a) = -2*m(a) - y(a). Find d, given that j(d) = 0.
-3/7, 2/3, 1, 2
Let n(c) be the first derivative of -29*c**3/3 + 37*c**2/8 - c/2 + 17. Factor n(b).
-(4*b - 1)*(29*b - 2)/4
Let l(y) be the third derivative of -19*y**2 + 2/27*y**3 + 0 - 1/540*y**6 + 0*y - 5/108*y**4 + 2/135*y**5. Suppose l(d) = 0. What is d?
1, 2
Suppose -16*b - 8*b + 72 = 0. Let f(j) be the third derivative of -1/20*j**5 + 1/4*j**4 + 0*j + 0*j**3 - b*j**2 + 0. Solve f(s) = 0 for s.
0, 2
Let j(n) = 25*n**2 - 325*n + 2. Let a be j(13). Let 0 + 3/2*i - 3/2*i**a = 0. What is i?
0, 1
Let r = 22 - 21. Factor 0*n**3 + 4*n - r + n**2 - 6*n**3 + 2*n**3.
-(n - 1)*(n + 1)*(4*n - 1)
Let b(h) be the third derivative of 0*h + 0*h**4 + 6*h**2 - 6/35*h**7 + 0*h**3 - 9/112*h**8 + 0 + 0*h**5 - 1/10*h**6. Factor b(x).
-3*x**3*(3*x + 2)**2
Let f(l) be the second derivative of l**6/10 + 9*l**5/20 - 3*l**4/4 - 11*l**3/2 - 9*l**2 + 67*l. Let f(n) = 0. Calculate n.
-3, -1, 2
Let m(s) = s**2 - 5*s - 14. Let a be m(-2). Suppose a = 11*b - 3*b - 24. Determine c so that 3/7*c**2 + 3/7*c**4 - 6/7 - 9/7*c**b + 9/7*c = 0.
-1, 1, 2
Let b(y) = -2*y**2 + y. Let r(s) = -18*s**2 - 36*s. Let q(g) = -8*b(g) + r(g). Find u such that q(u) = 0.
-22, 0
Let d(u) = -19*u**2 - 59*u - 72. Let p(w) be the first derivative of 5*w**3/3 + 15*w**2/2 + 18*w - 10. Let n(k) = 6*d(k) + 22*p(k). Factor n(s).
-4*(s + 3)**2
Let h(m) be the third derivative of m**6/270 - 38*m**5/135 - 82*m**4/27 - 112*m**3/9 + 189*m**2. Factor h(z).
4*(z - 42)*(z + 2)**2/9
Let l(m) be the first derivative of -m**3/9 + 7*m**2 - 147*m + 220. Factor l(p).
-(p - 21)**2/3
Let y(i) = i**4 + i**3 - i. Let d(a) = 40*a**5 - 130*a**3 - 145*a**2 - 45*a - 10. Let q(c) = d(c) + 20*y(c). Factor q(u).
5*(u - 2)*(u + 1)*(2*u + 1)**3
Let n be (16/40)/((-168)/(-5)). Let y(j) be the third derivative of -j**2 + 0 + 0*j**3 + 1/210*j**5 - n*j**4 + 0*j. Factor y(i).
2*i*(i - 1)/7
Let w(j) be the first derivative of j**7/280 + j**6/40 + j**5/20 - 4*j**3/3 + 7. Let k(y) be the third derivative of w(y). Solve k(p) = 0 for p.
-2, -1, 0
Factor 45*d - 16*d**2 - 23*d + 10*d + 2*d**3.
2*d*(d - 4)**2
Let p(q) be the second derivative of 1/16*q**4 + 1/8*q**2 - 1/6*q**3 + 0 + 3*q. Factor p(x).
(x - 1)*(3*x - 1)/4
Suppose -27 = -10*j + 3. Determine y, given that 4*y**2 + 10*y**j - 6*y**3 - y**4 + y**2 = 0.
-1, 0, 5
Factor -j**3 - 27 - 111*j**4 - 2*j**3 + 114*j**4 + 54*j - 24*j**2 - 3*j**3.
3*(j - 3)*(j - 1)**2*(j + 3)
Let f(o) be the third derivative of -o**8/504 + o**7/105 - o**6/90 + 2*o**2 + 2*o. Factor f(d).
-2*d**3*(d - 2)*(d - 1)/3
Determine v, given that 20/7*v + 0 + 36/7*v**2 + 12/7*v**4 - 68/7*v**3 = 0.
-1/3, 0, 1, 5
Let d(y) be the third derivative of y**8/3360 + y**7/630 - y**6/90 + y**5/20 - 3*y**2. Let x(j) be the third derivative of d(j). Find q such that x(q) = 0.
