 + 0*d - 89*d**4 + 188*d**4 + 9*d.
3*d*(d + 1)**2*(d + 3)
Let q(c) = -20*c**2 + 117*c + 40. Let f(v) = 6*v**2 - 29*v - 10. Let z(n) = -22*f(n) - 6*q(n). Suppose z(x) = 0. What is x?
-5, -1/3
Determine n, given that -26*n**4 - 2 + 4*n**5 - 115/2*n**2 + 19*n + 241/4*n**3 = 0.
1/4, 2
Let v(i) be the first derivative of 3*i**5/20 - 15*i**4/16 - i**3/4 + 51*i**2/8 + 9*i + 270. Suppose v(y) = 0. What is y?
-1, 3, 4
Suppose 707*b = 684*b. Let 4*d**3 + 4/3*d**5 + 0 + b*d - 20/3*d**4 + 12*d**2 = 0. What is d?
-1, 0, 3
Let o(t) = -t**2 + 16*t - 46. Let h be o(4). Factor -121*w**h + 2*w + w + 127*w**2.
3*w*(2*w + 1)
Factor -49*w**2 - 102*w**2 + 5*w + 194*w**2 + 84 - 5*w**3 - 349 + 222*w**2.
-5*(w - 53)*(w - 1)*(w + 1)
Let a(p) be the first derivative of 3*p**4/20 + 8*p**3/15 - p**2/2 - 6*p/5 - 10. Determine j so that a(j) = 0.
-3, -2/3, 1
Suppose -2*o + 3*o = 5. Suppose -o*a = -2*a - 15. What is p in 2*p**3 - 8*p**2 + 23*p**2 - 7*p**3 - 19*p + a + 4*p = 0?
1
Suppose 4*t - 7 = 1. Let f be -2 + -1 - (t - 12). Let d(h) = -13*h**2 + 12*h + 1. Let r(g) = 7*g**2 - 6*g - 1. Let b(v) = f*r(v) + 4*d(v). Factor b(i).
-3*(i - 1)**2
Let s(c) be the first derivative of 0*c + 6*c**2 + 1/2*c**6 - 12*c**3 + 13 - 18/5*c**5 + 39/4*c**4. Factor s(t).
3*t*(t - 2)**2*(t - 1)**2
Solve -43*o**3 + 134*o**3 + 3640*o - 275*o**2 + 3920 - 39*o**3 - 47*o**3 = 0 for o.
-1, 28
Suppose 12 = 3*b - 4*a - 0, -a - 3 = 3*b. Let z(u) be the third derivative of 0 + b*u + 3*u**2 - 1/15*u**5 - 6*u**3 + u**4. Factor z(j).
-4*(j - 3)**2
Suppose 5*q + 2*z = 30, 24 = q - 0*z + 4*z. Let b(u) = u**3 - 3*u**2 - 4*u + 3. Let p be b(q). What is c in 4*c**5 - 2*c**5 - 2*c**5 - c**5 - c + 2*c**p = 0?
-1, 0, 1
Suppose 2*a = -10*a + 48. Let x(w) = 63*w**3 + 258*w**2 + 252*w + 111. Let l(p) = 9*p**3 + 37*p**2 + 36*p + 16. Let y(q) = a*x(q) - 27*l(q). Factor y(n).
3*(n + 1)*(n + 2)*(3*n + 2)
Let w = -20/2023 - -157894/10115. Find m, given that w*m + 18/5*m**3 + 58/5*m**2 + 2/5*m**4 + 36/5 = 0.
-3, -2, -1
Let t(c) = -20*c - 2. Let l be t(-1). What is m in 4 + 41*m**4 + 10*m**2 + 18*m**3 - l*m - 96*m**4 + 41*m**4 = 0?
-1, 2/7, 1
Suppose 9*u - 12*u + 12 = 0. Factor 4*z**2 + 2*z + 0*z - 2*z + u*z.
4*z*(z + 1)
Let c = -303 - -306. Let t(u) be the first derivative of 3/4*u**4 - 3*u**c + 9/2*u**2 - 3*u - 3. Factor t(q).
3*(q - 1)**3
Suppose -197*r + 875 = -22*r. Suppose 3/4*g - 3/2*g**3 - 3/4*g**4 - 3/4 + 3/4*g**r + 3/2*g**2 = 0. What is g?
-1, 1
Suppose -k - 2*h = -2, 4*k - 6*k + 2*h + 4 = 0. Factor 6 + 7*r**3 - 3*r**4 + r**3 - 9*r + 2*r**k + r**3 - 5*r**2.
-3*(r - 2)*(r - 1)**2*(r + 1)
Let r = 7 - 5. Factor -p - p**3 + 7*p - 2*p + 3*p + 4 + r*p**2.
-(p - 4)*(p + 1)**2
Suppose 250*h = 198*h + 156. Factor -1/4 + 1/4*t**2 + 1/4*t - 1/4*t**h.
-(t - 1)**2*(t + 1)/4
Let c(i) be the first derivative of -i**6/2160 + i**5/180 - i**4/48 + 13*i**3/3 - 16. Let s(f) be the third derivative of c(f). Factor s(g).
-(g - 3)*(g - 1)/6
Let f(c) be the second derivative of -c**6/105 - c**5/7 - 25*c**4/42 + 147*c. Determine i, given that f(i) = 0.
-5, 0
Factor 539 + 1155 + 52*l + 14*l - 605 - l**2 + 2*l**2.
(l + 33)**2
Suppose -3*b = -0*b - 5*r - 10, 0 = -3*b + 3*r + 6. Let x(q) be the first derivative of 1/12*q**2 + b*q + 1/18*q**3 - 5. Factor x(o).
o*(o + 1)/6
Let a(j) be the third derivative of j**7/105 - j**6/10 + 2*j**5/5 - 2*j**4/3 - 86*j**2. Factor a(k).
2*k*(k -