5/360 - i**4/6 + 17*i**2. Let q(c) be the second derivative of u(c). Factor q(y).
-(y - 1)**2/3
Factor 2/11*c**2 + 76/11 - 78/11*c.
2*(c - 38)*(c - 1)/11
Let f(h) be the third derivative of -h**7/42 + 7*h**6/6 - 37*h**5/2 + 455*h**4/6 - 845*h**3/6 - 59*h**2. Find a, given that f(a) = 0.
1, 13
Suppose -2 = -4*u - 5*x - 5, 0 = -4*u + 5*x + 27. Let -f - 10*f + 6*f + 11*f + u*f**2 + 3 = 0. Calculate f.
-1
Suppose 0 = -10*m + 43 - 13. Factor 0*l**3 - m*l + l**3 + 2*l**3.
3*l*(l - 1)*(l + 1)
Let g(m) be the third derivative of -m**9/1680 - m**8/315 - m**7/252 + m**6/90 - m**5/3 + 28*m**2. Let p(l) be the third derivative of g(l). Factor p(i).
-4*(i + 1)**2*(9*i - 2)
Let q be 3 + -11 + 847/105. Let k(u) be the second derivative of 0*u**2 + 0*u**3 + 0 - 3/50*u**5 - 1/75*u**6 - 5*u - q*u**4. Let k(j) = 0. What is j?
-2, -1, 0
Let v = 86 + -6. Suppose v*n**2 + 9*n - 92*n**2 + 2*n**3 + n**3 = 0. Calculate n.
0, 1, 3
Let j(x) be the second derivative of -5*x**7/42 + 71*x**6/6 - 1295*x**5/4 + 6125*x**4/12 - 8*x - 16. Factor j(f).
-5*f**2*(f - 35)**2*(f - 1)
Suppose 104*b = -78*b + 207*b - 50. Let -8 - 9/2*t**b + 1/2*t**3 + 12*t = 0. What is t?
1, 4
Let o(c) be the first derivative of -11 - 3/4*c**4 + 1/2*c**2 + 2/3*c**3 + 0*c. Factor o(a).
-a*(a - 1)*(3*a + 1)
Let d = 71 - 100. Let p = -14 - d. Factor -5*z**4 + 14*z**2 - 4*z**4 - 8*z - 7*z - 8 + p*z**3 + 3*z.
-(z - 2)*(z - 1)*(3*z + 2)**2
Let m = -1/1608 + 1079/11256. Let 8/21*q - 2/7*q**2 + 8/21 + m*q**4 - 4/21*q**3 = 0. What is q?
-1, 2
Suppose -767*g + 761*g + 42 = 0. Let p(o) be the first derivative of -g + 2/3*o**2 + 1/6*o**4 - 5/9*o**3 - 1/3*o. Factor p(l).
(l - 1)**2*(2*l - 1)/3
Let -20*x + 3/2*x**2 - 14 = 0. Calculate x.
-2/3, 14
Let a(l) be the first derivative of 7 - 1/18*l**3 + 0*l**2 - 1/36*l**4 + 4*l. Let y(m) be the first derivative of a(m). Suppose y(r) = 0. What is r?
-1, 0
Let m be 17/5 - 6/(-10). Let h(v) = -v**3 + v**2 - v - 1. Let r(y) = -9*y**4 - 4*y**3 - y**2 + 3*y + 3. Let o(d) = m*r(d) + 12*h(d). Factor o(a).
-4*a**2*(a + 1)*(9*a - 2)
Let z(l) be the first derivative of 1/3*l**3 + 2*l**2 + 4 + 3*l. Determine u, given that z(u) = 0.
-3, -1
Factor 0*h - 12*h**2 - 3/2*h**4 + 0 - 27/2*h**3.
-3*h**2*(h + 1)*(h + 8)/2
Let v(d) = -22*d**2 + 60*d + 172. Let j(r) = 9*r**2 - 24*r - 69. Let o(w) = 12*j(w) + 5*v(w). Factor o(i).
-2*(i - 8)*(i + 2)
Find v such that -13/9*v**3 + 4/3*v**2 + 1/9*v**4 + 0 + 0*v = 0.
0, 1, 12
Suppose 58 - 16 = 2*n. What is q in -5 + n*q - 25*q**2 - 5 - 56*q = 0?
-1, -2/5
Let i be 45/(-105) + (3 - 15/(-42)*-3). Suppose 0*d - i*d**2 + 0 = 0. What is d?
0
Let t(y) be the third derivative of -y**5/30 - 7*y**4/12 + 6*y**3 - 272*y**2. Let t(r) = 0. Calculate r.
-9, 2
Let q be (-30)/144*8/(-20). Let r(s) be the first derivative of -q*s**3 + 0*s - 1/8*s**2 - 5. Factor r(j).
