 z(q) be the first derivative of -52 + 256/3*q**2 - 8192/9*q + 1/18*q**4 - 32/9*q**3. Factor z(h).
2*(h - 16)**3/9
Let l be 1 - ((-4)/6 + (-4)/3). Suppose -9 = -6*j + l. Factor -2/7 + 2/7*m**j + 0*m.
2*(m - 1)*(m + 1)/7
Factor 2/7*x**2 + 40/7 - 2/7*x**3 + 32/7*x.
-2*(x - 5)*(x + 2)**2/7
Let x(s) = 39*s**3 - 207*s**2 + 468*s - 420. Let j(m) = -3*m**3 + 16*m**2 - 36*m + 32. Let a(n) = -27*j(n) - 2*x(n). Factor a(y).
3*(y - 2)**3
Let l = 452 - 3152/7. What is o in -l*o**2 + 8/7*o**3 + 8/7*o - 2/7*o**4 - 2/7 = 0?
1
Let h(f) be the first derivative of 1/48*f**4 + 5*f + 1/24*f**3 + 0*f**2 - 2. Let j(a) be the first derivative of h(a). Find v such that j(v) = 0.
-1, 0
Let x(a) be the first derivative of 0*a**2 - 4/27*a**3 - 1/18*a**4 + 0*a + 2/45*a**5 + 46. Solve x(h) = 0 for h.
-1, 0, 2
Let p(a) = -2*a**3 - 2*a**2 - 16*a + 8. Let n(r) = -r**3 + r**2 - 2*r. Let q(f) = 6*n(f) - p(f). Factor q(l).
-4*(l - 2)*(l - 1)*(l + 1)
Let s(x) be the second derivative of 0*x**3 + 0*x**4 + 1/30*x**6 + 0*x**5 + 0 + 0*x**2 - 5*x. Factor s(i).
i**4
Let c(s) be the third derivative of s**6/60 + s**5/5 - 7*s**4/12 + 476*s**2. Find o, given that c(o) = 0.
-7, 0, 1
Let c be (-2)/18*(228/140)/(-19). Let s(g) be the second derivative of -1/70*g**5 + 0 - c*g**6 - 8*g + 0*g**2 + 0*g**4 + 0*g**3. Factor s(r).
-2*r**3*(r + 1)/7
Factor 46*y**3 + 6*y**5 + 24*y**4 - 10*y**3 + 16*y**2 - 2*y**5.
4*y**2*(y + 1)**2*(y + 4)
Let i = 1606 + -1603. Find k such that 6/7*k**2 + 1/7*k - 2/7*k**i - 3/7 + 1/7*k**5 - 3/7*k**4 = 0.
-1, 1, 3
Let r(z) = -8*z + 4*z**2 + 9*z**3 - 10*z + 10 + 3*z. Let j(g) = 55*g**3 + 25*g**2 - 90*g + 60. Let i(m) = -4*j(m) + 25*r(m). Let i(v) = 0. Calculate v.
-2, 1
Let a(c) be the first derivative of c**6/51 - 32*c**5/85 + 97*c**4/34 - 556*c**3/51 + 380*c**2/17 - 400*c/17 + 308. Factor a(j).
2*(j - 5)**2*(j - 2)**3/17
Let n(q) = 246*q**5 + 4239*q**4 + 17157*q**3 - 12684*q**2 - 7992*q - 975. Let j(p) = -p**5 + 3*p**2 + 1. Let r(a) = 3*j(a) + n(a). Let r(m) = 0. Calculate m.
-9, -2/9, 1
Let p(i) = i**2 - 40*i - 41. Let k be p(41). Let 2/3*u - 1/3*u**2 + k = 0. What is u?
0, 2
Let k(j) be the third derivative of -j**6/80 - 69*j**5/20 - 4761*j**4/16 - 145*j**2. Suppose k(u) = 0. What is u?
-69, 0
Find i such that 4*i**2 + 4/3*i + 0 = 0.
-1/3, 0
Let y(g) be the second derivative of -1/165*g**5 + 4*g**2 - 3*g + 0*g**3 + 1/220*g**6 + 0 - 1/132*g**4. Let t(c) be the first derivative of y(c). Factor t(d).
2*d*(d - 1)*(3*d + 1)/11
Let r = 385 - 385. Determine i, given that -44/7*i**2 + r - 12/7*i**5 - 8/7*i - 52/7*i**4 - 76/7*i**3 = 0.
-2, -1, -1/3, 0
Let z(g) be the second derivative of -g**5 + 10/3*g**3 - 5/6*g**4 + 0 - 1/6*g**6 - 21*g + 15/2*g**2. Let z(c) = 0. What is c?
-3, -1, 1
Let c(a) be the second derivative of a**6/15 - 4*a**5/5 - a**4/2 + 130*a**3/3 - 200*a**2 - 580*a. What is z in c(z) = 0?
