h - 4. Let k be (-8)/6*(-3)/2. Factor 1/4 - 3/4*u**k - 1/2*u**4 + 1/4*u - 5/4*u**s.
-(u + 1)**3*(2*u - 1)/4
Suppose -2*s + z + 121 = -4*z, -3*z = -5*s + 293. Let u = s + -56. Factor b - 1/2*b**u - 1/2.
-(b - 1)**2/2
Let r = 1313 - 17065/13. Determine b, given that 0*b + 0*b**3 + 2/13*b**4 + 2/13 - r*b**2 = 0.
-1, 1
Let y(t) be the second derivative of t**4/18 + 424*t**3/9 + 44944*t**2/3 + 708*t. Find x such that y(x) = 0.
-212
Suppose 0 = -y + 4*y - 15. Factor -8*g**2 + 2*g**y + 3*g**5 - 4*g**3 + 0*g**5 - g**5 + 8*g**4.
4*g**2*(g - 1)*(g + 1)*(g + 2)
Let w(d) be the third derivative of -3*d**6/10 + 7*d**5/15 + d**4/3 + 151*d**2. Let w(o) = 0. Calculate o.
-2/9, 0, 1
Let q(j) be the first derivative of -j**6/30 + 3*j**5/5 - 9*j**4/2 + 18*j**3 - 3*j**2/2 + 11. Let g(b) be the second derivative of q(b). Factor g(v).
-4*(v - 3)**3
Suppose -25 = 4*g - 4*i - 53, 3*g - 25 = 4*i. Let m(t) be the first derivative of 2/3*t**g - 6*t - 10 - 2*t**2. Find a, given that m(a) = 0.
-1, 3
Let r = 37/1302 + 4/93. Let m(t) be the third derivative of 1/2*t**5 + 2*t**2 + 1/2*t**3 + 1/112*t**8 + 5/8*t**4 + 1/4*t**6 + 0 + 0*t + r*t**7. Factor m(c).
3*(c + 1)**5
Let q be (1 + (-15)/25)*354/(-4). Let t = -35 - q. Factor 2*j**3 + 0*j + 8/5*j**4 + 0 + t*j**5 + 4/5*j**2.
2*j**2*(j + 1)**2*(j + 2)/5
Let p(q) be the second derivative of q**6/90 + q**5/15 + q**4/6 - 9*q**3/2 - 19*q. Let k(r) be the second derivative of p(r). Determine u, given that k(u) = 0.
-1
Let k(x) be the first derivative of 1/8*x**2 + 1/2*x - 1/12*x**3 - 3. Suppose k(y) = 0. Calculate y.
-1, 2
Suppose -4 = r + 4*z, -3 = -1448*r + 1446*r + 3*z. Factor r - 2/15*q + 2/15*q**2.
2*q*(q - 1)/15
Let d(w) = 32*w**2 - 288*w - 11. Let p(k) = -6*k**2 + 58*k + 2. Let x(h) = -2*d(h) - 11*p(h). Factor x(u).
2*u*(u - 31)
Let w(t) = t**2 + 17*t - 138. Let n be w(6). Factor n - 3/7*b**3 + 2/7*b + 1/7*b**5 - 1/7*b**2 + 1/7*b**4.
b*(b - 1)**2*(b + 1)*(b + 2)/7
Factor -32/13*b**2 + 0*b - 2/13*b**3 + 0.
-2*b**2*(b + 16)/13
Let c(t) be the first derivative of -3*t**5/25 + 9*t**4/20 - 3*t**3/5 + 3*t**2/10 + 20. What is i in c(i) = 0?
0, 1
Let a = 1590/13 + -47687/390. Let u(r) be the first derivative of 0*r**4 - 1/18*r**3 + 13 + a*r**5 + 0*r + 0*r**2. Factor u(p).
p**2*(p - 1)*(p + 1)/6
Let t(x) be the second derivative of 9*x - 3/50*x**5 - 1/10*x**4 + 1/70*x**7 + 1/50*x**6 + 0 + 1/10*x**3 + 3/10*x**2. Find f, given that t(f) = 0.
-1, 1
Let w(c) = 14*c**4 - 16*c**3 - 4*c**2 + 6*c + 5. Let a(z) = 69*z**4 - 78*z**3 - 21*z**2 + 30*z + 24. Let x(d) = 5*a(d) - 24*w(d). Solve x(t) = 0.
-1, 0, 2/3, 1
Let q(d) = -7*d + 2 + 6*d - 13. Let a be q(-13). Factor -1 - 1 - 8*z + 7*z + 10*z**a.
(2*z - 1)*(5*z + 2)
Let z(u) be the first derivative of 2*u**3/21 + 176*u**2/7 + 15488*u/7 - 472. Factor z(a).
