 the second derivative of 1/30*j**i + 0 - 2/5*j**2 + 1/15*j**3 - 13*j. Factor h(s).
2*(s - 1)*(s + 2)/5
Let o be 8/4 + -5 + 7. Find d, given that 3*d + 6*d**2 + 3*d**3 - o*d + 4*d = 0.
-1, 0
Let t(i) be the third derivative of -i**7/1365 + 2*i**5/65 - 4*i**4/39 + i**2 + 5. Factor t(s).
-2*s*(s - 2)**2*(s + 4)/13
Let k = 3 + -1. Factor 0*n**2 - 5*n**2 + 3*n**k - n - 6 - 7*n.
-2*(n + 1)*(n + 3)
Let z = 1404 - 1404. Solve -3/8*p**4 - 3/8*p**3 + 0*p**2 + z*p + 0 = 0 for p.
-1, 0
Let h = -687/4 - -174. Solve 3/4*a**4 + h*a**3 - 3/2 + 3/4*a**2 - 9/4*a = 0.
-2, -1, 1
Let b = -59 + -15. Let f = b - -74. Factor -1/2*v**5 + 0*v**4 + v**3 - 1/2*v + 0*v**2 + f.
-v*(v - 1)**2*(v + 1)**2/2
Suppose -155 = -5*c + 5*f, -4*c + 131 = c + f. Solve -20 + c - 28*d**3 - 15 + 8*d**2 + 28*d = 0 for d.
-1, 2/7, 1
Let n be 28/(840/(-78)) - -3. Suppose 0 - n*k**2 - 4/5*k + 2/5*k**3 = 0. What is k?
-1, 0, 2
Let i be (-25)/30*-4*6. Suppose 4*r = p - r - 9, 4*p - 4*r = i. Suppose 1/4*n**p + 0*n**2 - 1/2*n**3 + 1/2*n - 1/4 = 0. What is n?
-1, 1
Suppose -2*v + 17 = 3*h, 2*h - 22 = -2*h - 2*v. Let a(f) = -f + 9. Let l be a(h). Factor -32/9 + 512/9*b - 3056/9*b**2 + 896*b**3 - 882*b**l.
-2*(7*b - 2)**2*(9*b - 2)**2/9
Solve -234 + 120*v - 3/2*v**2 = 0.
2, 78
Suppose 17*s = 22*s - 20. Suppose -s*f = -214 + 202. What is c in 0*c + 27/2*c**3 + 18*c**4 + 15/2*c**5 + f*c**2 + 0 = 0?
-1, -2/5, 0
Let a(i) be the first derivative of 2*i**5/5 - i**4/2 - 10*i**3 - 23*i**2 - 20*i - 142. Factor a(p).
2*(p - 5)*(p + 1)**2*(p + 2)
Find z, given that 29*z**3 - 69*z**3 + 4*z - 2*z**2 + 38*z**3 = 0.
-2, 0, 1
Solve 24*z - 5 + z**2 + 17 + 3*z**2 - 8*z = 0 for z.
-3, -1
Let c(z) be the second derivative of z**5/25 - 2*z**4/15 - 2*z**3 + 72*z**2/5 - 89*z. Determine q so that c(q) = 0.
-4, 3
Let o(h) = 3*h**3 - 80*h**2 + 509*h - 437. Let q(d) = d**2 - d + 1. Let g(c) = -o(c) - 5*q(c). Solve g(s) = 0 for s.
1, 12
Let z(h) be the third derivative of -h**9/9072 - h**8/1008 - h**4/8 + 19*h**2. Let d(u) be the second derivative of z(u). Solve d(x) = 0.
-4, 0
Let w(h) be the second derivative of h**6/225 + h**5/150 - h**4/90 - h**3/45 - 12*h - 3. Determine g, given that w(g) = 0.
-1, 0, 1
Suppose -4*z - 5*w - 10 = 0, 2 = z - w - 0. Suppose 0 + z = q. Factor 0 + q*u - 1/4*u**3 - 1/4*u**4 + 0*u**2.
-u**3*(u + 1)/4
Suppose 122/9*h - 20/9 - 4/3*h**2 = 0. Calculate h.
1/6, 10
Let t(l) be the second derivative of l**5/45 - 4*l**4/9 + 32*l**3/9 + 7*l**2/2 - 2*l. Let g(f) be the first derivative of t(f). Factor g(p).
4*(p - 4)**2/3
Suppose -j - 481 = -118. Let k = 4723/13 + j. Factor -2/13*q**3 - k*q**2 + 0 - 2/13*q.
-2*q*(q + 1)**2/13
Let w(b) = -b**3 + 23*b**2 - 63*b - 245. Let u be w(19). Let -u*m**4 + 8/7 - 54/7*m**2 - 8/7*m - 52/7*m**3 = 0. What is m?
