h(k) = c*u(k) + 7*a(k). Factor h(f).
-3*f**3
Let c(r) be the third derivative of -r**6/72 - r**5/12 - 5*r**4/24 + r**3/3 - 13*r**2. Let v(k) be the first derivative of c(k). Factor v(i).
-5*(i + 1)**2
Let u(i) = -6*i**3 - 5*i**2 + 11*i - 5. Let t(j) = 3*j**3 + 3*j**2 - 6*j + 3. Let o = -4 - -7. Let b = 2 + 3. Let z(n) = b*t(n) + o*u(n). Factor z(d).
-3*d*(d - 1)*(d + 1)
Suppose 0 = 5*u + 2*c - 0*c - 14, 20 = 2*u - 4*c. Suppose 2*h - l = h + 7, -5*l = 2*h. Factor 19*j**4 - 3*j**u - j**h + 2*j - 5*j**5 - 12*j**3 + 0*j**5.
-2*j*(j - 1)**3*(3*j + 1)
Let b = 133/671 - 1/61. Suppose -47 = -13*f - 21. Suppose -2/11*d - 4/11 + b*d**f = 0. Calculate d.
-1, 2
Let l(u) be the third derivative of 529*u**7/735 + 92*u**6/35 + 311*u**5/105 + 4*u**4/7 + u**3/21 - 70*u**2 - 3. Suppose l(v) = 0. Calculate v.
-1, -1/23
Let z = -5/4513 + 4533/18052. Let 0 - z*u**2 - u = 0. Calculate u.
-4, 0
Let w be 2/(-10)*(13 - 13). Let -2/3*c**2 + w*c + 0 = 0. Calculate c.
0
Let i = 76 - 301/4. Let h(t) be the first derivative of 9 + i*t**3 - 3/4*t - 3/4*t**2. Factor h(o).
3*(o - 1)*(3*o + 1)/4
Suppose -4*d = z - 14, -3*d + 3 + 2 = -2*z. Suppose -2*k - 2*y = -4, 8 = -4*k + y + d*y. Suppose k*i - 2*i**2 - i + 7*i - 5*i = 0. Calculate i.
0, 1/2
Let r(t) be the third derivative of -t**5/60 + 8*t**4/3 - 512*t**3/3 - 32*t**2. Find b, given that r(b) = 0.
32
Let m = 43/252 - 1/36. Suppose 11*j + 2 = -32 + 56. Suppose -2/7 + 1/7*o - m*o**3 + 2/7*o**j = 0. Calculate o.
-1, 1, 2
Factor 6*b**2 - 188*b - 426*b - 70 + 160 - 66*b + 136.
2*(b - 113)*(3*b - 1)
Let s(z) be the first derivative of -z**3/2 - 267*z**2/2 - 23763*z/2 - 543. Find u such that s(u) = 0.
-89
Solve 878 - 16*i**2 - 12*i**2 + 4*i**3 - 878 = 0 for i.
0, 7
Let r(n) be the second derivative of 11*n - 1/18*n**4 + 0 + 1/3*n**3 + 4/3*n**2. Let r(y) = 0. What is y?
-1, 4
Let k(h) be the first derivative of -h**4/14 - 4*h**3/21 + 32. Factor k(i).
-2*i**2*(i + 2)/7
Let q = -5/4 + 103/12. Let r(k) be the first derivative of -5*k**2 + 4 - 6*k - 3/2*k**4 + q*k**3. Factor r(c).
-2*(c - 3)*(c - 1)*(3*c + 1)
Let y(a) be the second derivative of -a**8/3360 + a**7/630 + a**6/360 - a**5/30 + 5*a**4/4 - 25*a. Let k(d) be the third derivative of y(d). Factor k(w).
-2*(w - 2)*(w - 1)*(w + 1)
Let a(u) be the second derivative of -24*u + 0 - 1/36*u**4 + u**2 - 1/18*u**3. Factor a(g).
-(g - 2)*(g + 3)/3
Let w(x) be the second derivative of x**4/3 + 34*x**3/3 - 36*x**2 - 323*x. Factor w(t).
4*(t - 1)*(t + 18)
Let i(j) be the third derivative of -j**5/15 + 23*j**4/24 + j**3 - 551*j**2. Find f such that i(f) = 0.
-1/4, 6
Let o be ((-96)/128)/((-21)/2). Let z(l) be the second derivative of -1/2*l**4 - 1/2*l**3 + 0 + 1/10*l**6 + 3/2*l**2 + 4*l + 3/10*l**5 - o*l**7. Factor z(h).
-3*(h - 1)**3*(h + 1)**2
Let g(m) be the first derivative of 9/2*m**2 - 6 - m**3 + 6*m - 9/4*m**4 - 3/5*m**5. Factor g(c).
