5)/15
Let a(j) be the third derivative of 0*j**3 - 1/4*j**5 + 0 + 0*j + 1/4*j**4 + 6*j**2. Factor a(z).
-3*z*(5*z - 2)
Suppose -4*j = -2*u + 60, 5*u - 135 + 10 = 5*j. Let w be 4/(-3*u/(-15)). Determine f so that 1/2*f**2 + 3/2*f + 1/2*f**4 - 3/2*f**3 - w = 0.
-1, 1, 2
Let a = -57 - -60. Find s such that 10 - 12*s**2 - 15*s - a*s**2 + 20*s**2 = 0.
1, 2
Let f(w) be the second derivative of -w**4/78 - 56*w**3/13 - 167*w**2/13 - 5*w + 2. Factor f(i).
-2*(i + 1)*(i + 167)/13
Suppose -3*d = -8 + 5. Let s(n) = -4*n**2 - 8*n + 12. Let v(h) = h. Let k(o) = d*s(o) + 16*v(o). Factor k(x).
-4*(x - 3)*(x + 1)
Let i be -10 + 2 + 5 + -4 + 7. Solve 15/2*k + 5/2*k**2 + i = 0.
-3, 0
Let k = 1049 - 1046. Let d(h) be the third derivative of -h**2 - 1/105*h**7 + 1/10*h**5 + 1/60*h**6 - 1/12*h**4 + 0*h + 0 - 2/3*h**k. Let d(i) = 0. Calculate i.
-1, 1, 2
Let c(y) be the third derivative of -6*y**7/35 + 23*y**6/10 - 172*y**5/15 + 88*y**4/3 - 128*y**3/3 + 81*y**2. What is z in c(z) = 0?
1, 4/3, 4
Suppose 2*f - 3*f = -3*t + 11, 0 = t + 3*f + 3. Suppose 7*p - 24 = -t. Factor 4*a**3 + a**3 - 2*a**5 - 5*a**3 + 2*a**p.
-2*a**3*(a - 1)*(a + 1)
Let t(j) be the first derivative of j**4/2 + 29*j**3/3 + 20*j**2 + 13*j - 54. Determine a, given that t(a) = 0.
-13, -1, -1/2
Let a = 4 - 7/2. Let y be (21/63)/(4 + -2). Factor 0 + a*u**2 + 0*u + y*u**3.
u**2*(u + 3)/6
Let l(s) be the second derivative of s**6/30 - s**5/60 - s**4/6 + s**3/6 + 29*s**2/2 + 31*s. Let j(c) be the first derivative of l(c). Factor j(d).
(d - 1)*(d + 1)*(4*d - 1)
Suppose 6/5*f**3 + 24*f - 64/5 - 64/5*f**2 + 2/5*f**4 = 0. Calculate f.
-8, 1, 2
Suppose -8*q - 145 = -201. Let t(b) be the second derivative of 2*b**2 - 1/6*b**4 + 0 + 1/3*b**3 + q*b. Factor t(w).
-2*(w - 2)*(w + 1)
Let p(g) = g**2 - 36*g - 297. Let s be p(-7). Solve 8/7*u - 8/7*u**3 - 10/7 + 12/7*u**2 - 2/7*u**s = 0 for u.
-5, -1, 1
Let r(p) = -1 - 4 + 2*p**2 - 4 - 1 + 2*p. Let j(y) = 3*y**2 + 3*y - 21. Let m(l) = -2*j(l) + 5*r(l). Factor m(b).
4*(b - 1)*(b + 2)
Let u(k) be the third derivative of 1/105*k**7 + 1/30*k**5 + 0*k**4 + 0 + 0*k**3 - 9*k**2 + 0*k - 1/30*k**6. Factor u(q).
2*q**2*(q - 1)**2
Let d(y) = 41*y + 213. Let g be d(-5). Let x(o) be the second derivative of -2/3*o**3 - g*o + o**2 + 0 + 1/5*o**5 - 1/15*o**6 + 0*o**4. Factor x(b).
-2*(b - 1)**3*(b + 1)
Let r(g) be the first derivative of -4*g**3 + 7*g**2 + 20*g - 7. Factor r(i).
-2*(i - 2)*(6*i + 5)
Factor 9*v**3 + 6*v**3 - 106*v**2 - 44*v - 16*v + 14*v**4 - 96*v**2 + 17*v**3.
2*v*(v - 3)*(v + 5)*(7*v + 2)
Let a(o) be the third derivative of o**6/60 - o**5/2 + 4*o**4 + 64*o**3/3 + 13*o**2. Factor a(k).
2*(k - 8)**2*(k + 1)
Factor 2*u**2 - 2419 + 2503 + 18*u**2 - 152*u.
