h - 71. Factor 5*i**h - 5*i + 6*i**3 - 25*i**3 + 10*i**3 + 19*i**3.
5*i*(i + 1)*(2*i - 1)
Let j be (4*-2)/(5/10). Let a(s) = -91*s**2 + 2566*s + 744. Let k(b) = 212*b**2 - 5988*b - 1736. Let h(f) = j*a(f) - 7*k(f). Factor h(o).
-4*(o - 31)*(7*o + 2)
Let w(u) be the first derivative of 84 + 0*u + 20/3*u**3 + 8/3*u**2 + 7/6*u**4. Suppose w(v) = 0. Calculate v.
-4, -2/7, 0
Let 3 + 110144*k**3 + 3486*k**4 + 1311*k**2 - 114794*k**3 + 672*k - 822*k**4 = 0. Calculate k.
-1/4, -1/222, 1
Let h(l) be the second derivative of 11/18*l**6 - l + 0*l**3 + 5/126*l**7 + 35/12*l**5 + 125 + 0*l**2 + 125/36*l**4. Factor h(c).
5*c**2*(c + 1)*(c + 5)**2/3
Suppose 0 = -8*t - 19 + 3. Let d be 252/54 + t/3. Suppose 6*i**2 - 8/3 + 14/3*i**d + 34/3*i**3 - 10/3*i = 0. What is i?
-1, 4/7
Let q(c) be the third derivative of -29/12*c**4 - 8*c**2 - 1/20*c**6 + 0 - 7/3*c**3 - 5/6*c**5 + 0*c. Factor q(h).
-2*(h + 1)*(h + 7)*(3*h + 1)
Let 58/7*t**2 + 8/7 - 120/7*t = 0. What is t?
2/29, 2
Let z be (-225)/(-25) + 4 + -7. Let p be (-30)/(36/z) - (-10 - 0). Factor -7/3*c**2 - p*c**3 - 1/3*c - 3*c**4 + 0.
-c*(c + 1)*(3*c + 1)**2/3
Factor -105/2 + 12*n**2 + 3/4*n**3 + 159/4*n.
3*(n - 1)*(n + 7)*(n + 10)/4
Factor -120 + 27628*v - 11*v**2 + 41*v**2 + 37*v**3 - 27723*v - 32*v**3.
5*(v - 3)*(v + 1)*(v + 8)
Let j(h) be the first derivative of -31*h - 22 + 5/6*h**3 + 25/2*h**2 + 1/48*h**4. Let z(a) be the first derivative of j(a). Factor z(d).
(d + 10)**2/4
Suppose 39*p - 236 + 158 = 0. Let j = 112/255 + -2/51. Determine s so that p - 8/5*s - j*s**2 = 0.
-5, 1
Let w = -17341 - -17345. Factor -2/7*b**w + 864/7 - 32/7*b**3 + 0*b - 144/7*b**2.
-2*(b - 2)*(b + 6)**3/7
Factor 1682/5*r**2 + 928/5*r + 128/5.
2*(29*r + 8)**2/5
Let g(y) be the second derivative of -33/20*y**5 + 432*y**2 + 169/8*y**4 - 132*y**3 + 0 + 121*y + 1/20*y**6. Find c such that g(c) = 0.
3, 8
Let y(i) be the second derivative of -i**7/1260 + i**6/90 + i**5/12 - 52*i**4/3 - 230*i. Let x(k) be the third derivative of y(k). Let x(q) = 0. What is q?
-1, 5
Let q be (11 - (-72)/(-8))/(2 - 0). Let w(y) = 2*y**3 - 2*y. Let r(d) = -16*d**3 + 40*d**2 + 20*d. Let v(x) = q*r(x) + 10*w(x). Suppose v(n) = 0. What is n?
-10, 0
Let n(p) = -6*p**2 + 2*p - 4. Let r(q) = q**2. Let g(u) = -3 + 0*u + 6 - 2*u**2 + 4*u - 2. Let k be g(2). Let l(h) = k*n(h) + 8*r(h). Factor l(a).
2*(a - 1)*(a + 2)
Let v(s) be the third derivative of -s**7/1260 - 71*s**6/720 + 17*s**5/40 + 515*s**4/144 + 73*s**3/9 + s**2 - 6*s + 59. Factor v(r).
-(r - 4)*(r + 1)**2*(r + 73)/6
Let s(b) be the first derivative of -21*b**4 + 2*b**2 + 15 + 319*b**5 - 327*b**5 - 16*b**3 - 5*b**2 + b**2. Solve s(h) = 0 for h.
-1, -1/10, 0
Suppose 16/7*l**2 - 660/7 - 2/7*l**3 + 646/7*l = 0. Calculate l.