2*(a + 88)**2/7
Let c = -142 - -714/5. Suppose -c*y**2 + 1/5*y**5 + 0 + 3/5*y**4 + 0*y + 0*y**3 = 0. What is y?
-2, 0, 1
Suppose 0 - 4/9*i**4 + 4/9*i**2 + 164/9*i - 164/9*i**3 = 0. What is i?
-41, -1, 0, 1
Let w be ((-2)/4)/((-5)/(10 + -5)). Factor 5*f - 25/2 - w*f**2.
-(f - 5)**2/2
Let f(x) be the third derivative of x**9/90720 - x**8/3780 + x**7/1080 - 7*x**5/15 - 21*x**2. Let s(v) be the third derivative of f(v). Factor s(b).
2*b*(b - 7)*(b - 1)/3
Let w(z) = z**2 - 8. Let c be w(0). Let p = 10 + c. Factor 4 - 4 - 2*o**2 + p*o.
-2*o*(o - 1)
Let n = 705/2 - 352. Let h(o) be the second derivative of 6*o + 11/12*o**4 + 1/4*o**5 + 0 + 7/6*o**3 + n*o**2. Solve h(k) = 0 for k.
-1, -1/5
Suppose -3/7*s**2 - 16875/7 - 450/7*s = 0. Calculate s.
-75
Let y = -39 + 43. Let h be (0 - y/(-8))*0. Factor -16/9*t**3 - 8/9*t**2 + 0*t - 2/9*t**5 - 10/9*t**4 + h.
-2*t**2*(t + 1)*(t + 2)**2/9
Let r(n) be the first derivative of -34/21*n**3 + 16/7*n**2 + 3/7*n**4 - 10/7*n + 31. Factor r(g).
2*(g - 1)**2*(6*g - 5)/7
Let -11/2*b - 3 - 3/2*b**2 = 0. What is b?
-3, -2/3
Let t = -9 - -14. Determine r, given that -t*r - 25*r**2 - 21*r - 5*r**3 + 8*r - 20 - 22*r = 0.
-2, -1
Let v(a) be the third derivative of -3*a**6/20 + 47*a**5/30 + 11*a**4/3 - 4*a**3 + 10*a**2 + a. Factor v(y).
-2*(y - 6)*(y + 1)*(9*y - 2)
Let l(r) = -r**3 + 5*r**2 + r - 11. Let n be l(3). Let h = -7 + 11. Factor -1 - 3*b**h - n*b**3 - 5*b - 2*b**4 - 10*b**2 + b**5 + 0*b**5 - 2*b**5.
-(b + 1)**5
Let i(q) be the third derivative of -q**6/120 + q**5/3 - 3*q**4/4 - 8*q**3/3 - q**2. Let g be i(19). Find j such that 1/2*j**4 + j**g - 2*j + 2 - 3/2*j**2 = 0.
-2, 1
Find q, given that -24/13*q + 16/13 + 12/13*q**2 - 2/13*q**3 = 0.
2
Suppose 88/9*m + 64/3 - 4/9*m**2 = 0. What is m?
-2, 24
Let -91*c**4 + 0 - 753571*c**2 - 1/4*c**5 - 24843/2*c**3 - 68574961/4*c = 0. What is c?
-91, 0
Solve 2*n**2 + 0*n**2 - 12 + 16*n**3 - 4*n**3 - 4*n - 8*n**3 + 10*n**2 = 0.
-3, -1, 1
Let o(k) be the second derivative of 0 + 0*k**2 + 21*k + 0*k**3 - 3/40*k**5 + 1/12*k**4 + 1/60*k**6. Let o(p) = 0. What is p?
0, 1, 2
Let x(z) be the second derivative of 0*z**2 - 12*z - 3/2*z**4 + 0 + 2/3*z**3. Factor x(o).
-2*o*(9*o - 2)
Let f(d) be the first derivative of d**4/5 - 4*d**3/15 - 4*d**2 - 32*d/5 - 45. Determine m, given that f(m) = 0.
-2, -1, 4
Suppose 60 = 2*s + 3*s. Suppose 6 - s = -3*i. Factor -77/2*q**2 + 49/2*q**3 + 16*q - i.
(q - 1)*(7*q - 2)**2/2
Let d = -497 + 500. Let s(o) be the first derivative of 4 + 1/9*o**d + 4/3*o - 2/3*o**2. What is q in s(q) = 0?
2
Let k(m) be the third derivative of m**6/1020 + m**5/85 - 5*m**4/68 + 8*m**3/51 - 6*m**2. What is x in k(x) = 0?
