/2
Let k(r) be the first derivative of 1 - 2/7*r**2 + 3/7*r + 1/21*r**3. Factor k(o).
(o - 3)*(o - 1)/7
Let y(v) be the first derivative of v**3/3 + 8*v**2 - 113. Factor y(k).
k*(k + 16)
Let j(t) be the first derivative of -4*t**3/15 - 16*t**2 - 156*t/5 + 3. Factor j(r).
-4*(r + 1)*(r + 39)/5
Let k(x) be the third derivative of -1/180*x**5 + 0 + 5/72*x**4 + 0*x - 4*x**2 - 1/6*x**3 - 1/360*x**6. Factor k(a).
-(a - 1)**2*(a + 3)/3
Suppose r + 4*u - 14 = 0, 4*r - 5*u + 4 = -24. Let d be r*1*3/(-8). Suppose -1/4*o + 1/4*o**4 + 1/4*o**3 + 1/2 - d*o**2 = 0. Calculate o.
-2, -1, 1
Let p be (0*2/(-8))/(-2) - -2. Find n, given that -19*n**p - 26*n**2 + 225*n + 3*n**3 - 286 - 89 = 0.
5
Let p = 20 + -13. Let -3 + 21*r + 2*r + 2 + p + 7*r**2 = 0. What is r?
-3, -2/7
Let k(h) be the second derivative of -h**7/504 + h**6/48 - 9*h**4/4 - 5*h. Let n(c) be the third derivative of k(c). Factor n(d).
-5*d*(d - 3)
Let q(s) = 64 - 7*s**2 - 80 - 9*s**2 + s**3 - 16*s. Let c be q(17). Find d such that -3/2*d + c + 1/2*d**2 = 0.
1, 2
Suppose -2*w = -h - 5, -3*w + 15 = 3. Factor -3 + h - 1 - 25*z + 35*z**2 - 9.
5*(z - 1)*(7*z + 2)
Let c = 59/40 - 11/10. Let r(q) be the second derivative of -1/48*q**4 + 1/12*q**3 + 2*q + c*q**2 + 0. Find o such that r(o) = 0.
-1, 3
Find f such that 2*f**3 + 0 - 9/2*f**2 + 5/2*f = 0.
0, 1, 5/4
Let c be 312/(-21) + (-2)/14. Let l = c + 18. Factor -2*u - 3*u + 15*u**2 + 28*u**3 + 5*u**2 - l*u.
4*u*(u + 1)*(7*u - 2)
Let v(s) be the second derivative of s**4/114 - 3*s**3/19 + 20*s**2/19 - 111*s. Factor v(i).
2*(i - 5)*(i - 4)/19
Let c(b) = -4*b**2 - 8*b + 3. Let z(r) = -5*r**2 - 8*r + 1. Let p(q) = 4*c(q) - 3*z(q). Factor p(f).
-(f - 1)*(f + 9)
Let o(t) = 3*t**3 + 15*t**2 - 51*t - 192. Let j(s) = -3*s**3 - 16*s**2 + 52*s + 192. Let u(d) = 3*j(d) + 4*o(d). Factor u(h).
3*(h - 4)*(h + 4)**2
Let v(r) be the first derivative of 1/18*r**2 - 1/27*r**3 + 7 + 1/9*r - 1/36*r**4. Factor v(k).
-(k - 1)*(k + 1)**2/9
Let z(t) be the first derivative of -t**4/6 - 8*t**3/9 + 4*t**2/3 + 32*t/3 + 84. Determine p so that z(p) = 0.
-4, -2, 2
Let p(x) = 7*x**2 - 19*x + 21. Let c(h) = 4*h**2 - 9*h + 11. Let s(l) = -11*c(l) + 6*p(l). Let o(t) = t**2 + 8*t - 3. Let f(u) = 5*o(u) + 3*s(u). Factor f(j).
-j*(j + 5)
Let t(l) = l**4 + 1. Let a be -1*((-6)/1 - -2). Let b(g) = -2 - 3 - 1 + a. Let w(k) = b(k) + 2*t(k). What is u in w(u) = 0?
0
Let x(o) be the second derivative of 5*o**8/672 - 3*o**7/280 + o**6/240 - 11*o**2/2 - o. Let t(r) be the first derivative of x(r). Factor t(n).
n**3*(2*n - 1)*(5*n - 2)/4
Let b(n) = 7*n**3 - n**2 - 1. Let k(q) = 9*q**3 + 33*q**2 - 36*q - 1. Let i(w) = b(w) - k(w). Determine t so that i(t) = 0.
-18, 0, 1
Factor 225 - 285 - 10*g**2 + 96*g - 29*g**2 + 3*g**3.