-15, 1, 22
Let s = 10823610 + -50827671989/4696. Let o = s - -2/587. Factor o*p**2 + 0*p - 1/2.
(p - 2)*(p + 2)/8
Let i be 7/(63/6)*(-24)/(-32). Let v(l) be the first derivative of -2*l**3 + 15 + l**2 - i*l**4 + 2/5*l**5 + 4*l. Factor v(h).
2*(h - 2)*(h - 1)*(h + 1)**2
Let -136 - 90/7*u - 2/7*u**2 = 0. Calculate u.
-28, -17
Let i be (6 - 0) + (3 - 7). Find a such that -51*a**2 + 15*a**2 - 54*a + 20*a**2 + 13*a**i = 0.
-18, 0
Let f = 44 + -35. Suppose 3*j = 4*i - f - 6, -2*j = 2*i - 4. Determine r, given that 5 - 5*r**2 - 3*r + 0*r - i = 0.
-1, 2/5
Let v(p) = p**2 - 31*p + 153. Let i be v(25). Factor -6 - 10*j - 6 + 11*j + 2*j**i + 2*j**2 - 9*j + 4.
2*(j - 2)*(j + 1)*(j + 2)
Let h(o) = -o**3 + 96*o**2 - 21*o - 30. Let n(v) = v**3 - 51*v**2 + 11*v + 15. Let k(g) = 6*h(g) + 11*n(g). Determine x, given that k(x) = 0.
-3, -1, 1
Determine n so that 24/5*n**3 + 182 - 3264/5*n - 302*n**2 = 0.
-7/3, 1/4, 65
Let i(t) be the third derivative of -t**5/120 + t**4/6 - 5*t**3/4 - 6971*t**2. Let i(o) = 0. Calculate o.
3, 5
Factor -5260*q - 4*q**5 + q**5 + 195*q**3 - 6730 - 2*q**5 + 100*q**4 + 2530 - 1630*q**2 + 0*q**5.
-5*(q - 21)*(q - 5)*(q + 2)**3
Let y(d) be the third derivative of 0 + 1/6*d**4 + 2*d + 0*d**3 + 5*d**2 - 1/30*d**5. Factor y(x).
-2*x*(x - 2)
Let y be -4*4/(-48)*12. Let d(h) be the first derivative of -y*h + 2 + h**2 - 14*h**2 - 24*h**3 - 5*h**2. Let d(j) = 0. Calculate j.
-1/3, -1/6
Suppose 3*w - 4*u + 2*u - 20 = 0, -5*w + 4 = 4*u. Factor m**2 - 16 + 3*m**2 + 8*m**2 + w*m - 10*m**2.
2*(m - 2)*(m + 4)
Let l(z) be the first derivative of z**6/1440 - z**5/160 + z**4/48 + 37*z**3/3 + 32. Let y(n) be the third derivative of l(n). Factor y(v).
(v - 2)*(v - 1)/4
Let d be (-16)/(-6) + (-3)/(-9) - -238. Let q be d + 0 + 0 + -2 + 3. Solve 233*c**4 + 4*c - 3*c**2 + c**5 + q*c**4 - 472*c**4 - 5*c**3 = 0.
-4, -1, 0, 1
Let j(z) = 15*z**2 - 1834*z + 1263. Let b(r) = 21*r**2 - 1834*r + 1276. Let u(y) = -3*b(y) + 4*j(y). Factor u(k).
-(k + 612)*(3*k - 2)
Let m(n) be the first derivative of 2*n**5/15 - 53*n**4/30 - 2144*n**3/45 - 28*n**2 + 5577. Find k such that m(k) = 0.
-10, -2/5, 0, 21
Let y(k) be the first derivative of 1/80*k**5 + 3/8*k**3 + 0*k + 8*k**2 + 1/8*k**4 - 12. Let g(o) be the second derivative of y(o). Factor g(b).
3*(b + 1)*(b + 3)/4
Let k(v) be the second derivative of -675*v**2 + 0 - 8*v**4 - 285/2*v**3 - 34*v - 3/20*v**5. Factor k(a).
-3*(a + 2)*(a + 15)**2
Let x(u) = 5*u**2 - 3*u - 13. Let s be x(4). Find h such that 2*h**5 - 28*h**3 - s + 24*h**2 + 55 + 2*h**5 = 0.
-3, 0, 1, 2
Let w(b) = -17*b**2 - 5*b + 106. Let x(o) = -5*o**2 - 2*o + 31. Let n(k) = -6*w(k) + 21*x(k). Factor n(f).
-3*(f - 1)*(f + 5)
Let p(y) be the first derivative of y**3/9 - 131*y**2/6 - 266*y/3 + 4299. Factor p(v).