-2, -1, 2/7
Let j be (921/12)/(220/160). Let g = 56 - j. Factor -2/11*t**4 + 2/11*t**2 + 0*t + 0 - g*t**3 + 2/11*t**5.
2*t**2*(t - 1)**2*(t + 1)/11
Let j = -66076/5 + 13216. Find a such that j*a + 2/5*a**2 + 0 = 0.
-2, 0
Find c such that 768/5 - 4*c**3 + 1888/5*c - 88/5*c**2 = 0.
-12, -2/5, 8
Let m = -43279/9 - -4809. What is g in 2/3*g**4 + 0 + m*g + 10/9*g**2 + 14/9*g**3 = 0?
-1, -1/3, 0
Let w(i) = 2*i**2 + 15*i + 10. Let h be w(-7). Let r(q) be the first derivative of -4/21*q**3 + 0*q**2 + 0*q - h. Find n such that r(n) = 0.
0
Let d(t) be the first derivative of -3*t**5/20 + 3*t**4/4 - t**3/2 - 3*t**2/2 + 9*t/4 + 216. Let d(y) = 0. Calculate y.
-1, 1, 3
Let i(x) be the third derivative of 2*x**7/105 + x**6/10 + x**5/15 - x**4/2 - 4*x**3/3 - 72*x**2. Suppose i(r) = 0. What is r?
-2, -1, 1
Let n be ((-80)/(-50))/(-1 + 21/15). Factor 0 + 0*t**3 + 1/4*t**n - 1/4*t**2 + 0*t.
t**2*(t - 1)*(t + 1)/4
Let f = -765 + 768. Determine g so that -2/3*g**2 + 2/3 - 2/3*g + 2/3*g**f = 0.
-1, 1
Let n(s) = -s**2 + 5*s + 1554. Let k be n(42). Factor k + 4/3*r**2 + 1/3*r.
r*(4*r + 1)/3
Let a(o) = 44*o - 1. Let v be a(-1). Let n be ((-36)/v)/(((-2)/5)/(-2)). Find d, given that -2/13*d**3 + 0*d**2 + 0*d**n + 0 + 0*d + 2/13*d**5 = 0.
-1, 0, 1
Let l = -3/677 - -683/1354. Let a(t) be the first derivative of 1/5*t**5 + 0*t**2 + 1/3*t**3 + 8 + 0*t + l*t**4. Solve a(x) = 0.
-1, 0
Let j(x) be the third derivative of -x**6/660 + x**5/165 + 29*x**2 - 1. Find c such that j(c) = 0.
0, 2
Let m(q) be the third derivative of 0 - 3/2*q**6 + 0*q**3 - 5/24*q**4 - 45/112*q**8 - q**2 + 5/6*q**5 + 0*q + 9/7*q**7. Let m(r) = 0. Calculate r.
0, 1/3, 1
Let v be 6/(-36) + 3/((-36)/(-62)). Solve -2*q**v - 9*q**5 - 3*q**3 + 3*q**2 - 3*q**4 + 14*q**5 = 0 for q.
-1, 0, 1
Factor -7/5 - 6/5*j + 1/5*j**2.
(j - 7)*(j + 1)/5
Let u(r) = -16*r**3 - 16*r**2 + 80*r + 14. Let l(h) = 49*h**3 + 48*h**2 - 239*h - 43. Let i(q) = -4*l(q) - 14*u(q). Determine m, given that i(m) = 0.
-3, -1/7, 2
Let x(r) be the third derivative of 0 - 25/3*r**3 - 5/6*r**4 - 1/30*r**5 + 3*r**2 + 0*r. Factor x(d).
-2*(d + 5)**2
Factor -55 + 5/2*d**2 + 45/2*d.
5*(d - 2)*(d + 11)/2
Let d(g) be the first derivative of -g**4/26 + 2*g**3/3 + 46*g**2/13 + 64*g/13 - 117. Factor d(w).
-2*(w - 16)*(w + 1)*(w + 2)/13
Let a(n) be the first derivative of 3*n**4/4 - 14*n**3/3 - 7*n**2/2 + 10*n + 8. Find z such that a(z) = 0.
-1, 2/3, 5
Let c(n) = 4*n**3 + n**2 - n + 3. Let p be c(2). Determine u, given that p*u + 9*u + 50*u**3 + 2*u - 90*u**2 - 8 = 0.
2/5, 1
Let u(x) = -15*x**4 + 2*x**3 + 103*x**2 - 137*x - 216. Let w(a) = -8*a**4 + 52*a**2 - 68*a - 108. Let t(m) = -4*u(m) + 7*w(m). Factor t(d).
4*(d - 3)**2*(d + 1)*(d + 3)
Let q(d) be the third derivative of d**7/490 - 9*d**6/280 + 2*d**5/35 - 8*d**2 - 1. Solve q(r) = 0 for r.
