**2 - 2*g - 8. Let j(s) = a*k(s) + 2*m(s). Factor j(c).
(c + 1)*(2*c - 1)
Let n(g) be the third derivative of -g**8/336 - g**7/56 + g**5/6 + 7*g**3/3 - 48*g**2. Let x(r) be the first derivative of n(r). Determine l so that x(l) = 0.
-2, 0, 1
Suppose 0 + 27/4*m**3 - 15/2*m - 33/4*m**2 + 33/4*m**4 + 3/4*m**5 = 0. Calculate m.
-10, -1, 0, 1
Suppose 0 = 4*d - 113 + 93. Let l be 2/54*(-48)/((-20)/d). Factor 0 - 2/9*j**4 - l*j**2 - 2/3*j**3 + 0*j.
-2*j**2*(j + 1)*(j + 2)/9
Let g = -1826/81 - -10048/405. Solve -154/15*d**4 + 8/15 - 98/15*d**5 + g*d**3 + 146/15*d**2 + 64/15*d = 0.
-1, -2/7, 1
Let c(s) be the third derivative of s**5/160 - 3569*s**4/32 + 12737761*s**3/16 + 2*s**2 - 29*s - 50. Find j such that c(j) = 0.
3569
Let w(a) be the second derivative of a**7/84 + 19*a**6/60 - 21*a**5/20 + a**4/12 + 41*a**3/12 - 21*a**2/4 + 3040*a. Factor w(d).
(d - 1)**3*(d + 1)*(d + 21)/2
Factor 7/4*k**2 + 639/4*k + 91/2.
(k + 91)*(7*k + 2)/4
Let 4*q**5 - 60*q**3 + 56*q + 5*q**4 - 51 + 100*q**2 - 18*q**4 + 7*q**4 + 2*q**4 - 45 = 0. What is q?
-4, -1, 1, 2, 3
Let q(z) = 6*z**2 + 2*z - 10. Let l(w) = -5*w**2 - 2*w + 8. Suppose 28 = -333*u + 326*u. Let r(g) = u*q(g) - 5*l(g). Factor r(y).
y*(y + 2)
Let v(p) be the first derivative of -p**4/6 - 7*p**3/3 - 12*p**2 - 133*p + 68. Let j(r) be the first derivative of v(r). Factor j(n).
-2*(n + 3)*(n + 4)
Let y be (-10)/(-63) + (-4)/(-14). Let c be 522/(-6786) - (140/(-117))/4. Factor y*h - 2/9*h**3 + 0 - c*h**2.
-2*h*(h - 1)*(h + 2)/9
Let u(t) be the second derivative of t + t**2 - 1/3*t**3 + 1/10*t**5 - 1/8*t**4 - 11 - 1/60*t**6. Factor u(j).
-(j - 2)**2*(j - 1)*(j + 1)/2
Let q(j) be the first derivative of j**3/3 - 13*j + 469. Let o be q(4). Factor 38/15*b**2 + 4/5*b - 14/15*b**o + 0.
-2*b*(b - 3)*(7*b + 2)/15
Suppose 30/7*c**4 + 4/7*c**5 + 88/7*c - 102/7*c**2 + 0 - 164/7*c**3 = 0. Calculate c.
-11, -1, 0, 1/2, 4
Let q(z) be the first derivative of z**5/30 - z**4/8 - z**3/9 + z**2 - 4*z/3 + 1159. Factor q(t).
(t - 2)**2*(t - 1)*(t + 2)/6
Suppose 2630*s - 2726*s = 0. Let j(h) be the second derivative of 43*h + s - 1/3*h**3 - 1/4*h**2 - 1/8*h**4. Factor j(x).
-(x + 1)*(3*x + 1)/2
Let d(u) = -208*u**2 + 412*u**2 - 210*u**2 - 18 - 35*u - 4. Let y(o) = -o**2 - o + 1. Let v(n) = -5*d(n) + 35*y(n). Factor v(h).
-5*(h - 29)*(h + 1)
Let 750*y + 1165*y + y**4 + 1344 + 73*y**3 + 426*y - 3*y**4 - 53*y - 763*y**2 = 0. What is y?
-1/2, 8, 21
Suppose 0 + 0*a + 0*a**2 - 86/7*a**3 - 2/7*a**4 = 0. Calculate a.
-43, 0
Let q(w) be the third derivative of -35*w**5/6 + 117*w**4/4 - 2*w**3/3 - w**2 + 2969*w. Factor q(y).
-2*(y - 2)*(175*y - 1)
Let j = 3722/835 - -1794/167. Factor 4/5 + 124/5*s**3 + 96/5*s**2 + 34/5*s + j*s**4 + 18/5*s**5.