-j*(j + 1)/4
Let r be 63/(-90) + (-6)/(-5). Determine a so that -25/2 - r*a**2 + 5*a = 0.
5
Let u = -493 + 213. Let d = -278 - u. Let 0 - 4*i**4 + 1/2*i**3 - d*i + 4*i**2 + 3/2*i**5 = 0. Calculate i.
-1, 0, 2/3, 1, 2
Let g(w) = w**2 + 2*w - 6. Let x be g(2). Factor 5*a**2 - a**2 - 22*a**3 + 24*a**3 - x*a**4.
-2*a**2*(a - 2)*(a + 1)
Let i(z) = -5*z**3 - 42*z**2 - 106*z - 75. Let h(k) = -9*k**3 - 84*k**2 - 214*k - 149. Let d(a) = -3*h(a) + 5*i(a). Determine s so that d(s) = 0.
-18, -2, -1
Let u(x) = 10*x**3 + 122*x**2 + 228*x - 336. Let a(n) = 4*n**3 + 49*n**2 + 91*n - 134. Let v(d) = 12*a(d) - 5*u(d). Factor v(i).
-2*(i - 1)*(i + 6)**2
Let k(g) be the second derivative of -1/60*g**6 + 1/4*g**2 + 1/6*g**3 + 0 - 1/20*g**5 + 8*g + 0*g**4. Factor k(q).
-(q - 1)*(q + 1)**3/2
Let v(x) be the first derivative of x**4/12 - 2*x**2/3 - 138. Solve v(i) = 0.
-2, 0, 2
Let m be (-4)/(-14) - 96/(-21). Let j = m - 31/7. Factor 6/7 + j*t**5 + 24/7*t**2 - 6/7*t**4 - 3*t - 6/7*t**3.
3*(t - 1)**4*(t + 2)/7
Let h(k) be the second derivative of -k**6/150 + 7*k**5/50 - k**4 + 52*k**3/15 - 32*k**2/5 - 244*k. Factor h(b).
-(b - 8)*(b - 2)**3/5
Let x = -27524 + 27529. Find b, given that -9/2*b**4 + 0 + 39/4*b**3 + 3*b - 9*b**2 + 3/4*b**x = 0.
0, 1, 2
Let r(c) = 85*c**3 + 205*c**2 + 205*c + 85. Let w(d) = 0*d**2 + 15*d**2 - 2*d**3 + 17*d + 7 + 9*d**3 + 2*d**2. Let g(s) = -2*r(s) + 25*w(s). Factor g(i).
5*(i + 1)**3
Let i(r) be the third derivative of 7*r**5/120 + 25*r**4/12 + 7*r**3/3 + 9*r**2 + 5*r. Let i(c) = 0. Calculate c.
-14, -2/7
Let f(v) be the first derivative of v**5 + 5*v**4/4 - 10*v**3 + 105. Factor f(l).
5*l**2*(l - 2)*(l + 3)
Let n(l) be the second derivative of -3*l**5/80 + 5*l**4/16 - 3*l**3/8 - 27*l**2/8 + 2*l + 198. Determine g, given that n(g) = 0.
-1, 3
Let w(f) = -f**3 + 34*f**2 - 34*f + 40. Let m be w(33). Let a be (4 - (m - 2))*(1 - 1). Factor -8/5*v**4 + 0*v - 4/5*v**2 + 2/5*v**5 + a + 2*v**3.
2*v**2*(v - 2)*(v - 1)**2/5
Determine t, given that 37*t - t - 9*t**3 - 6*t**3 + 9*t**2 + 12 = 0.
-1, -2/5, 2
Let i(k) be the third derivative of -k**8/6 - 10*k**7/21 + k**6/2 + 4*k**5/3 + 2*k**4/3 + 26*k**2 + 2. What is p in i(p) = 0?
-2, -1/2, -2/7, 0, 1
Let v(t) be the first derivative of -21*t**4/20 - 13*t**3/5 - 9*t**2/5 + 161. What is g in v(g) = 0?
-1, -6/7, 0
Let a(y) be the first derivative of 5*y**4 + 0*y**3 + 4/5*y**5 + 0*y + 0*y**2 + 27. Factor a(t).
4*t**3*(t + 5)
Let f = 19/60 + 1/60. Let c(s) be the first derivative of 1/2*s**2 - 2 + 0*s - f*s**3. Factor c(q).
-q*(q - 1)
Let j(q) be the third derivative of -8*q**5/15 + 9*q**4/2 + 40*q**3/3 - 7*q**2 + 40*q. Factor j(m).
-4*(m - 4)*(8*m + 5)
Suppose -30*v + 5*v**3 + 1/2*v**4 + 18 + 13/2*v**2 = 0. What is v?