4*(u - 7)*(5*u - 3)
Let z(v) be the third derivative of -v**8/1176 + 4*v**7/735 - v**6/84 + v**5/105 - 3*v**2. Find x, given that z(x) = 0.
0, 1, 2
Let p(w) be the first derivative of 2*w**5/55 + 3*w**4/11 - 16*w**3/33 - 6*w**2/11 + 14*w/11 + 600. Suppose p(a) = 0. What is a?
-7, -1, 1
Let i = -204/5 - -3269/80. Let c(w) be the first derivative of 1/8*w**2 + 0*w + i*w**4 + 2 - 1/6*w**3. Find t such that c(t) = 0.
0, 1
Let c be 220/(-56) - 0 - -4. Let v(n) be the second derivative of -c*n**4 - n + 0*n**2 + 0 + 1/70*n**5 + 2/21*n**3. Factor v(k).
2*k*(k - 2)*(k - 1)/7
Let o be (-217)/(-56) + ((-2)/(-16) - 0/19). Let 3/4*v**3 + 0 - 1/2*v**5 - 1/4*v**2 + 1/4*v**o - 1/4*v = 0. What is v?
-1, -1/2, 0, 1
Let u(w) = 3*w - 31. Let v(i) = -i + 16. Let r(q) = -2*u(q) - 5*v(q). Let b be r(-20). Factor 12*p**2 + b*p**3 - 14*p**2 + 3*p + 10*p**2 + 5*p.
2*p*(p + 2)**2
Let q = -8243/30 + 1651/6. Factor q - 7/5*u**2 - u.
-(u + 1)*(7*u - 2)/5
Let i(n) be the second derivative of n**5/35 - 176*n**4/21 + 15488*n**3/21 - n + 12. Factor i(u).
4*u*(u - 88)**2/7
Suppose 3*w = -55*y + 57*y + 12, -5*w + 2*y = -16. Suppose 2/3*u**w - 4/3 + 2/3*u = 0. Calculate u.
-2, 1
Let y(g) be the third derivative of g**8/56 + g**7/70 - g**6/8 - g**5/20 + 3*g**4/8 + 7*g**2 - 4. Find d such that y(d) = 0.
-3/2, -1, 0, 1
Let m(c) = 32*c + 226. Let g be m(-7). Factor 33/4*o**3 - 3/4 + 3/4*o + 27/4*o**g + 3*o**4.
3*(o + 1)**3*(4*o - 1)/4
Let m(o) be the third derivative of -1/450*o**5 + 1/180*o**4 + 0 + 2/45*o**3 - 33*o**2 + 0*o. Factor m(s).
-2*(s - 2)*(s + 1)/15
Let n(g) be the first derivative of 1/4*g**2 - 4 + 1/12*g**3 + 0*g. Factor n(s).
s*(s + 2)/4
Let j(w) be the third derivative of w**5/15 - 5*w**4/2 + 24*w**3 - 12*w**2 - 12. Find n, given that j(n) = 0.
3, 12
Let k = 70 - 9099/130. Let g(f) be the second derivative of k*f**5 - 13*f + 1/78*f**4 - 1/39*f**3 - 1/195*f**6 + 0 + 0*f**2. Factor g(y).
-2*y*(y - 1)**2*(y + 1)/13
Let g(f) = -4*f**2 + 27*f + 72. Let q be g(-2). Suppose 39/5*p**q + 0 - 3/5*p = 0. Calculate p.
0, 1/13
Let w(c) = -c**3 + c**2 - 2*c - 2. Let v(x) = -7*x**3 - 27*x**2 + 24*x - 10. Let t(u) = -v(u) + 5*w(u). Factor t(a).
2*a*(a - 1)*(a + 17)
Let h(o) be the second derivative of -o**5/40 - 11*o**4/24 - 3*o**3 - 9*o**2 - 288*o. Factor h(d).
-(d + 2)*(d + 3)*(d + 6)/2
Let o(p) = -p + 7. Let s be o(3). Suppose 16 = -0*a + s*a. Factor 5 - 8*i + a*i**2 + 1 - 2 + 0.
4*(i - 1)**2
Let s(t) be the first derivative of 0*t**4 - 4 + 1/3*t**3 + 0*t - 1/5*t**5 + 0*t**2. Let s(u) = 0. Calculate u.
-1, 0, 1
Let m(h) = h**3 - 5*h**2 + 6*h - 4. Let u be m(4). Let x be ((-1)/5)/(-2*2/u). Determine d so that -x*d**2 + 1/5*d**3 + 1/5 - 1/5*d = 0.
-1, 1
Let d = 34 + -23. Let y = -6 + d. Let x(a) = 4*a**2 + 7*a + 6. Let j(l) = 4*l**2 + 6*l + 5. Let w(k) = y*x(k) - 6*j(k). Find z, given that w(z) = 0.