-4, 2, 5
Let r = -1352 + 1354. Factor 1/2*j + 1/4 + 1/4*j**r.
(j + 1)**2/4
Let w(n) be the third derivative of -n**7/105 + 2*n**6/45 - 7*n**5/90 + n**4/18 + 39*n**2 - 2. Factor w(i).
-2*i*(i - 1)**2*(3*i - 2)/3
Let l(m) = -m**5 + m**4 - m**2 - 2*m. Let h(v) = 4*v**5 - 15*v**4 + 21*v**3 - 7*v**2 + 6*v. Let t(f) = -h(f) - 3*l(f). Determine k so that t(k) = 0.
0, 1, 10
Let d(w) be the second derivative of 3/4*w**2 + 0 + 1/6*w**3 + 1/72*w**4 + 4*w. Factor d(o).
(o + 3)**2/6
Let s be (-88)/(-14) + (-1 - 20/(-28)). Let p be 1 + (s/14)/3. Factor 2/7*l**5 + 0 + 12/7*l**3 + 8/7*l**2 + 2/7*l + p*l**4.
2*l*(l + 1)**4/7
Let i = -1 - -3. Suppose 0 = -3*d + i + 4. Factor 0*r**2 - r**3 - 2*r**2 + 4*r**d.
-r**2*(r - 2)
Let d(a) be the third derivative of 0 + 1/24*a**6 + 0*a + 0*a**4 + 1/15*a**5 + 23*a**2 + 1/210*a**7 + 0*a**3. Determine b, given that d(b) = 0.
-4, -1, 0
Let y = -1189 + 1197. Let w(t) be the third derivative of 0*t**3 + 0*t**5 - 3/350*t**7 - 1/280*t**y - 1/200*t**6 + 0*t + 0 + 0*t**4 + 11*t**2. Factor w(p).
-3*p**3*(p + 1)*(2*p + 1)/5
Factor 100/13 - 12/13*g**2 + 90/13*g - 2/13*g**3.
-2*(g - 5)*(g + 1)*(g + 10)/13
Suppose 5*p = 0, 9 = -0*m + 3*m + p. Suppose -m*s = 7 - 13. Factor -1/2*n**3 - 1/4*n**s + 1/2*n + 0 + 1/4*n**4.
n*(n - 2)*(n - 1)*(n + 1)/4
Let k(y) be the third derivative of y**7/630 - y**6/180 - y**5/60 + y**4/18 + 2*y**3/9 - 3*y**2 - 148*y. Factor k(z).
(z - 2)**2*(z + 1)**2/3
Let l = 26 - 22. Factor -54 - c**3 + 2*c**3 - c**5 + 54 - c**l + c**2.
-c**2*(c - 1)*(c + 1)**2
Suppose 5*p - 25 = 2*w, -2*p + 3 = -5*w - 7. Let h be w/((5/15)/(2/12)). Solve -1/2*d**3 - 1/2*d**4 + d**5 + 0 + 0*d**2 + h*d = 0.
-1/2, 0, 1
Factor 3312*b - 1155*b**2 - 1728 + 225/2*b**3.
3*(3*b - 2)*(5*b - 24)**2/2
Suppose 21*d = -54 + 159. Let n(i) be the second derivative of 6*i - 1/2*i**4 + 1/15*i**6 + 2*i**2 + 0 - 1/10*i**d + 1/3*i**3. Factor n(b).
2*(b - 2)*(b - 1)*(b + 1)**2
Let n(y) = -16*y**3 + 12*y**2 + 28*y. Let u(p) = -p**3 + p. Let r(q) = n(q) - 12*u(q). Determine b, given that r(b) = 0.
-1, 0, 4
Suppose -6 = 2*y - 5*x, 2*x - 10 = -3*y - 0*x. Let c(b) be the first derivative of -1/12*b**3 + 1/2*b**2 - 3/4*b + y. Factor c(f).
-(f - 3)*(f - 1)/4
Let g(t) be the first derivative of 8*t**6/15 + 52*t**5/25 + 7*t**4/5 - 44*t**3/15 - 22*t**2/5 - 8*t/5 - 14. Find o, given that g(o) = 0.
-2, -1, -1/4, 1
Let k(n) be the second derivative of 10/3*n**3 - 26*n - 1/6*n**6 + 0*n**4 - 3/4*n**5 + 0 + 0*n**2. Factor k(u).
-5*u*(u - 1)*(u + 2)**2
Let f(p) be the first derivative of -2*p**5/5 - 9*p**4/5 - 8*p**3/5 + 8*p**2/5 + 148. Solve f(u) = 0.