3*(g - 10)*(g - 2)*(g - 1)
Let a(w) = -w**2 - 3*w + 8. Let p be a(-9). Let m = p - -50. Factor -1/2*h + 1/4*h**m - 1/4 + 1/2*h**3 + 0*h**2.
(h - 1)*(h + 1)**3/4
Let r(k) = 8*k**2 + 274*k + 4898. Let w(a) = 18*a**2 + 545*a + 9795. Let h(b) = 5*r(b) - 2*w(b). Find f such that h(f) = 0.
-35
Suppose -w = -28*w + 378. Let o = w + -10. Factor -o*l**3 - 8/3*l**2 - 2/3*l**5 + 0 - 8/3*l**4 - 2/3*l.
-2*l*(l + 1)**4/3
Let g(n) be the second derivative of -n**7/105 - n**6/30 - n**5/30 - 29*n**2/2 - 20*n. Let m(q) be the first derivative of g(q). Factor m(d).
-2*d**2*(d + 1)**2
Let r(q) = 3*q**4 - 9*q**3 + 3*q**2 + 12*q + 3. Let j(l) = -6*l**4 + 18*l**3 - 7*l**2 - 24*l - 7. Let m(f) = -3*j(f) - 7*r(f). Factor m(b).
-3*b*(b - 2)**2*(b + 1)
Let x = 6/3179 - -82612/22253. Factor -4/7*i - 6/7*i**3 - 16/7 + x*i**2.
-2*(i - 4)*(i - 1)*(3*i + 2)/7
Let 29/6*q - 1/6*q**2 - 14/3 = 0. What is q?
1, 28
Factor 60/7*w - 2/7*w**2 - 450/7.
-2*(w - 15)**2/7
Factor -10/9*j**2 - 2/3*j + 0 + 4/9*j**3.
2*j*(j - 3)*(2*j + 1)/9
Let j = 2161 - 2159. Find a such that 5 - 7*a - 3/4*a**j = 0.
-10, 2/3
Let s(l) be the first derivative of 1/8*l**3 + 0*l**2 + 5*l + 1/48*l**4 - 2. Let t(b) be the first derivative of s(b). Factor t(v).
v*(v + 3)/4
Let w = -3956 + 11869/3. Determine j, given that 1/6*j**2 - w*j + 1/6 = 0.
1
Let m = -382/5 - -1543/20. Factor -m*r**2 + 3/2*r + 0.
-3*r*(r - 2)/4
Let z = 12528 - 37583/3. Factor 2/9*p - 1/9*p**2 + z.
-(p - 3)*(p + 1)/9
Let x(r) be the first derivative of -r**4/12 - 13*r**3/9 + 3*r**2/2 + 135*r - 105. Factor x(p).
-(p - 5)*(p + 9)**2/3
Suppose 0 = 3*v + 3*t - 12, 30*v - 5*t + 8 = 31*v. Factor 0*o + 0 - 1/3*o**v - 1/3*o**2.
-o**2*(o + 1)/3
Let l be 12/2 + (12 - 14). Factor -w + 4*w**2 + 3*w**4 - 3*w**4 + 2*w**l - 6*w**4 + w**3.
-w*(w - 1)*(w + 1)*(4*w - 1)
Find w such that -13*w - 27*w + 16*w**2 - 100*w**3 + 32 + 98*w**3 = 0.
2, 4
Factor -3/4*g**2 + 0 + 15*g.
-3*g*(g - 20)/4
Let u be 4/(-5)*420/(-24). Suppose -4*r - 2 + u = 0. Factor -o + o**3 - 6*o**r + 3*o**3 + 4 + 7*o.
-2*(o - 2)*(o + 1)**2
Suppose -2*z + 10 + 26 = 0. Determine c so that -39 + 16 + z + 5*c**2 = 0.
-1, 1
Let d(b) = 2*b**2 - 4*b - 6. Let a be d(-3). Suppose -a = -5*r - r. Let -32/5*s**r + 2/5 + 6*s**2 + 16/5*s - 16/5*s**3 = 0. What is s?
-1, -1/4, 1
Let f(b) be the third derivative of b**7/18900 + b**6/5400 + b**4/3 - 7*b**2. Let o(p) be the second derivative of f(p). Factor o(r).
2*r*(r + 1)/15
Factor -64*r**3 + 86*r**3 - 34*r**2 - 2*r**4 + 24*r**2 - 46*r**2.
-2*r**2*(r - 7)*(r - 4)
Suppose 0 = 5*l - 138 + 153. Let b be (l + -4 + -39)/(-14) + -3. Factor b*n**3 - 2/7 - 2/7*n + 2/7*n**2.
2*(n - 1)*(n + 1)**2/7
Let n(a) be the first derivative of -a**7/70 - a**6/40 + 3*a**5/20 + a**4/8 - a**3 - 4*a**2 + 12. Let l(r) be the second derivative of n(r). Factor l(j).