-2, 2/3
Suppose -5*q - 187 = -572. Let o = q - 537/7. Solve -2/7*n**4 + 0 + 0*n - 2/7*n**5 + o*n**3 + 2/7*n**2 = 0.
-1, 0, 1
Let o(t) be the third derivative of -t**7/945 - t**6/270 - t**5/270 + 17*t**2 - 3*t. Factor o(l).
-2*l**2*(l + 1)**2/9
Suppose b - 2*b + 23 = -5*x, 0 = 5*x + 20. Let y = 46 - 42. Solve 6*p - 2*p - p - 2 - p**b + y = 0.
-1, 2
Let a = -112 + 114. Let t(h) be the third derivative of -1/12*h**3 + 0*h - 1/120*h**5 + 1/24*h**4 + 0 + h**a. Suppose t(o) = 0. What is o?
1
Suppose -4*x**3 + 21*x**2 - 140*x**2 + 99*x**2 - 12 - 28*x = 0. Calculate x.
-3, -1
Suppose -35*f + 32*f = 30. Let t be (-1)/1 + (-15)/f. Factor -t*m**2 - 3/2 - 2*m.
-(m + 1)*(m + 3)/2
Let z(x) be the third derivative of x**7/840 + 7*x**6/160 - 51*x**5/80 + 81*x**4/32 + 509*x**2. Factor z(g).
g*(g - 3)**2*(g + 27)/4
Solve 59*q**2 - 26*q**2 - 9*q + q**3 + 9 - 34*q**2 = 0.
-3, 1, 3
Let y(h) = -h**2 - 5*h + 3. Let w be y(-4). Suppose 0 = -i + o + w, 2*i + 3*i + 3*o + 5 = 0. Factor 0*s + 3*s**2 - s**i - s**2 - s.
s*(s - 1)
Let w(s) = -9*s**3 + 3*s**2 + 6*s - 6. Suppose -k = -6*k + 30. Let h(v) = 19*v**3 - 6*v**2 - 11*v + 11. Let g(z) = k*h(z) + 13*w(z). Let g(r) = 0. Calculate r.
-2, 1, 2
Let a(d) = d + 2. Let k be a(0). Factor -6*n - 4 - 3 - 3*n**3 + 7 - 9*n**k.
-3*n*(n + 1)*(n + 2)
Let k(l) be the first derivative of 4*l**5/95 + l**4/38 - 4*l**3/19 - 7*l**2/19 - 4*l/19 + 61. Let k(d) = 0. What is d?
-1, -1/2, 2
Let z(u) be the second derivative of 5*u**4/36 + 13*u**3/2 + 23*u**2/3 - 354*u. Solve z(y) = 0.
-23, -2/5
Let p(a) = 1. Let j(r) = r**2 - 5*r - 7. Let h be -24 + (2 + -4 - 2). Let q(z) = h*p(z) - 4*j(z). Factor q(n).
-4*n*(n - 5)
Let c(o) = 5*o**3 - 34*o**2 + 5*o - 84. Let q be c(7). Let 0 + q*x**2 - 2/9*x - 2/9*x**5 + 0*x**4 + 4/9*x**3 = 0. Calculate x.
-1, 0, 1
Let t(l) be the first derivative of -1/18*l**4 + 1 + l**2 - 2*l - 2/9*l**3. Let p(u) be the first derivative of t(u). Factor p(i).
-2*(i - 1)*(i + 3)/3
Let o(t) be the first derivative of -3*t**5/35 - 9*t**4/7 + t**3/7 + 18*t**2/7 - 294. Let o(v) = 0. What is v?
-12, -1, 0, 1
Let c be (-1)/(-2)*(13 - -9). Suppose 3*q + 4*r - 43 = -0*q, 0 = -3*r - 6. Factor 0 - q*g**2 + 3*g**5 + 9*g**4 + 6*g**3 - 9*g + c*g**2 - 3.
3*(g - 1)*(g + 1)**4
Let l be 26/(-12)*-4*1 + 15 + -23. Determine u, given that -l - 1/3*u + 2/3*u**2 + 1/3*u**3 = 0.
-2, -1, 1
Let v(n) = 5*n**2 + 15*n - 5. Let j(o) = 2*o**2 + 7*o - 3. Let g(r) = 4*r**2 - 21*r + 10. Let l be g(5). Let p(i) = l*j(i) - 3*v(i). Factor p(z).
-5*z*(z + 2)
Let p(v) be the third derivative of -v**8/6720 - v**7/2520 + v**6/360 + 13*v**4/24 + 16*v**2. Let x(g) be the second derivative of p(g). Factor x(h).
-h*(h - 1)*(h + 2)
Let t(f) be the first derivative of -7*f**4 - 27 + 12/5*f**5 + 4*f + 32/3*f**3 - 9*f**2 - 1/3*f**6. Factor t(d).