-2, 0, 2/5
Let f(q) = 4*q**4 - 4*q**3 + 20*q**2 + 8*q - 20. Let u(v) = -v**3 - 1. Let g(x) = f(x) - 20*u(x). Solve g(p) = 0.
-2, -1, 0
Let s = 7548 + -98120/13. Factor 6/13 - s*r - 2/13*r**2.
-2*(r - 1)*(r + 3)/13
Let m(k) be the first derivative of 5*k**4/4 - 325*k**3/3 - 665*k**2/2 - 335*k + 741. Factor m(q).
5*(q - 67)*(q + 1)**2
Let h(o) be the third derivative of 0*o - 1/240*o**5 - 1/840*o**7 + 1/12*o**3 + 3*o**2 + 1/160*o**6 + 0 - 1/32*o**4. Solve h(k) = 0 for k.
-1, 1, 2
Factor -2/5*c**4 + 32/5*c - 14/5*c**3 + 4*c**2 + 0.
-2*c*(c - 2)*(c + 1)*(c + 8)/5
Let g(p) be the third derivative of p**6/70 - 2*p**5/21 - 23*p**4/42 - 20*p**3/21 + 6*p**2 - 29*p. Factor g(q).
4*(q - 5)*(q + 1)*(3*q + 2)/7
Let y be (140/2436)/(-1*2/6). Let j = y - -73/87. Factor -2/3*x**4 + 0*x**3 + 0*x + 4/3*x**2 - j.
-2*(x - 1)**2*(x + 1)**2/3
Let l(r) be the third derivative of r**8/672 - 19*r**7/840 + 13*r**6/480 + 83*r**5/120 + 5*r**4/8 - 3*r**3 - 411*r**2. Let l(h) = 0. Calculate h.
-2, -1, 1/2, 6
Suppose -r + 11 = 4*i, 0*r = r - 3*i + 3. Let c(p) = -267*p + 803. Let l be c(3). Suppose 2/9*x**r + 0 + 2/9*x**l - 4/9*x = 0. Calculate x.
-2, 0, 1
Factor -5487*v**2 + 5483*v**2 + 22*v + 334*v - 40*v.
-4*v*(v - 79)
Let o(m) be the third derivative of 9*m**6/320 + 11*m**5/160 + m**4/32 - 208*m**2. Factor o(j).
3*j*(j + 1)*(9*j + 2)/8
Let d(q) be the second derivative of -q**6/120 + q**5/80 - 398*q. Factor d(z).
-z**3*(z - 1)/4
Let f = -5087 + 55967/11. Suppose -2/11*q**5 - 4/11 + 8/11*q**4 - 4/11*q**2 - 8/11*q**3 + f*q = 0. Calculate q.
-1, 1, 2
Let i(z) be the first derivative of z**4/20 - 4*z**3/5 + 21*z**2/10 + 39*z - 5. Let n(y) be the first derivative of i(y). Suppose n(j) = 0. What is j?
1, 7
Let j(z) be the third derivative of -z**6/144 - 43*z**5/72 + 25*z**4/8 + 477*z**2. Determine i, given that j(i) = 0.
-45, 0, 2
Let a(k) be the third derivative of 1/280*k**7 - 1/80*k**5 + 0*k**3 - 1/80*k**6 + 1/16*k**4 + 0*k + 10*k**2 + 0. Determine h, given that a(h) = 0.
-1, 0, 1, 2
Let m(v) = -3*v**2 + 2*v - 11*v**3 - 5 - 9*v**3 + 16*v**3. Let q(o) = o**3 + 1. Let w(u) = 4*m(u) + 20*q(u). Factor w(c).
4*c*(c - 2)*(c - 1)
Suppose -5*w = -13*w + 32. Factor 73 + 7 + 37*z**w + 20*z**3 - 42*z**4 - 80*z.
-5*(z - 2)**3*(z + 2)
Suppose 2*s = 19 - 15, 3*s + 21 = -t. Let p be 1/((t/(-12))/9). Factor 0*h**2 + 0*h + 0 + 1/3*h**p + 0*h**3.
h**4/3
Let m(q) be the second derivative of -q**6/30 + q**5/10 - q**4/12 + 8*q + 4. What is j in m(j) = 0?
0, 1
Suppose -15 = 4*g - 35. Suppose -3*y = -y - 5*t - 5, -3*y = g*t + 5. Solve y - 2/5*j + 2/5*j**3 + 0*j**2 = 0 for j.
-1, 0, 1
Suppose -3*u - 5*m = 10, -15*m + 16*m + 2 = 0. Find q such that u - 10/9*q**2 + 2/9*q**3 + 2/3*q + 2/9*q**4 = 0.
-3, 0, 1
Suppose -3*p - q + 12 = 0, 5*p = -13*q + 12*q + 18. Let -2/5*w**4 + 0*w + 4/5*w**p - 2/5*w**2 + 0 = 0. 