-8, 1
Let l(h) be the first derivative of -2 - 6*h**2 + h**4 - 1/5*h**5 - 9*h + 2/3*h**3. Factor l(a).
-(a - 3)**2*(a + 1)**2
Let j(z) be the first derivative of 1/20*z**5 + 0*z - 1/180*z**6 - 1/6*z**4 + 3*z**3 + 4 + 0*z**2. Let h(w) be the third derivative of j(w). Factor h(s).
-2*(s - 2)*(s - 1)
Let b(m) be the second derivative of m**5/360 + 5*m**4/144 + m**3/9 - 49*m**2/2 - 25*m. Let t(p) be the first derivative of b(p). Find w, given that t(w) = 0.
-4, -1
Let u(w) be the first derivative of w**3/3 - 20*w**2 + 675. Factor u(l).
l*(l - 40)
Let p = -932 + 934. Let b(m) be the first derivative of 2/9*m**2 + p + 0*m**4 + 0*m - 2/45*m**5 + 2/9*m**3. Find d such that b(d) = 0.
-1, 0, 2
Let h(b) = -2*b + 38. Let r be h(18). Solve -14*o**2 + 17*o**r + 12*o**2 - 5*o**3 = 0.
0, 3
Let k(f) be the third derivative of f**6/320 + 3*f**5/160 - f**4/16 + 12*f**2 + 7*f. Let k(t) = 0. What is t?
-4, 0, 1
Factor -8*f**3 + 20*f**4 + 14*f**5 - 22*f**5 - 4*f**2 - 4*f**3 + 4*f.
-4*f*(f - 1)**3*(2*f + 1)
Let a be 12/18 + 2/(-12). Let o(z) = z**2 + 2*z - 61. Let n be o(-9). Factor -a*i**n - 4*i - 8.
-(i + 4)**2/2
Let x(l) be the second derivative of -l**7/105 + 4*l**5/25 - l**4/5 - 7*l**3/15 + 6*l**2/5 - 6*l - 2. Find s, given that x(s) = 0.
-3, -1, 1, 2
Suppose -296*o = -291*o - 10. Find i such that -i**o - 2/5*i + 1/5*i**4 - 3/5*i**3 + 1/5*i**5 + 0 = 0.
-1, 0, 2
Factor 1/5*v**2 + 1/5*v - 4.
(v - 4)*(v + 5)/5
Let c(z) be the second derivative of 2*z**2 - 12*z - z**4 + 0 + 0*z**3 + 2/5*z**5. Factor c(o).
4*(o - 1)**2*(2*o + 1)
Let s be (3/3 + -1)/(-3). Let p(m) be the first derivative of s*m**2 + 0*m**3 - 1/5*m**4 - 1/5*m**6 - 2 + 0*m - 2/5*m**5. Factor p(i).
-2*i**3*(i + 1)*(3*i + 2)/5
Let n(t) be the third derivative of -t**9/241920 - t**8/40320 - t**7/20160 + t**5/20 - 10*t**2. Let z(q) be the third derivative of n(q). Factor z(d).
-d*(d + 1)**2/4
Let q(f) = -f**2 + 3. Let s(b) = -2*b**2 - 10*b + 24. Let i(c) = 4*q(c) - s(c). Factor i(k).
-2*(k - 3)*(k - 2)
Let j(b) be the second derivative of -13/60*b**5 + 2*b**2 + 1/6*b**4 + 7*b + 0 + 2/3*b**3 + 1/24*b**6. Let d(w) be the first derivative of j(w). Factor d(f).
(f - 2)*(f - 1)*(5*f + 2)
Let k = -9279 + 64965/7. Factor 8/7*g**4 + k*g**3 - 4/7*g**5 + 0 + 0*g**2 + 0*g.
-4*g**3*(g - 3)*(g + 1)/7
Find i such that -4*i**4 + 1372*i - 588*i**2 + 149 - 149 + 87*i**3 - 3*i**3 = 0.
0, 7
Let b(g) = 54*g + 108. Let f be b(-2). Find j such that 0 - 2/5*j**3 + 0*j + f*j**4 + 0*j**2 + 2/5*j**5 = 0.
-1, 0, 1
Solve 32*c**2 + 1 + 16*c + 4 - 6*c - 27*c**2 = 0.
-1
Let d(x) be the third derivative of 0*x**3 + 0 - 1/50*x**5 + 1/100*x**6 - 3*x**2 + 0*x + 1/75*x**7 - 1/30*x**4 + 1/280*x**8. What is o in d(o) = 0?
-1, 0, 2/3
Suppose -m - 5*h + 24 = -15, -5*m = 4*h - 174. Let n = m - 32. Factor -19*b**2 - 2*b**4 + 21*b**n - 6*b + 0*b**4 + 6*b**3.
-