-3*(c - 1)*(c + 1)**2*(c + 2)
Let u be (2 - 0) + (9117/15)/3. Let v = u - 204. Factor -v*c**2 - 6/5*c + 0.
-3*c*(c + 2)/5
Let x(i) be the second derivative of -i**7/420 - i**6/75 - 3*i**5/200 + 8*i + 3. Factor x(j).
-j**3*(j + 1)*(j + 3)/10
Suppose 0 = 3*c - 18, 4*p + 3*c = 50. Factor -8/3*t**2 - p*t - 6.
-2*(2*t + 3)**2/3
Suppose 3*w + o = 84, 0 = 6*w - w + 5*o - 140. Suppose 0 = -n - 5*n + 12. Determine v, given that 28 - 4*v**3 + n*v**4 - w + 2*v**2 = 0.
0, 1
Let l be 110/100 + 4/8. Factor 8/5*m + l + 2/5*m**2.
2*(m + 2)**2/5
Let f(b) be the second derivative of -b**4/12 + 7*b**3/6 + 5*b**2 - 8*b. Let y be f(8). Factor -v**3 - v + 2*v**y + 3*v**3 - 2*v**3 + v**3 - 2.
(v - 1)*(v + 1)*(v + 2)
Let m(g) be the second derivative of -18*g + 1/2*g**4 + 0 - 1/10*g**6 + 3/20*g**5 + 0*g**3 + 0*g**2. Find o such that m(o) = 0.
-1, 0, 2
Let o be (4/(-14) - -2) + -12*(-20)/(-420). Factor 0 - 4/7*i**2 - 4/7*i**3 + o*i.
-4*i*(i - 1)*(i + 2)/7
Let t(u) be the first derivative of -3*u**5/5 - 39*u**4/4 - 63*u**3 - 405*u**2/2 - 324*u - 357. Factor t(p).
-3*(p + 3)**3*(p + 4)
Let -7/5*v**2 + 2/5 + 2/5*v**5 + 1/5*v**4 - 7/5*v**3 + 1/5*v = 0. Calculate v.
-1, 1/2, 2
Suppose -4 - 8 = -2*c - 4*m, 0 = 5*c + 2*m - 22. Factor 0 - 1/6*s + 0*s**c + 0*s**2 - 1/6*s**5 + 1/3*s**3.
-s*(s - 1)**2*(s + 1)**2/6
Let t(r) = -r**2 - 19*r - 45. Let f be t(-16). Factor -8/9 - 56/9*j - 50/9*j**4 - 46/3*j**2 - 140/9*j**f.
-2*(j + 1)**2*(5*j + 2)**2/9
Let x(h) = 3*h**4 - 7*h**3 + 6*h**2 + 19*h. Let a(n) = -2*n**4 - n**3 + 3*n**2 - n. Let p(f) = -3*a(f) - 3*x(f). Determine i, given that p(i) = 0.
-1, 0, 3, 6
Factor -41 - 7*p + p**2 + 101 - 50.
(p - 5)*(p - 2)
Factor -18/5*x + 2/5*x**2 + 28/5.
2*(x - 7)*(x - 2)/5
Let t(b) be the second derivative of -b**8/1680 + b**7/420 + 3*b**3 + 2*b. Let v(w) be the second derivative of t(w). Let v(i) = 0. What is i?
0, 2
Let p(a) be the second derivative of 15/2*a**3 - 2*a + 0*a**2 + 5/3*a**4 + 0. Factor p(d).
5*d*(4*d + 9)
Let n(s) be the first derivative of s**6/18 - 7*s**5/15 + 13. Determine o so that n(o) = 0.
0, 7
Let u = -5/71 - -5771/284. Find b such that 0 + 81/2*b**2 - u*b + 15/2*b**4 - 3/4*b**5 - 27*b**3 = 0.
0, 1, 3
Let r(p) = -p**2 + 4*p - 1. Let x be r(3). Factor -8*k - k + 0*k**3 + 3*k**x + 8*k - 3 + k**3.
(k - 1)*(k + 1)*(k + 3)
Let d(r) be the second derivative of r**7/84 - r**6/30 - r**5/40 + r**4/12 + 183*r. Factor d(w).
w**2*(w - 2)*(w - 1)*(w + 1)/2
Let q(r) be the first derivative of r**6/18 - 4*r**5/15 + r**4/6 + 4*r**3/9 - r**2/2 + 41. What is o in q(o) = 0?
-1, 0, 1, 3
Let u(j) be the third derivative of -7*j**2 + 7/6*j**3 + 0 - 1/40*j**5 + 1/120*j**6 - 1/4*j**4 + 0*j. Let g(c) be the first derivative of u(c). Factor g(w).