-6, 1
Let s(d) be the third derivative of -d**6/24 - 3*d**5/4 + 245*d**4/24 - 65*d**3/2 - 29*d**2 - 2. Solve s(h) = 0.
-13, 1, 3
Let j be 170/204 - 74/(-12). Let f(h) be the first derivative of j + 2/9*h**2 + 1/18*h**4 + 2/9*h**3 + 0*h. Factor f(g).
2*g*(g + 1)*(g + 2)/9
Let n(y) = 28*y**5 + 44*y**4 + 54*y**3 - 50*y**2 - 64*y - 30. Let m(w) = -w**5 - w**3 + w**2 + w + 1. Let k(q) = -36*m(q) - 2*n(q). What is g in k(g) = 0?
-3, -1, -2/5, 1
Let u = 3887/15580 + 2/3895. Factor 1/4*g**3 + 1/4 - u*g**2 - 1/4*g.
(g - 1)**2*(g + 1)/4
Let k be ((-99)/(-9) - 11)/(-1*1). Let i = 8/13 + -19/52. Factor -i*j**3 + 0*j + k*j**2 + 0.
-j**3/4
Let w(f) be the second derivative of 0 - 13*f + 0*f**4 + 1/40*f**5 + 0*f**3 + 0*f**2. What is y in w(y) = 0?
0
Suppose 2*m + 20*m = 44. What is x in 2/3*x**4 + 2/3*x**2 - 2*x**3 - 4/3 + m*x = 0?
-1, 1, 2
Let d(h) be the first derivative of 3*h**4/4 + h**2 - h - 8. Let j be d(1). Factor 0*l**4 - l**4 - j*l**4 + 7*l**4 - 2*l**2.
2*l**2*(l - 1)*(l + 1)
Let p(v) = 22*v**3 - 383*v**2 + 742*v - 360. Let l(n) = 7*n**3 - 128*n**2 + 247*n - 120. Let g(j) = -7*l(j) + 2*p(j). Factor g(f).
-5*(f - 24)*(f - 1)**2
Let i(w) be the first derivative of -2*w**5/85 - 13*w**4/34 - 110*w**3/51 - 75*w**2/17 - 143. Let i(x) = 0. Calculate x.
-5, -3, 0
Suppose 0 = -3*g + x + 22, 2*g - 4*x - 40 = -2*g. Let m be -2 + g/39 - -2. Let m*w**3 + 2/13*w**2 - 2/13 - 2/13*w = 0. What is w?
-1, 1
Let g(w) = -2*w - 6. Let q(m) = m**3 + 9*m**2 - 9*m + 5. Let h be q(-10). Let y be g(h). Factor 9*z**3 + 17*z**y - 8*z**4 + 8*z - 8*z + 3*z**2 + 3*z**5.
3*z**2*(z + 1)**3
Suppose v = -r + 3*v - 8, -5*r + 5*v - 40 = 0. Let c = r - -15. Suppose c*y**2 + 8*y - 6*y**2 - 3*y**2 - 2*y**2 = 0. What is y?
0, 2
Let x be 18/(-84)*2*(-50)/15. Factor -2/7*d**4 - 4/7*d - x*d**2 - 8/7*d**3 + 0.
-2*d*(d + 1)**2*(d + 2)/7
Factor -13/3*d**2 + 1/3*d**3 - 29/3*d - 5.
(d - 15)*(d + 1)**2/3
Let y be (-1)/(-3) - 10/30. Suppose -230 = -16*f - 30*f. Factor 0*v**4 + y + 9/5*v**3 - 6/5*v**2 - 3/5*v**f + 0*v.
-3*v**2*(v - 1)**2*(v + 2)/5
Let s(u) be the third derivative of u**6/120 - u**5/60 - u**4/12 - 295*u**2. Let s(o) = 0. What is o?
-1, 0, 2
Let h(v) be the second derivative of -1/6*v**4 + 2/3*v**3 + 0*v**2 - 2*v - 1/10*v**5 + 0. Determine b, given that h(b) = 0.
-2, 0, 1
Let z(g) be the second derivative of 5/42*g**7 + 13*g - 5/6*g**4 - 25/6*g**3 - 5*g**2 + g**5 + 2/3*g**6 + 0. Factor z(q).
5*(q - 1)*(q + 1)**3*(q + 2)
Suppose 5*m = -w - 11, -11*m - 3 = -10*m. Let f(t) be the second derivative of 3*t - 1/9*t**2 + 0 - 1/54*t**w + 2/27*t**3. Factor f(l).
-2*(l - 1)**2/9
Let i(c) = -7*c**4 - 2*c**3 + 35*c**2 + 14*c - 8. Let t(w) = w**4 + w**3 - 3*w**2 - w + 1. Let a(f) = 3*i(f) + 24*t(f). What