-3*(j - 1)**2*(j + 1)*(j + 2)
Let b(v) = v**3 + 48*v**2 + 2. Let i be b(-48). Let k be 4 + (0 + 0)/1. Factor -2/5 + 8/5*n - 12/5*n**i + 8/5*n**3 - 2/5*n**k.
-2*(n - 1)**4/5
Let b = -826 - -830. Let x(h) be the first derivative of 1/2*h**6 - 12/5*h**5 + 0*h + 8 + 9/2*h**4 - b*h**3 + 3/2*h**2. Factor x(j).
3*j*(j - 1)**4
Determine s, given that 212*s**4 + 375*s**2 + 632*s**5 - 44*s**4 + 73 + 812*s**3 - 668*s**5 + 624*s + 55 + 729*s**2 = 0.
-1, -2/3, 8
Let i(d) be the first derivative of 3*d**7/280 - d**6/20 + 3*d**5/80 + d**4/16 - 8*d**2 + 17. Let f(p) be the second derivative of i(p). Solve f(y) = 0.
-1/3, 0, 1, 2
Let g(d) be the first derivative of 4 + 6/5*d**5 + 0*d**4 + 0*d**2 + 0*d - 1/3*d**6 - 8/3*d**3. Suppose g(v) = 0. Calculate v.
-1, 0, 2
Let -528 + 100*r + 4*r**4 - r**4 + 100*r**2 + 35*r**3 + 560 = 0. Calculate r.
-8, -2, -1, -2/3
Let 0 - 16/9*k**4 - 16/3*k**2 + 76/9*k**3 + 0*k = 0. What is k?
0, 3/4, 4
Let x(d) = d**2 - 11*d + 36. Let q be x(6). Solve 14*o - 6 - 2*o + 3*o**3 + q*o**2 - 15*o = 0 for o.
-2, -1, 1
Let g(t) = t**3 - 9*t**2 + 93*t - 676. Let s be g(8). Suppose 0 - 2/5*o**s - 4/5*o + 6/5*o**2 + 0*o**3 = 0. Calculate o.
-2, 0, 1
Let 2*k**3 + 108*k**2 - 4*k**3 + 680*k - 2624*k + 12671 - 1007 = 0. Calculate k.
18
Let t(h) be the first derivative of -h**4/24 + 11*h**3/18 - 19*h**2/12 + 3*h/2 + 303. Factor t(j).
-(j - 9)*(j - 1)**2/6
Let l(r) be the second derivative of -1/18*r**3 + 2/63*r**7 + 0*r**2 + 0 - 1/20*r**5 + 31*r + 5/36*r**4 - 1/18*r**6. Suppose l(s) = 0. What is s?
-1, 0, 1/4, 1
Suppose -5*k = -x + 2*x - 109, 2*k = -x + 46. Let c = -4 + 6. Factor -k - 6 - 5*u**c - u - 17*u + 2*u**2.
-3*(u + 3)**2
Let m(a) be the first derivative of -a**3/5 + 3*a**2 - 48*a/5 - 226. Solve m(c) = 0 for c.
2, 8
Let b = -61 + 61. Let q be (b/1)/(8/(-8)). Factor 4/5*h**3 - 2/5*h**5 - 2/5*h + q*h**4 + 0 + 0*h**2.
-2*h*(h - 1)**2*(h + 1)**2/5
Let j = -2/5745 - -11512/63195. Find y, given that 0 + 4/11*y - j*y**2 = 0.
0, 2
Let p = 74 - 70. Suppose -3*y - 3 = 3*q, -q = p*q - 2*y - 16. Factor 1/4*v**q + v + 3/4.
(v + 1)*(v + 3)/4
Let x(m) be the second derivative of m**5 - 10*m**4/3 + 25*m**3/6 - 5*m**2/2 + 14*m. Factor x(v).
5*(v - 1)*(2*v - 1)**2
Suppose 3*k - l = 1036, 6*k + 5*l = 3*k + 1066. Suppose k*z**3 + z - 2 + 2*z - 348*z**3 = 0. What is z?
-2, 1
Let k(j) be the second derivative of j**7/14 + 7*j**6/10 + 3*j**5/2 - j**4/2 - 11*j**3/2 - 15*j**2/2 + 20*j + 2. Suppose k(o) = 0. Calculate o.
-5, -1, 1
Let s(w) = 7*w**3 + 83*w**2 - 172*w + 85. Let f(x) = -x**3 - x**2 + 1. Let j(r) = -3*f(r) - s(r). Let j(k) = 0. Calculate k.
-22, 1
Let b = -92 - -98. Let a(s) be the first derivative of -s**3 - 3/2*s**2 + 3 + b*s. Find r such that a(r) = 0.
-2, 1
Let