3*(w - 2)*(w + 1)
Suppose 0 = -4*h + 3*h - 5*w + 17, h + w = 5. Factor 0*t**3 + t**3 - 149*t**2 - t + 151*t**2 + h*t.
t*(t + 1)**2
Find g such that 6*g - 10*g + 8*g**2 + 4*g**3 + 8*g = 0.
-1, 0
Let q(g) be the third derivative of -1/16*g**4 + 0*g**3 + 0*g - 1/40*g**6 + 0 - 4*g**2 + 1/280*g**7 + 1/16*g**5. Suppose q(d) = 0. Calculate d.
0, 1, 2
Solve -10/17*k**2 + 8*k - 78/17 = 0.
3/5, 13
Let t(z) be the second derivative of 0 + 46/15*z**6 + 4*z**3 + 1/3*z**4 - 7*z - 10/21*z**7 - 5*z**5 + 0*z**2. What is w in t(w) = 0?
-2/5, 0, 1, 3
Let c(b) be the third derivative of 0 + 1/300*b**5 + 12*b**2 - 1/200*b**6 + 1/1680*b**8 + 0*b**3 + 0*b - 1/1050*b**7 + 1/60*b**4. Factor c(h).
h*(h - 2)*(h - 1)*(h + 1)**2/5
Let z(a) be the third derivative of 7*a**5/510 - a**4/4 + 14*a**3/51 - 3*a**2 + 27. Find x, given that z(x) = 0.
2/7, 7
Suppose -2*g**3 + 6 + 113*g - 104*g - g**3 = 0. Calculate g.
-1, 2
Let f be (-66)/44*8/(-42). Let -f*k + 2/7*k**2 - 4/7 = 0. What is k?
-1, 2
Suppose -36/5 - 12/5*n + 3/5*n**2 = 0. Calculate n.
-2, 6
Suppose -43*r = -50*r. Let f(j) be the third derivative of 0*j**5 - 1/1008*j**8 + 0 + 1/180*j**6 + 3*j**2 + 0*j**4 - 1/630*j**7 + r*j + 0*j**3. Factor f(t).
-t**3*(t - 1)*(t + 2)/3
Let l = 717 - 715. Find k such that 2/9*k**l + 2/3*k - 8/9 = 0.
-4, 1
Let n be (-2)/((-312)/141) + ((-504)/(-234))/(-14). Factor -n - 3/2*z - 3/4*z**2.
-3*(z + 1)**2/4
Let v(t) be the third derivative of t**8/112 + t**7/60 - 17*t**6/240 - 3*t**5/40 + 11*t**4/48 + t**3/6 + t**2 - 4*t. What is w in v(w) = 0?
-2, -1, -1/6, 1
Let y = -3689/10 + 369. Let s(f) be the second derivative of 0 - 1/3*f**4 + 2*f**2 - 1/3*f**3 + 4*f + y*f**5. Factor s(n).
2*(n - 2)*(n - 1)*(n + 1)
Factor 2*o + 16*o**2 - 600*o**3 + 604*o**3 + 8 + 18*o.
4*(o + 1)**2*(o + 2)
Let o = 112 + 28. Solve 128*b**2 - o*b**2 + 12*b**3 + 0*b**4 - 3*b**4 = 0 for b.
0, 2
Let d = -69 - -74. Factor -22*l**2 + 5*l**4 + 0*l**4 - 5*l**d + 17*l**2 + 5*l**3.
-5*l**2*(l - 1)**2*(l + 1)
Let i(t) be the first derivative of t**3/3 + 2*t**2 + 4*t - 4. Determine o, given that i(o) = 0.
-2
Let u = -2178 - -2184. Factor u - 2*w**3 - 14*w - 34/3*w**2.
-2*(w + 3)**2*(3*w - 1)/3
Let p(n) be the second derivative of -29*n**6/105 + 2*n**5/35 + n + 16. Suppose p(k) = 0. What is k?
0, 4/29
Let t be (((-15)/21)/5)/((-1)/117). Let g = -1273/77 + t. Factor 6/11*p**4 + 0*p + g*p**2 + 2/11*p**5 + 6/11*p**3 + 0.
2*p**2*(p + 1)**3/11
Let i be ((2 - 5)/(-3))/(2/6). Solve -32*y**i - 24*y**2 + 96*y**3 + 12*y - 49*y**3 - 3*y**4 = 0.
0, 1, 2
Let l(w) = -2*w**3 - 40*w**2 - 102*w - 64. Let s(d) = d**3 - 2*d**2 - 3*d. Let j(v) = -l(v) + 2*s(v). Factor j(b).
4*(b + 1)*(b + 4)**2
Determine w so that 11/2 