2
Let h(a) be the third derivative of 0*a**3 + 1/2688*a**8 - 27*a**2 - 1/960*a**6 + 0 + 1/160*a**5 + 0*a**4 + 0*a - 1/560*a**7. Solve h(w) = 0 for w.
-1, 0, 1, 3
Let g(v) be the third derivative of -1/30*v**5 + 0*v**3 + 0*v + 4/105*v**7 + 0 + 5/336*v**8 + 0*v**4 - 27*v**2 + 1/120*v**6. Let g(u) = 0. Calculate u.
-1, 0, 2/5
Let n = -4/3923 + 3955/31384. Find h, given that n + 1/4*h + 1/8*h**2 = 0.
-1
Factor -51/2*a**2 + 45*a + 12.
-3*(a - 2)*(17*a + 4)/2
Let j(z) be the first derivative of 16 + 0*z - 9/20*z**5 + 3/2*z**2 - 4*z**3 + 39/16*z**4. Suppose j(w) = 0. What is w?
0, 1/3, 2
Let h = -260 - -262. Let a(v) be the third derivative of 0*v + 0 - 5*v**h - 1/5*v**4 + 7/150*v**5 - 4/15*v**3. Find i, given that a(i) = 0.
-2/7, 2
Let t(q) be the third derivative of 0*q**3 + 0*q**5 + 0*q**6 + 0*q**7 + 0*q + 1/896*q**8 + 0*q**4 + 0 + 5*q**2. Factor t(f).
3*f**5/8
Let o be (-2)/(-6) - 16/(-6). Suppose o*h = 5 + 10. Factor 2*m**3 + h*m**5 - 4*m**5 - 3*m**5 + 4*m**4 - 2*m**2 - 2*m**4.
-2*m**2*(m - 1)**2*(m + 1)
Let h(g) be the first derivative of g**4/38 - 16*g**3/57 - 111. Find i, given that h(i) = 0.
0, 8
Let m = 154386/7 + -22054. Suppose 0*n**2 + 0 + 4/7*n**5 + 0*n**4 - m*n**3 + 4/7*n = 0. Calculate n.
-1, 0, 1
Let h(g) be the first derivative of g**3/12 + 9*g**2 + 324*g + 23. Factor h(i).
(i + 36)**2/4
Let n(b) be the first derivative of b**6/840 - b**5/28 + 3*b**4/8 - 7*b**3/6 + 7*b**2/2 + 10. Let k(z) be the second derivative of n(z). Factor k(g).
(g - 7)**2*(g - 1)/7
Let t(j) be the second derivative of 1/10*j**5 - 46*j + j**2 - 1/6*j**4 + 0 - 1/3*j**3. Suppose t(n) = 0. Calculate n.
-1, 1
Let h(v) be the third derivative of v**7/1365 + v**6/156 - 7*v**5/130 + 23*v**4/156 - 8*v**3/39 + 2*v**2 - 4*v. Factor h(r).
2*(r - 1)**3*(r + 8)/13
Let g(k) be the first derivative of k**4/8 - 10*k**3/3 + 17*k**2/4 + 19*k - 29. Factor g(l).
(l - 19)*(l - 2)*(l + 1)/2
Let c = 7/1150 - -2279/3450. Factor 2/3*o**2 + 4/3*o + c.
2*(o + 1)**2/3
Let f(g) be the second derivative of 0*g**2 - 2/9*g**4 - 12*g - 1/15*g**5 + 0 - 2/9*g**3. Factor f(z).
-4*z*(z + 1)**2/3
Suppose 2*k + 3*k = -13*k. Let y(h) be the third derivative of -1/4*h**5 - 11*h**2 + 0 - h**4 - 1/40*h**6 - 2*h**3 + k*h. Factor y(r).
-3*(r + 1)*(r + 2)**2
Let v = 83451/19 + -4387. Suppose 120/19*o**2 + 16/19*o + 0 + v*o**4 + 252/19*o**3 = 0. What is o?
-2, -2/7, 0
Let w(o) be the second derivative of o**6/270 - o**5/30 + o**4/9 + 5*o**3/3 - 9*o. Let l(j) be the second derivative of w(j). Factor l(u).
4*(u - 2)*(u - 1)/3
Let w(y) be the first derivative of 7/2*y**3 - 3 - 30*y**2 + 50*y - 1/8*y**4. What is f in w(f) = 0?
1, 10
Let r(u) = -u**2 + 9*u + 13. Suppose -4*j = 3*m - 43, 4*m - 54 = -4*j - j. Let h be r(j). Suppose 4*q**3 - h*q**4 - 4 - 4*q - 3 + 5 + 5*q**4 = 0. Calculate q.