0, 1, 8
Suppose -13*w = -40*w. Suppose w*t - 1/3 + 1/3*t**2 = 0. Calculate t.
-1, 1
Let h(k) be the third derivative of k**7/210 - k**6/12 - k**5/5 + 5*k**4/12 + 11*k**3/6 + 3*k**2 + 17*k. Factor h(z).
(z - 11)*(z - 1)*(z + 1)**2
Solve -2*c - 292*c**4 + 5*c**5 + 2*c + 297*c**4 = 0 for c.
-1, 0
Let h(j) = 2*j**3 - j. Let o(s) = -28*s**3 - 44*s**2 - 108*s. Let w(c) = 12*h(c) + o(c). Let w(r) = 0. What is r?
-6, -5, 0
Factor -24/7*k**2 - 12/7*k**4 + 26/7*k**3 + 8/7*k + 2/7*k**5 + 0.
2*k*(k - 2)**2*(k - 1)**2/7
Suppose 9*c - 27 = 27. Let s be (-14)/(-4)*20/35. Factor 3*p**3 - p**3 + 3*p**5 - s*p**3 + c*p**2 - 6*p**4 - 3*p.
3*p*(p - 1)**3*(p + 1)
Let i(w) be the second derivative of 2*w**5/5 - 11*w**4/6 + 5*w**3/3 + 2*w**2 + w + 7. What is s in i(s) = 0?
-1/4, 1, 2
Let o be -1*0*(-3)/(-12). Let x be (-6)/4 + o + 3. Determine w so that 3/2*w**2 + 0*w - x = 0.
-1, 1
Factor -253*a**2 - 150*a + 218*a**2 - 46 + 6.
-5*(a + 4)*(7*a + 2)
Let j = 3881/6285 - 22/1257. Factor -18/5*v + 0 - 3*v**2 + j*v**3.
3*v*(v - 6)*(v + 1)/5
Let u(o) = 6*o**2 - 65*o - 21. Let m(n) = -11*n**2 + 129*n + 42. Let q(i) = -6*m(i) - 10*u(i). Factor q(w).
2*(w - 21)*(3*w + 1)
Factor -2/5*t**2 - 26/5*t - 16.
-2*(t + 5)*(t + 8)/5
Suppose -3*j - 131 + 146 = 0. Suppose 71 = j*r + 56. Suppose -1/4*w**r + 0 - 3/4*w - w**2 = 0. What is w?
-3, -1, 0
Let m(y) = 2*y**5 - 32*y**4 + 127*y**3 + y**2 + 1. Let i(p) be the second derivative of p**5/20 - p**4/12 - p**2/2 - 19*p. Let o(u) = i(u) + m(u). Factor o(w).
2*w**3*(w - 8)**2
Let d(l) be the first derivative of l**3/9 + l**2/6 - 2*l - 142. Determine s, given that d(s) = 0.
-3, 2
Factor 1/4*o**3 - 3/4*o + 0*o**2 - 1/2.
(o - 2)*(o + 1)**2/4
Let m(g) = 4*g**4 + 16*g**3 + 16*g**2 - 8*g - 12. Let p(d) = -4*d**4 - 17*d**3 - 15*d**2 + 11*d + 13. Let t(q) = -3*m(q) - 4*p(q). Find c, given that t(c) = 0.
-4, -1, 1
Let f = 22 - 6. Suppose -2*i = -i + z - 7, -3*i - 2*z = -f. What is b in -b**3 + 5*b**i + b + 2*b**2 - 7*b**2 = 0?
-1, 0, 1
Let o(c) be the first derivative of -35*c**3/2 - 27*c**2/4 + 3*c - 347. Factor o(t).
-3*(5*t + 2)*(7*t - 1)/2
Solve -2/3*h**4 - 448/3*h**2 + 0 + 512/3*h - 62/3*h**3 = 0.
-16, 0, 1
Let r be (-6)/(-4)*2/(-9)*-6. Suppose -16 = -r*s - 3*m, 2*s + s + m - 10 = 0. Find y such that -10/3*y + 25/3 + 1/3*y**s = 0.
5
Let t(u) = 13*u**3 - 17*u**2 - 9. Let o(m) = 3*m**3 - 4*m**2 - 2. Let n(p) = 2*p**3 + 7*p**2 + 9*p. Let a be n(-3). Let y(d) = a*o(d) + 4*t(d). Factor y(b).
-2*b**2*(b - 2)
Let t(k) be the first derivative of -2*k**3 - 31*k**2/2 + 144*k - 43. Let x(m) = m**2 + m. Let z(i) = 5*t(i) + 35*x(i). Factor z(j).
5*(j - 12)**2
Let u(b) = b**3 + 95*b**2 - 9*b - 87. Let y(h) = 4*h**3 + 285*h**2 - 26*h - 263. Let