+ 2)*(g + 6)/5
Let z(s) be the second derivative of 18*s + 0 + 0*s**2 + 1/10*s**4 - 9/100*s**5 + 1/50*s**6 + 0*s**3. Determine w, given that z(w) = 0.
0, 1, 2
Let b(x) be the third derivative of x**5/450 - x**4/60 - 2*x**3/5 - 3*x**2 - 11*x. Factor b(d).
2*(d - 6)*(d + 3)/15
Find l such that 10/7*l + 2/7*l**2 - 2/7*l**3 + 6/7 = 0.
-1, 3
Let y(f) = -f**2 - 6*f + 13. Let t be y(-6). Suppose -o + 0*k = 4*k - 13, 3*o - t = k. Let 5*l**2 - l**2 - 6*l**5 + 2*l**3 - 8*l**4 + 0*l**o = 0. Calculate l.
-1, 0, 2/3
Let v(w) = 4*w**2 - 37*w + 13. Let o be v(9). Let a be 2/o - 423/(-126). Determine k so that -2/7*k + 18/7*k**3 - a*k**4 + 12/7*k**2 - 1/7 = 0.
-1/3, 1/3, 1
Let s(f) be the third derivative of 3*f**5/40 + 47*f**4/8 - 16*f**3 + 28*f**2 - 1. Factor s(u).
3*(u + 32)*(3*u - 2)/2
Let q(w) be the second derivative of 4*w**6/15 + 25*w**5 + 861*w**4 + 11466*w**3 - 18522*w**2 + 18*w + 3. Factor q(n).
4*(n + 21)**3*(2*n - 1)
Let c(k) = k**2 - 16*k - 2638. Let a be c(60). Factor 2/5*y**4 - 6/5*y**3 + 0 + 6/5*y**a - 2/5*y.
2*y*(y - 1)**3/5
Let a = -18782 - -132344/7. Let t = a - 124. Find y such that -t*y**2 + 0 + 2/7*y = 0.
0, 1
Let d(f) = -25*f**2 + 4*f + 21. Let y(w) = 21*w**2 - 4*w - 21. Let k(q) = 5*d(q) + 6*y(q). Factor k(i).
(i - 7)*(i + 3)
Let r be (5/3)/(125/150). Suppose -8 + 9*y**r - 2*y + 2*y**3 + 4*y**2 - 5*y**2 = 0. Calculate y.
-4, -1, 1
Let v = 19 + -16. Let y be v/4*(-5)/(-15). Determine w, given that 0*w + 0 + 1/4*w**2 + y*w**3 = 0.
-1, 0
Suppose 21*x = -2119 - 1892. Let t = x - -192. Solve -t - 3/2*b + b**2 = 0 for b.
-1/2, 2
Let q be 65 - (-3 - (-2 + 3)). Let h(z) = 3*z**2 + 59 - q - 11*z**2. Let p(o) = -9*o**2 - o - 11. Let r(v) = -7*h(v) + 6*p(v). Find d, given that r(d) = 0.
1, 2
Find z such that -25799 + 8*z + 25799 - 4*z**2 = 0.
0, 2
Factor 5*v**3 + 22 - 5 + 5*v - 10*v**3 - 15*v**2 - 2.
-5*(v - 1)*(v + 1)*(v + 3)
Let t(a) be the first derivative of 18/7*a**2 - 11 + 108/7*a + 1/7*a**3. Suppose t(q) = 0. What is q?
-6
Let g be (92/253)/(7/(7/2)). Factor -g*r**2 - 8/11 - 10/11*r.
-2*(r + 1)*(r + 4)/11
Let y = 21 + -56/3. Let m be (28/(-3) + 10)/((-2)/(-5)). Factor -m*t**3 + 0 - y*t**4 + 16/3*t**2 - 4/3*t.
-t*(t - 1)*(t + 2)*(7*t - 2)/3
Let f(i) be the third derivative of -i**6/360 - 29*i**5/60 - 43*i**4/36 - 167*i**2 - 2*i. Factor f(o).
-o*(o + 1)*(o + 86)/3
Let y(a) be the third derivative of a**6/30 - 14*a**5/5 + 147*a**4/2 + 96*a**2. Let y(g) = 0. Calculate g.
0, 21
Let p(q) be the second derivative of q**5/100 + 3*q**4/20 - 2*q - 213. Factor p(y).
y**2*(y + 9)/5
Let c(v) = -12*v**3 - 8*v**2 + 10*v + 12. Let x(q) = -q**4 + 23*q**3 + 15*q**2 - 18*q - 24. Let h(j) = 5*c(j) + 2*x(j). Let h(d) = 0. Calculate d.
-6, -1, 1
Let t(a) be the third derivative of a**6/360 + a**5/36 + a**4/24 - a**3/2 + 86*a**2. Factor t(i).