-1, 1
Let s be (-6)/(-5)*(-30)/(-9). Factor s*k**2 + 2*k**4 - 4*k**3 - 4*k**3 - 6*k**3 + 8*k**3.
2*k**2*(k - 2)*(k - 1)
Let g(v) be the second derivative of -1/12*v**3 - 20*v + 3/2*v**2 + 0 - 1/24*v**4. Factor g(o).
-(o - 2)*(o + 3)/2
Suppose -13*j + 24 = -9*j. Let t(p) = -p**3 + p**2 - 2*p + 2. Let d(o) = -2*o**3 + o**2 - 2*o + 3. Let c(r) = j*t(r) - 4*d(r). Factor c(f).
2*f*(f - 1)*(f + 2)
Let p(n) be the second derivative of n**5/30 + 11*n**4/18 + 10*n**3/9 - 31*n - 3. Factor p(y).
2*y*(y + 1)*(y + 10)/3
Suppose -3*y - 2*p + 54 = 0, 5*p - 23 + 8 = 0. Find b, given that y*b**3 - 196*b**4 + 48*b + 18 + 44*b**2 + 385*b**4 - 187*b**4 = 0.
-3, -1
Let f(u) be the third derivative of 0 - 1/60*u**4 - 1/75*u**5 + 2/15*u**3 + 1/300*u**6 + 0*u + 17*u**2. Let f(s) = 0. What is s?
-1, 1, 2
Suppose 0 = -q - v - 5, 11*v - 7 = -4*q + 10*v. Determine t, given that 1/2*t**5 - 6*t + 11/2*t**3 - 3*t**4 + q - t**2 = 0.
-1, 1, 2
Let h(n) = -n**4 + 23*n**3 + 20*n**2 - 28*n - 24. Let u(g) = -4*g**4 + 68*g**3 + 60*g**2 - 84*g - 72. Let b(k) = 16*h(k) - 5*u(k). Find o, given that b(o) = 0.
-6, -1, 1
Suppose -4*x - o + 22 + 12 = 0, 3*x = -2*o + 23. Let f be 2/4*(-2 - (-24)/x). Factor f*j**3 - 1/3*j - 1/3 + 1/3*j**2.
(j - 1)*(j + 1)**2/3
Let u(j) = 2*j**2 + 5*j - 27. Let g be u(3). Let z(q) = -q**4 - q**2 + 1. Let l(c) = 8*c**4 + 24*c**3 + 78*c**2 - 6. Let f(a) = g*z(a) + l(a). Factor f(i).
2*i**2*(i + 6)**2
Let u(f) be the third derivative of f**7/1155 + f**6/330 - 4*f**5/165 + 590*f**2. Factor u(a).
2*a**2*(a - 2)*(a + 4)/11
Suppose -29*h**5 + h - 60*h**2 - 2*h**3 + 15 + 11 + 30*h**4 - 33*h**5 + 63*h**5 + 4 = 0. What is h?
-30, -1, 1
Suppose 7*i - 31 + 10 = 0. Find j, given that 8*j**2 - 7*j**2 + i*j**2 = 0.
0
Let a(y) = y**3 + y**2. Let z be a(1). Let s be (-7)/35 + 16/5. Find k such that -5*k + 8 - 2*k**2 - 4*k + k + z*k**s = 0.
-2, 1, 2
Let q = -9537 + 47692/5. Find w such that 18/5*w - q*w**2 - 8/5 - 3/5*w**3 = 0.
-4, 2/3, 1
Let h(y) be the third derivative of 5*y**8/672 + 11*y**7/252 - 7*y**6/45 + y**5/5 + 11*y**4/24 - 5*y**2. Let j(f) be the second derivative of h(f). Factor j(l).
2*(l + 3)*(5*l - 2)**2
Suppose 21*q - 60 = 3. Suppose -12/7*o**2 - 8/7*o - 8/7*o**q - 2/7*o**4 - 2/7 = 0. Calculate o.
-1
Let p(w) be the third derivative of -w**5/60 - 7*w**4/8 + 2*w**3/3 + w**2. Let b(m) = 2*m**2 + 22*m - 3. Let r(g) = 6*b(g) + 7*p(g). What is q in r(q) = 0?
1, 2
Let d(l) be the first derivative of -2/15*l**5 + 0*l + 1/3*l**2 - 2/3*l**3 - 7 + 1/2*l**4. Factor d(b).
-2*b*(b - 1)**3/3
Suppose -2947*j + 2937*j = -20. Let w = -1/7 - -17/21. Factor w*q + 1/3 + 1/3*q**j.
(q + 1)**2/3
Let f = -19207 - -57622/3. Factor 2/3*j - 1/3*j**2 - f*j**3 + 0.