-1/4, 0
Factor -36*j**2 + 0 - 3/2*j**3 + 0*j.
-3*j**2*(j + 24)/2
Factor 34*j - 18*j + 56*j**2 - 235*j**3 + 175*j**4 - 12*j.
j*(j - 1)*(5*j - 2)*(35*j + 2)
Let o(y) = 28*y**4 - 28*y**3 - 116*y**2 + 92*y + 216. Let v(g) = 9*g**4 - 9*g**3 - 39*g**2 + 31*g + 72. Let t(m) = -5*o(m) + 16*v(m). Find h such that t(h) = 0.
-3, -1, 2, 3
Let z(b) be the first derivative of 5*b**3/3 - 155*b**2 + 4805*b - 126. Solve z(w) = 0.
31
Let m(i) = -7*i**3 - 11*i**2 - 26*i - 34. Let p(f) = -f**3 + f - 1. Let t(d) = 5*m(d) - 30*p(d). Factor t(k).
-5*(k + 2)**2*(k + 7)
Let w be 49/35 - (-6 + 5). Find s, given that -3/5*s**2 - w*s + 3/5 + 12/5*s**3 = 0.
-1, 1/4, 1
Let x be 1/((1/8)/((-3)/(-36))). Let t(k) be the first derivative of -x*k**3 + 0*k - 6 - 2*k**2. Factor t(n).
-2*n*(n + 2)
Suppose 2*b - 5*y + 26 - 7 = 0, -4*b + 2*y = -2. Factor -64*f + 64*f + b*f**4 - 3*f**3 + f**2 - f**5.
-f**2*(f - 1)**3
Let r(z) = 3*z**4 - 3*z**3 - 3*z**2 + z. Let c(n) = n - 7. Let p be c(8). Let i(l) = l**4 - l**3 - l**2. Let g(s) = p*r(s) - 2*i(s). Factor g(h).
h*(h - 1)**2*(h + 1)
Determine u, given that 15 + 108/7*u + 3/7*u**2 = 0.
-35, -1
Let d = 1661 - 1659. Let r(j) be the first derivative of -2 + 0*j + 0*j**d + 1/5*j**5 - 2/3*j**3 - 1/4*j**4. Determine w, given that r(w) = 0.
-1, 0, 2
Let z(k) be the first derivative of -k**4/18 + 10*k**3/27 + 13*k**2/9 + 14*k/9 - 39. Let z(y) = 0. What is y?
-1, 7
Let g = -7 - -9. Suppose -g = -2*o + o. Factor -4*p - 4*p**o + 2*p**2 + 0*p**2 - 2.
-2*(p + 1)**2
Let n = 322 - 317. Let w(l) be the third derivative of -1/35*l**7 + 1/40*l**6 + 0*l + 1/112*l**8 + 0 + n*l**2 + 0*l**4 + 0*l**3 + 0*l**5. Factor w(k).
3*k**3*(k - 1)**2
Solve -2/11*p**3 + 0 + 2/11*p**2 + 12/11*p = 0.
-2, 0, 3
Suppose -2*b - t + 5 = 0, -15 = 2*b - 4*t + t. Factor -83 - 3*q - 3*q**3 - 6*q**2 + 83 + b*q**2.
-3*q*(q + 1)**2
Let p be (-4)/((0 + -2)/2). Suppose -5*f + 134 = 4*h, -2*f = -p*f - 3*h + 55. Solve -b**2 + 10*b**3 + 14*b**3 + 4*b - f*b**3 + 3*b**2 = 0 for b.
-1, 0, 2
Let t(c) = 21*c**3 + 102*c**2 + 36*c - 6. Let j(q) = 20*q**3 + 101*q**2 + 36*q - 5. Let w = 49 + -55. Let n(f) = w*j(f) + 5*t(f). Solve n(v) = 0.
-6, -2/5, 0
Let 4165*b**4 + 3*b**3 + 25*b**2 - 3*b**3 - 4170*b**4 - 20 = 0. What is b?
-2, -1, 1, 2
Let h be (1/(25/15))/(21/70). Let z(f) be the second derivative of 0 - 3/40*f**5 + f**3 + 0*f**h - f + 0*f**4. Factor z(u).
-3*u*(u - 2)*(u + 2)/2
Let l(o) be the third derivative of 5*o**8/336 + 29*o**7/70 - 251*o**6/120 + 181*o**5/60 + 3*o**4/4 - 20*o**3/3 - 166*o**2. Factor l(r).
(r - 1)**3*(r + 20)*(5*r + 2)
Solve 8/3 + 0*h**2 + 2*h - 1/6*h**3 = 0.
-2, 4
Let b(v) = v + 14. Let s be b(-12). Suppose s*d - 110 = -m + 2*m, -286 = -5*d - 3*m. Factor -49/3*p**5 + d*p**4 - 32*p**2