-2*(d - 2)*(d - 1)**4
Let h(b) be the second derivative of 0 + 0*b**2 + 1/3*b**3 - 7/12*b**4 + 11*b. Let h(w) = 0. Calculate w.
0, 2/7
Let -4*p**4 - p**3 + 20*p + p**2 - 6*p**2 + 9*p**2 - 19*p**3 = 0. What is p?
-5, -1, 0, 1
Let i(s) be the third derivative of -s**8/6720 + s**7/1680 + s**6/120 + 7*s**5/60 - 18*s**2. Let d(g) be the third derivative of i(g). Factor d(k).
-3*(k - 2)*(k + 1)
Let q(g) be the third derivative of g**7/630 - g**6/210 + 15*g**4/8 + 3*g**2. Let t(n) be the second derivative of q(n). Find w such that t(w) = 0.
0, 6/7
Let q(p) be the third derivative of -1/156*p**4 + 0*p + 0*p**3 + 1/780*p**6 - 9*p**2 + 1/1365*p**7 + 0 - 1/390*p**5. Factor q(u).
2*u*(u - 1)*(u + 1)**2/13
Suppose 6*q + 8 = 38. Let i be q/((15/(-9))/(-5)). Let 6*r**3 - i*r**2 - 5*r**3 - 4*r**3 + 192 + 51*r**2 - 144*r = 0. What is r?
4
Let g(i) = i**3 + 4*i**2 - 12*i + 3. Let s be g(-7). Let l = 60 + s. Factor 0 - 2/3*v**2 + l*v**3 + 1/6*v**4 + 0*v.
v**2*(v - 2)*(v + 2)/6
Let a(t) = -2*t**2 + 184*t - 178. Let v(x) = 4*x**2 - 371*x + 357. Let j(o) = 5*a(o) + 2*v(o). Suppose j(m) = 0. What is m?
1, 88
Suppose 5*w - 5*h = -0*w - 25, -w - h = 1. Let p(u) = -u**2 + 12*u + 18. Let n(t) = -4*t**2 + 60*t + 90. Let r(k) = w*n(k) + 14*p(k). Factor r(x).
-2*(x + 3)**2
Suppose -5*y + 3*v = -y + 97, -3*y = -3*v + 72. Let n = -23 - y. Factor -8*s**n + 8 + 10*s**3 + 6*s**4 - 8*s - 8.
2*s*(s - 1)*(s + 2)*(3*s + 2)
Let g(l) be the second derivative of 7*l**6/180 - 23*l**5/120 + 5*l**4/18 - l**3/9 + 2*l + 16. Factor g(w).
w*(w - 2)*(w - 1)*(7*w - 2)/6
Let d(f) be the second derivative of f**10/6048 + f**9/3024 - 3*f**4/4 + 9*f. Let c(n) be the third derivative of d(n). Factor c(z).
5*z**4*(z + 1)
Let c(n) be the first derivative of -3/20*n**5 + 0*n**2 - 3/16*n**4 - 1/12*n**3 + 0*n - 1/24*n**6 - 9. Factor c(j).
-j**2*(j + 1)**3/4
Let f(i) = 44*i**2 - 44*i. Let u(v) = -9*v**2 + 9*v. Suppose 3*j - 23 = 4*d, -5*d + 4*j = 31 - 2. Let t(h) = d*f(h) - 24*u(h). Factor t(k).
-4*k*(k - 1)
Suppose 0*d + 3*d - 24 = 0. Let f be d/6*(-9)/(-33). Let -2/11 + 2*p**2 + 24/11*p**3 - f*p = 0. What is p?
-1, -1/4, 1/3
Factor 4/3*u + 2*u**3 + 10/3*u**2 - 2/3*u**4 - 2/3*u**5 + 0.
-2*u*(u - 2)*(u + 1)**3/3
Let h(w) = -w**3 + 12*w**2 - 2*w + 31. Let f be h(12). Suppose -3*o = f*o. Factor -4/7*g**3 + 2/7*g**4 - 2/7 + o*g**2 + 4/7*g.
2*(g - 1)**3*(g + 1)/7
Let g(b) = -b**4 + 2*b**3 + b**2 - 11*b. Let s(c) = c**4 + 2*c**3 - c**2 + c. Let r(o) = -g(o) - 3*s(o). Factor r(n).
-2*n*(n - 1)*(n + 1)*(n + 4)
Let r(u) be the first derivative of u**6/12 + u**5 - u**4/4 - 10*u**3/3 + u**2/4 + 5*u - 38. Let r(f) = 0. What is f?
-10, -1, 1
Let u(x) = -240*x**2 + 1