(i - 1)*(i + 3)**2/3
Suppose -m**4 + 45*m**2 - 10*m**3 + 0*m**4 - 54*m**2 = 0. Calculate m.
-9, -1, 0
Let p be (450/(-70) - -7)*(-12)/(-8). Suppose -8/7 - p*t**3 - 20/7*t**2 - 22/7*t = 0. Calculate t.
-4/3, -1
Suppose -5 + 3 = -r. Factor -5*d**2 - 11 + 9*d**r - 6*d**2 + 16*d - 21.
-2*(d - 4)**2
Let -38 + 50 - 13*y + 18*y**2 - 3*y**3 - 14*y = 0. Calculate y.
1, 4
Let g(l) = -6*l**2 + 5*l + 6. Let t(d) = 5*d**2 - 6*d - 7. Let f(i) = 4*g(i) + 5*t(i). Factor f(c).
(c - 11)*(c + 1)
Let b(o) = 24*o**3 + 112*o**2 + 128*o + 16. Let s(q) = -25*q**3 - 113*q**2 - 128*q - 16. Let v(l) = -3*b(l) - 4*s(l). What is j in v(j) = 0?
-2, -1/7
Let k(r) = -r**2 + r - 1. Let c(u) = u**3 + 10*u**2 - 3*u - 3. Let t(h) = -c(h) - 5*k(h). Determine s so that t(s) = 0.
-4, -2, 1
Suppose 0 = 2*f - 5*m - 3, f + 24 - 27 = 2*m. Suppose 3*d + f = 5*l + 11, -2*l - 5*d = -24. Solve -12/7 + 3/7*g**3 + 24/7*g - 15/7*g**l = 0.
1, 2
Let 65 - 6*l**2 - 66 + 3*l + l**3 + 3*l**2 = 0. Calculate l.
1
Let o = 23 + -18. Let f(h) be the third derivative of -5*h**2 - 1/24*h**6 + 0*h + 0 + 2/105*h**7 - 1/6*h**3 + 5/24*h**4 - 1/20*h**o. Factor f(w).
(w - 1)**2*(w + 1)*(4*w - 1)
Let n(r) be the third derivative of -r**8/60480 - r**7/3780 - 11*r**5/30 + 34*r**2. Let h(k) be the third derivative of n(k). Factor h(t).
-t*(t + 4)/3
Let q(b) = 9*b**3 - 27*b**2 + 29*b - 11. Let x = 12 - 1. Let w(h) = 3*h**3 - 9*h**2 + 10*h - 4. Let u(i) = x*w(i) - 4*q(i). Let u(y) = 0. What is y?
0, 1, 2
Let f(p) = -3*p**2 - 7*p + 30. Let t(u) = -2*u**2 - 9*u + 29. Let l(s) = 3*f(s) - 4*t(s). Factor l(d).
-(d - 13)*(d - 2)
Let y(c) be the first derivative of 0*c - 3/5*c**5 + 0*c**2 - 3/2*c**4 - 21 + 0*c**3. Factor y(r).
-3*r**3*(r + 2)
Let d(o) = 4*o**3 - 31*o**5 - o**4 - 6*o**4 + 5*o + 29*o**5. Let s(z) = z**5 + 3*z**4 - 2*z**3 - 2*z. Let g(t) = 3*d(t) + 7*s(t). Suppose g(x) = 0. What is x?
-1, 0, 1
Let f(p) be the first derivative of p**4/4 - 8*p**3/3 - 10*p**2 + 139. Solve f(s) = 0.
-2, 0, 10
Let x(p) be the third derivative of -p**10/45360 + p**9/7560 + 5*p**4/12 - 10*p**2. Let g(l) be the second derivative of x(l). Factor g(r).
-2*r**4*(r - 3)/3
Let f(q) be the third derivative of q**9/19656 + q**8/43680 - 7*q**4/24 - 5*q**2. Let b(w) be the second derivative of f(w). Solve b(y) = 0 for y.
-1/5, 0
Let c = 10076/5 + -90674/45. What is b in 0*b - c*b**2 + 2/9 = 0?
-1, 1
Determine p, given that 282*p - 3/2*p**2 - 13254 = 0.
94
Let -1/5*i**3 - 324/5 - 153/5*i - 22/5*i**2 = 0. What is i?
-9, -4
Factor -1356*a - 169*a**4 - 3 - 448*a**3 - 87*a**4 - 132*a**2 + 1412*a - 1.
-4*(a + 1)**2*(8*a - 1)**2
Let s(n) = -7*n**4 - n**3 + 11*n**2 - 16*n + 3. Let u(v) = v**4 + v**3 - v**2 + 1. Let z(l) = s(l) + 5*u(l). Solve z(p) = 0.