2*(s + 1)**4*(9*s + 2)/5
Let j be 12/8 + 5/((-10)/11). Let x be (j/2)/((-266)/76). Suppose -x*a**4 + 0 - 16/7*a + 16/7*a**3 + 4/7*a**2 = 0. Calculate a.
-1, 0, 1, 4
Let h(d) be the first derivative of 2*d**3/3 - 34*d**2 + 66*d + 111. Let w be h(33). Factor 2/7*a - 1/7*a**2 - 1/7*a**3 + w.
-a*(a - 1)*(a + 2)/7
Let i(h) be the second derivative of 10*h**4/3 - 605*h**3/6 - 685*h**2 + 15*h + 19. Find b such that i(b) = 0.
-2, 137/8
Suppose 107*r + 2*r - 274 = -28*r. Solve -9/7*c + 3/7*c**3 + 0*c**r - 6/7 = 0 for c.
-1, 2
Factor -694/13*j + 372/13 + 22/13*j**2.
2*(j - 31)*(11*j - 6)/13
Let f = -1006 - -2031. Factor f - 212*n - 3*n**2 - 1169 + 68*n - 1584.
-3*(n + 24)**2
Let t be -6*(-4)/(-10)*(-2540)/11176. Factor 0*z + 0*z**3 + 0 - t*z**2 + 6/11*z**4.
6*z**2*(z - 1)*(z + 1)/11
Let w(c) be the first derivative of 4*c**3/3 + 52*c**2 - 3168*c - 3591. Determine i so that w(i) = 0.
-44, 18
Suppose -5*x = 2*s + 1, s + x + x + 1 = 0. Let y be (-3)/(-36)*s*-1. Factor y*i**5 - 1/4*i**2 + 0*i + 0 + 1/4*i**4 - 1/4*i**3.
i**2*(i - 1)*(i + 1)**2/4
Let o(z) = -14*z**3 - 15*z**2 - 9*z + 5. Let d = 25 - 11. Let i(l) = 13*l**3 + 16*l**2 - 13*l - 4 + 7*l + d*l. Let y(g) = -5*i(g) - 4*o(g). Solve y(a) = 0.
-2, -2/9, 0
Suppose -24*v - 4/7*v**2 - 1088/7 = 0. Calculate v.
-34, -8
Factor 6*i**2 - 366 + 255*i - 623*i - i**2 - 4*i**2 - 3*i**2.
-2*(i + 1)*(i + 183)
Suppose -2*a = -g - 2, 3*a + 4*g = -88 + 113. Suppose -3/4*r**2 + 3/2*r + 0 - 3/4*r**a = 0. Calculate r.
-2, 0, 1
Let t(h) be the first derivative of -h**4/16 - 23*h**3/6 + 639*h**2/8 + 171*h - 4881. Factor t(b).
-(b - 12)*(b + 1)*(b + 57)/4
Let w(o) be the first derivative of 1/15*o**5 - 3/4*o**4 - 73 + 3/2*o**2 + 0*o - 1/9*o**3. Factor w(v).
v*(v - 9)*(v - 1)*(v + 1)/3
Let p(o) be the second derivative of -o**6/15 + 27*o**5/5 + 28*o**4/3 - 18*o**3 - 55*o**2 - 3*o - 200. Factor p(c).
-2*(c - 55)*(c - 1)*(c + 1)**2
Suppose -22*a - 4*p = -4, 163*a - 166*a - 2*p = 14. Solve -1/4*z**3 + 3/2*z**a + 0 - 9/4*z = 0.
0, 3
Let c(o) be the second derivative of o**6/90 - 3*o**5/10 - 83*o**4/36 - 6*o**3 - 22*o**2/3 - 513*o. Solve c(h) = 0.
-2, -1, 22
Let l(q) be the third derivative of 2*q**7/315 - 503*q**6/540 + 2338*q**5/45 - 10780*q**4/9 - 21952*q**3/27 - 540*q**2. Factor l(r).
2*(r - 28)**3*(6*r + 1)/9
Let l = 60 + -38. Let v(p) = -p**2 + 28*p - 55. Let o be v(l). Suppose 8*g + 77 - 8*g**3 - 36*g**4 + 36*g**2 - o = 0. Calculate g.
-1, -2/9, 0, 1
Let u = 551605/7 - 78787. Let 16/7 - 52/7*h**2 - u*h = 0. What is h?
-2, 2/13
Let o(a) be the first derivative of 2*a**5/45 - 11*a**4/18 + 64*a**3/27 - 4*a**2/9 - 32*a/3 + 902. Suppose o(b) = 0. Calculate b.
-1, 2, 4, 6
Let q(p) be the second derivative of -71*p**5/10 - 215*p**4/6 - 148*p**3/3 - 4*p**2 + 6*p + 82. Factor q(i).