-j*(j - 1)*(j + 2)/3
Factor 0*i**5 + i**5 - 158*i**3 + 332*i**3 + 13*i**4 - 144*i**3.
i**3*(i + 3)*(i + 10)
Suppose 2 + 10 = 4*o. Suppose 0 = -4*y + o*n + 14, 4*y = 5*n + 14 + 4. Factor 0 - 3/2*x - 1/2*x**y.
-x*(x + 3)/2
Let f(g) be the third derivative of g**6/180 - 43*g**5/90 + 161*g**4/12 - 49*g**3 + 211*g**2. Determine s, given that f(s) = 0.
1, 21
Let y(h) be the second derivative of -h**7/15120 + h**6/2160 + h**5/240 + h**4/3 - 22*h. Let z(u) be the third derivative of y(u). Factor z(a).
-(a - 3)*(a + 1)/6
Let l(y) = 16*y**2 - 7*y**3 - 2*y - 5 - 4*y - 21*y. Let h = -257 - -273. Let j(f) = 22*f**3 - 48*f**2 + 80*f + 16. Let v(x) = h*l(x) + 5*j(x). Factor v(a).
-2*a*(a - 4)**2
Let t(w) = -w**2 - 14*w + 35. Let n be t(-16). Factor 4*j**2 + n*j**3 - 18*j + 6*j**2 - 5*j**3 + 2*j**2.
-2*j*(j - 3)**2
Let k(c) = 2*c**2 + 20*c - 9. Let z(y) = 2*y**2 + 21*y - 8. Let v(h) = 5*k(h) - 6*z(h). Let x be v(-13). Factor -l**2 + 1 + 1/2*l - 1/2*l**x.
-(l - 1)*(l + 1)*(l + 2)/2
Let r(m) be the second derivative of -m**6/420 + m**5/70 + m**4/21 - 11*m**2/2 - 15*m. Let q(z) be the first derivative of r(z). Find p such that q(p) = 0.
-1, 0, 4
Let x(p) be the third derivative of p**5/180 + 5*p**4/9 + 200*p**3/9 + 3*p**2 - 2. Determine r so that x(r) = 0.
-20
Let a(n) be the first derivative of -n**6/2 - 12*n**5/5 + 9*n**4/4 + 22*n**3 + 6*n**2 - 72*n - 22. Find v such that a(v) = 0.
-3, -2, 1, 2
Factor 0*p - 27/8 + 9/4*p**2 + 1/8*p**4 + p**3.
(p - 1)*(p + 3)**3/8
Factor 7*f**2 - 5*f**3 - 73*f**4 + 74*f**4 + 0*f - 11*f + 8*f.
f*(f - 3)*(f - 1)**2
Let w(i) = 10*i**4 - 112*i**3 - 77*i**2 - 12*i + 1. Let n(b) = b**4 - b**3 + b + 1. Let x(g) = 4*n(g) - 4*w(g). Factor x(q).
-4*q*(q - 13)*(3*q + 1)**2
Let s be (-3)/1 + (-2)/(97110/(-2728771)). Let t = s - -4/9711. Find h, given that t*h**3 - 228/5*h + 36/5 + 49/5*h**4 + 277/5*h**2 = 0.
-3, 2/7
Let i(f) be the second derivative of f**4/30 + 27*f**3/5 - 82*f**2/5 + 83*f + 3. Factor i(d).
2*(d - 1)*(d + 82)/5
Let w = -3910 + 3912. Factor -4/3*u + 2/3*u**w - 2.
2*(u - 3)*(u + 1)/3
Let s = -1386 + 1388. Factor -1/5 + 1/5*i**s - 1/5*i**3 + 1/5*i.
-(i - 1)**2*(i + 1)/5
Let h be 1 - 213/72 - (0 - 2). Let n(v) be the second derivative of 0 + h*v**4 + 0*v**2 - 4*v - 1/12*v**3. What is r in n(r) = 0?
0, 1
Factor 2/5*c**2 - 12/5 + 2/5*c.
2*(c - 2)*(c + 3)/5
Let n(d) = 3*d**3 - 11*d**2 - 5*d. Let f(r) = -r**3 + 5*r**2 + 3*r. Let i(l) = -l**2 - l + 7. Let u be i(-4). Let j(c) = u*f(c) - 3*n(c). Factor j(g).
-4*g**2*(g - 2)
Suppose -3*a - c = -12, 2*a + 4 = 3*a + 3*c. Let b(d) = 6*d - 19. Let h be b(a). Factor 2/3*k**2 - 2/3*k**4 + 0 - 1/3*k + 0*k**3 + 1/3*k**h.
k*(k - 1)**3*(k + 1)/3
Let c = 127 + -120. Let n(m) be the third derivative of -1/18*m**3 + 0*m**4 - 4*m**2 + 0 - 1/630*m**c + 0*m**6 