-2, 1, 2
Suppose 0 = 17*s - 10*s - 336. Let u be (-22)/33 - (-38)/s. Factor 1/8 + 3/8*o**2 - 3/8*o - u*o**3.
-(o - 1)**3/8
Let q(t) = -3*t**2 + 275*t - 448. Let a be q(90). Factor -2/5*w**3 + 0 + 0*w + 2/5*w**5 + 0*w**a + 0*w**4.
2*w**3*(w - 1)*(w + 1)/5
Let l = -35 - -39. Factor 56*c + 42*c**3 - 8*c**3 + 106*c**3 + 6 - 50*c**l - 14 - 138*c**2.
-2*(c - 1)**2*(5*c - 2)**2
Let y(w) be the third derivative of -w**7/11340 + w**6/540 - w**5/60 - 7*w**4/12 - 11*w**2. Let m(a) be the second derivative of y(a). Factor m(s).
-2*(s - 3)**2/9
Let z = -6 - -12. Let q be z/(-39) - (-54)/13. Factor -2*w**3 + 3*w**q - w**5 + 10 - 10 + 0*w**5.
-w**3*(w - 2)*(w - 1)
Let d(g) = -4*g**3 - 12*g**2 - 4*g - 4. Let v(t) = -4*t**3 - 12*t**2 - 5*t - 3. Suppose -13 + 1 = -4*w. Let r(b) = w*d(b) - 4*v(b). Find m, given that r(m) = 0.
-2, -1, 0
Let x be (522/72 + -7)/((-10)/(-8)). Solve 0 - 1/5*i + x*i**2 = 0.
0, 1
Determine u, given that 0 + 5/2*u**3 - 25/2*u**2 + 10*u = 0.
0, 1, 4
Let b(x) = -231*x**2 + 405*x + 99. Let y(d) = 33*d**2 - 58*d - 14. Let p(w) = 2*b(w) + 15*y(w). Factor p(g).
3*(g - 2)*(11*g + 2)
Let o(j) be the third derivative of -j**8/336 + 29*j**7/1260 - 13*j**6/720 - 19*j**5/120 - j**4/16 + 4*j**2 - 37. Find v such that o(v) = 0.
-1, -1/6, 0, 3
Suppose 0 = 2*q + 2*g - 2, -4*g = -4*q - 0*q + 20. Let y = 27 - 24. Factor u**2 - 3*u**q - u**2 + y*u.
-3*u*(u - 1)*(u + 1)
Let f(q) be the second derivative of q**7/14 + 5*q**6 + 612*q**5/5 + 2023*q**4/2 - 4913*q**3/2 + 158*q. Factor f(m).
3*m*(m - 1)*(m + 17)**3
Let b(k) be the second derivative of k**4/9 + 46*k**3/3 + 136*k**2/3 - 41*k. Factor b(w).
4*(w + 1)*(w + 68)/3
Let p(v) = 2*v**3 + 4*v + 8 + v**2 + 0*v**3 + v**2. Let j(m) = 3*m**3 + 3*m**2 + 5*m + 10. Let q(y) = -4*j(y) + 5*p(y). Factor q(k).
-2*k**2*(k + 1)
Let i(p) = -6*p**2 - 22*p + 24. Let j(c) = 14*c**2 + 43*c - 47. Let u(w) = -5*i(w) - 2*j(w). Factor u(n).
2*(n - 1)*(n + 13)
Let u be ((-6)/10)/(10/50). Let y(n) = n**3 + 3*n**2 + 5. Let k be y(u). Suppose -12*i**4 - 3*i**3 + 4*i**2 + 3*i**3 - 4*i**k + 12*i**2 = 0. What is i?
-2, 0, 1
Let r(c) = 4*c**3 - 6*c + 10. Let i(l) = -13*l**3 - l**2 + 17*l - 31. Let o(g) = 4*i(g) + 14*r(g). Let o(u) = 0. Calculate u.
-2, 1, 2
Let a be 4/62 - 4*1071/(-2790). Determine r, given that 2/5*r**3 + 8/5 - 2/5*r**2 - a*r = 0.
-2, 1, 2
Let m(u) = 2*u**5 - 28*u**4 - 16*u**3 + 4*u**2 - 4*u + 4. Let s(j) = -j**5 - 2*j**4 + j**2 - j + 1. Let i(o) = -m(o) + 4*s(o). Factor i(h).
-2*h**3*(h - 4)*(3*h + 2)
Let l = -8457/11 + 533836/693. Let d = -11/9 + l. Find c, given that -d*c + 2/7*c**2 - 4/7 = 0.
-1, 2
Let y be 12/2*22/44. Suppose -d = 4*l + 5, -y*d + 2*l = 2*d - 19. Solve -10 + 31*x**3 - 20*x + 27*x**4 + 14*x**3 + 2 + 6*x**2 + 0*x**d = 0.
-1, -2/3, 2/3