-2*(i + 1)*(i + 2)*(71*i + 2)
Let b(t) be the first derivative of -t**5/30 + t**4/6 - t**3/3 + 23*t**2 + 33. Let j(d) be the second derivative of b(d). Find n such that j(n) = 0.
1
Let w(f) be the third derivative of 0*f**3 + 0*f + 0 - 1/350*f**7 + 3/20*f**4 + 76*f**2 - 1/100*f**5 - 1/50*f**6. Factor w(s).
-3*s*(s - 1)*(s + 2)*(s + 3)/5
Suppose 0*k = -2*p + 2*k - 322, p - 4*k + 158 = 0. Let f be (-10)/(-6) + 27/p. Factor f - 3/4*j**2 + 3/4*j.
-3*(j - 2)*(j + 1)/4
Let w(t) be the third derivative of t**7/105 - t**6/30 - t**5/2 + 8*t**4/3 - 16*t**3/3 - 201*t**2 + t. Suppose w(r) = 0. Calculate r.
-4, 1, 4
Let o be (-1)/(15/(-2007)) + (-1563)/(-2605). Let -536/5*z**3 + 32/5 + o*z**2 - 256/5*z - 34*z**4 + 30*z**5 = 0. What is z?
-2, 1/3, 2/5, 2
Let i(t) be the third derivative of t**5/30 - 51*t**4/2 - 307*t**3/3 + 86*t**2 + 2. Factor i(s).
2*(s - 307)*(s + 1)
Let y(j) = -7*j**2 + 10*j - 6. Suppose 19*f = -3 + 117. Let q(s) = s**2 + s + 1. Let v(o) = f*q(o) + 2*y(o). Suppose v(n) = 0. What is n?
1/4, 3
Let f(w) be the second derivative of -11 - 1/4*w**2 + w + 1/48*w**4 - 1/24*w**3. Factor f(h).
(h - 2)*(h + 1)/4
Determine p so that -6*p**3 - 34/5*p**2 + 2/5*p**5 - 12/5*p + 0 - 6/5*p**4 = 0.
-1, 0, 6
Factor -160 - 2/5*y**2 - 20*y.
-2*(y + 10)*(y + 40)/5
Let x(g) be the third derivative of 129*g**6/8 - 194*g**5/3 + 5*g**4/6 - 19*g**2 - 19*g. Determine k so that x(k) = 0.
0, 2/387, 2
Let g(o) be the third derivative of o**6/40 - 11*o**5/20 + 5*o**4 - 24*o**3 - 8*o**2 + 45. Suppose g(z) = 0. What is z?
3, 4
Solve -1333/5*o**2 + 0 + 2/5*o = 0.
0, 2/1333
Let k(b) be the second derivative of -b**6/120 - b**5/10 + 752*b. Let k(q) = 0. What is q?
-8, 0
Let f = 320636564582/401707793715 - 8/72971443. Let v = 2/1101 + f. Factor v*u**4 + 0 - 12/5*u**3 + 0*u**2 + 16/5*u.
4*u*(u - 2)**2*(u + 1)/5
Factor 0*v + 16/15*v**2 + 0 - 4/5*v**3 + 2/15*v**4.
2*v**2*(v - 4)*(v - 2)/15
Let s = -6/39817 + 79664/199085. Factor -2/5*r**2 + 2/15*r - 2/15*r**3 + s.
-2*(r - 1)*(r + 1)*(r + 3)/15
Let s(w) be the first derivative of 18 - 1/32*w**4 + 3/8*w + 5/16*w**2 + 1/24*w**3. Let s(m) = 0. Calculate m.
-1, 3
Let j(w) be the second derivative of 1/30*w**5 + 0 - 1/2*w**2 + 1/6*w**3 + 1/240*w**6 + 5*w + 5/48*w**4. Let c(g) be the first derivative of j(g). Factor c(h).
(h + 1)**2*(h + 2)/2
Let t be 3/21*-1*(3798/(-216) - -17). Let g(m) be the second derivative of 1/2*m**3 + 0 - t*m**4 + 0*m**2 + 2*m. Solve g(p) = 0.
0, 3
Let k(t) be the third derivative of -t**6/300 + 19*t**5/150 + 29*t**4/12 + 25*t**3/3 - 1164*t**2. Find u, given that k(u) = 0.
-5, -1, 25
Let u = 298314/5 + -59638. Solve -28*a**2 - 12/5*a**4 + 72/5 + 44/5*a - u*a**3 = 0.
-9, -1, 2/3
Let i(t) be the second derivative of -t**6/10 - t**5/10 + t**4/12 + 126*t. Find z such that i(z) = 0.
-1