(v - 133)*(v + 2)/3
Let b(y) = 822*y**2 - 6*y - 2. Let w be b(-3). Suppose -w - i**3 + 4*i**2 - 7*i + 7416 + 0*i + 2*i = 0. What is i?
1, 2
Let y be ((-94)/2)/((-11)/(-2)) - (354 - 364). Factor 0 + y*q**3 + 30/11*q**2 - 4/11*q.
2*q*(q + 2)*(8*q - 1)/11
Let d = 61123/3 + -244465/12. Factor d*j**2 - 3 + 0*j - 3/4*j**3.
-3*(j - 2)**2*(j + 1)/4
Let u be 390/(-624) + 363/120. Factor p**3 + 1/10*p**4 + u*p + 14/5*p**2 + 0.
p*(p + 2)**2*(p + 6)/10
Let j(r) be the first derivative of r**6/720 - 3*r**5/80 - 2*r**3/3 + 26*r**2 - 58. Let c(l) be the third derivative of j(l). Factor c(d).
d*(d - 9)/2
Suppose 0*h + 2*k + 10 = 3*h, k = -3*h + 13. Suppose -4*c = 3*t, 0*t - h*c = t + 8. Factor 5*u**3 - 5*u - 10*u**4 - 5*u**2 - 5*u**t + 20*u**4.
5*u*(u - 1)*(u + 1)**2
Let q(l) be the second derivative of -l**4/60 - 1063*l**3/15 - 1129969*l**2/10 - 19*l - 58. Determine a so that q(a) = 0.
-1063
Let c(i) = -15*i**3 + 3*i**2 + 3*i. Let g be c(-1). Suppose 5*x = -5*v + 30, -5*v - 3*x + 49 = g. Factor 16*d - 4/3*d**4 - 16/3 - 52/3*d**2 + v*d**3.
-4*(d - 2)**2*(d - 1)**2/3
Let j(v) be the second derivative of -23*v - 6/7*v**3 - 5 - 81/7*v**2 - 1/42*v**4. Factor j(c).
-2*(c + 9)**2/7
Factor 58/3*f**2 - 4/3*f + 0.
2*f*(29*f - 2)/3
Let j(w) = -228*w**2 - 3*w + 16. Let i be j(0). Factor -33/4*q**2 - 1/4*q**4 + 7/2*q**3 - i - 28*q.
-(q - 8)**2*(q + 1)**2/4
Let g(q) = -42*q**3 - 371*q**2 - 4153*q - 17424. Let u(f) = 5*f**3 + 46*f**2 + 519*f + 2178. Let o(i) = -2*g(i) - 17*u(i). Factor o(v).
-(v + 11)**2*(v + 18)
Factor 139 - 2*x**3 - 139*x**2 + 37*x - 220*x + 159*x**2 + 23 + 3*x**3.
(x - 6)*(x - 1)*(x + 27)
Determine g, given that -2/7*g**3 + 104/7*g**2 + 222/7*g - 324/7 = 0.
-3, 1, 54
Let o be ((-8)/6)/(2/(-3)). Suppose -10*i + 58 = 38. Solve o*x**i - 1164*x + 1164*x - 2*x**3 = 0.
0, 1
Let s(l) = l**3 - l**2 - 54*l - 15. Let r be s(8). Let f(n) = -n**2 + 12*n - 9. Let t be f(r). Let 1 + 15/2*k + 21/2*k**3 + 5/2*k**4 + 29/2*k**t = 0. What is k?
-2, -1, -1/5
Let b(g) = 2*g**3 + 154*g**2 - 141*g - 3. Let v(c) = 3*c**3 + 307*c**2 - 285*c - 5. Let q(i) = 5*b(i) - 3*v(i). Suppose q(o) = 0. What is o?
0, 1, 150
Let k(o) be the third derivative of -8/3*o**3 - 1/60*o**5 - 1/3*o**4 + 0 - 3*o + 17*o**2. Factor k(i).
-(i + 4)**2
Let l = 1/844 - -417/4220. Let g(q) be the second derivative of -l*q**6 - 3/4*q**4 + 0*q**2 - 9/20*q**5 - 1/2*q**3 + 0 + 2*q. Let g(m) = 0. Calculate m.
-1, 0
Let w(l) = 6*l**2 - 84*l - 84. Let x(i) = i**2 + i + 2. Suppose 0 = -4*m - 3*o + 19 - 6, 3*o = 2*m + 7. Let c(a) = m*w(a) - 3*x(a). Factor c(p).
3*(p - 30)*(p + 1)
Let v(z) be the first derivative of -z**4/24 + z**3/12 - 43*z + 96. Let x(y) be the first derivative of v(y). Factor x(p).
-p*(p - 1)/2
Suppose 216 = -26*w + 17*w. Let x be w/(-60) - 28/120. Solv