37*l**3/18 - 79*l**2/12 + 11*l/3 + 392. What is r in t(r) = 0?
-2, 1/4, 11
Let w(c) be the third derivative of c**6/480 + 21*c**5/80 + 441*c**4/32 + 3087*c**3/8 - c**2 + 230. Factor w(m).
(m + 21)**3/4
Let k(h) be the first derivative of 4/3*h**4 - 4/9*h**3 + 8 - 8/3*h**2 + 4/3*h. Suppose k(j) = 0. What is j?
-1, 1/4, 1
Suppose -92 = -m + 12*a, 5*m + 14*a = 10*a + 588. Determine z so that -8*z**4 + 48/5 + 342/5*z**3 + 296/5*z - 10*z**5 + m*z**2 = 0.
-2, -1, -2/5, 3
Factor -2/11*l**2 + 20/11*l - 50/11.
-2*(l - 5)**2/11
Suppose -b + 1926 = 2*f + 1910, 5*b - 3*f = -24. Factor -4/9*x**3 + b*x**2 - 2/9*x**4 + 0 + 0*x.
-2*x**3*(x + 2)/9
Suppose -h**2 - 525 + 257 - 5*h + 264 = 0. What is h?
-4, -1
Factor 0 + 4/3*u**2 - 1/3*u**4 - 4/3*u + 1/3*u**3.
-u*(u - 2)*(u - 1)*(u + 2)/3
Let q(i) = 52*i**5 - 26*i**4 - 4*i**3 - 28*i**2 + 6*i. Let b(d) = 3*d**5 - d**4 - 2*d**2. Let w(f) = 36*b(f) - 2*q(f). Factor w(o).
4*o*(o - 1)*(o + 1)**2*(o + 3)
Let m be 378/(-297) - (-2 + 0). Factor m*y + 2/11*y**2 + 6/11.
2*(y + 1)*(y + 3)/11
Suppose -40*j**2 - 6*j**2 - 160*j - 89*j**2 - 20*j**2 + 5*j**3 = 0. What is j?
-1, 0, 32
Factor -g**2 + 5*g + 0*g - 5*g**5 + 18*g**2 - 10*g**4 - 7*g**2.
-5*g*(g - 1)*(g + 1)**3
Let r(j) be the first derivative of -1/2*j**4 + 0*j**2 + 2/5*j**5 + 16 - 4/3*j**3 + 0*j. Find b such that r(b) = 0.
-1, 0, 2
Let y = -3961 - -3963. Solve 1/2*h - 1/4 - 1/4*h**y = 0.
1
Let q(p) be the second derivative of p**5/4 - 25*p**4/12 - 5*p**3/6 + 25*p**2/2 + 4*p + 2. Factor q(d).
5*(d - 5)*(d - 1)*(d + 1)
Suppose 0 = -h - 4*h - 20. Let y be 22/8 - h/16. Solve 9*d**4 - 15*d**5 + 6*d**3 + 1 + y - 4 = 0 for d.
-2/5, 0, 1
Suppose -16 = 10*a - 6. Let t(l) = -l**2. Let g(b) = 10*b**2 + 48*b + 144. Let j(n) = a*g(n) - 6*t(n). Factor j(i).
-4*(i + 6)**2
Let r(o) be the third derivative of -o**6/24 + 7*o**5/12 - 5*o**4/2 - 11*o**2 + 13*o. Suppose r(p) = 0. What is p?
0, 3, 4
Factor -30/11 - 2/11*c**2 + 16/11*c.
-2*(c - 5)*(c - 3)/11
Let u(g) be the first derivative of -5*g**3/3 - 55*g**2/2 - 50*g - 175. Factor u(i).
-5*(i + 1)*(i + 10)
Let m(b) be the third derivative of -b**8/1008 - b**7/105 + 2*b**6/45 - b**5/90 - 5*b**4/24 + 4*b**3/9 + 8*b**2 + 4*b. Factor m(g).
-(g - 1)**3*(g + 1)*(g + 8)/3
Suppose -4*a + 4*a**2 + 4 + a**3 - 7 - 1 + 3*a**3 = 0. What is a?
-1, 1
Let n(a) be the first derivative of a**6/4 - 39*a**5/20 + 33*a**4/8 - 2*a**3 + 122. Let n(o) = 0. What is o?
0, 1/2, 2, 4
Let y(r) be the third derivative of -r**8/784 + 2*r**7/245 - r**6/56 + r**5/70 - 106*r**2. Factor y(b).
-3*b**2*(b - 2)*(b - 1)**2/7
Let p(d) = 43*d - 97*d + 50*d + 26. Let c be p(6). Find u such that 2/3*u + 2/3 - 4/3*u**c = 0.
-1/2, 1
What is d in 80/21 - 2/21*d**3 - 88/21*d + 4/3*d**2 = 0?
2, 10
Let w be 2/(-9) - (-11904)/8370. Factor 0 - 2/5*j**2 + w*j.
-2*j*(j - 3)/5
Let k = 41 - 38. Factor 13*g**2 + k*g + g**2 + 3*g**3 - 20*g**2.
3*g*(g - 1)**2
Suppose -393/8*p - 165/4 - 3/8*p**3 - 33/4*p**2 = 0. Calculate p.
-11, -10, -1
Suppose 0 = -35*v + 39*v - 56. Let p(l) be the second derivative of v*l + 6*l**4 + 0 + 10/3*l**3 - 4*l**2. Solve p(q) = 0 for q.
-1/2, 2/9
Let o(u) be the second derivative of u**5/120 - 7*u**4/36 - 143*u**3/36 + 169*u**2 + 1031*u. What is r in o(r) = 0?
-12, 13
Suppose 9*v + 8*v = 816. Solve 32 - 4*j**3 + 0*j**3 + 70*j**2 - 46*j**2 - v*j = 0.
2
Factor -2*p**2 - 154 + 0*p**2 + p - 29*p - 8*p.
-2*(p + 7)*(p + 11)
Let u(y) be the third derivative of y**6/120 + 3*y**5/10 + 5*y**4/2 - 100*y**3/3 + 3*y**2 + 4*y. Find f such that u(f) = 0.
-10, 2
Suppose 23*l - 19*l - 100 = 0. Factor y**4 + 8 - 5*y**2 - 4 - l*y - 3*y**3 + 28*y.
(y - 4)*(y - 1)*(y + 1)**2
Let p(l) be the third derivative of l**5/60 - l**4/12 - 4*l**3 - 158*l**2. Suppose p(h) = 0. Calculate h.
-4, 6
Determine z so that -81 - 4*z**2 + 2*z**2 - 4*z**2 + 121*z - 6*z + 50*z = 0.
1/2, 27
Suppose 3*d + 50 = 1046. Factor 2*x**4 - 340*x**2 - x**3 + d*x**2 - 3*x**3 + x**5.
x**2*(x - 2)*(x + 2)**2
Let x = 188 + -153. Let y = x + -33. Factor -48/5*b**y - 27/5 - 72/5*b.
-3*(4*b + 3)**2/5
Factor -6/7*j**2 - 2/7*j**3 - 2/7 - 6/7*j.
-2*(j + 1)**3/7
Suppose -l = -o - 6, 6*l - 2 = l - 2*o. Suppose -40 + 4*s**2 + 0*s**2 - 6*s**l + 7*s**2 + 10*s = 0. What is s?
-4, 2
Suppose -4 = -4*u, 4*u + 6 + 2 = 2*h. Suppose -6*o + h = -4*o. Factor 27 + 8*c + 5*c**2 - o*c**2 - 19.
2*(c + 2)**2
Let u(b) be the third derivative of -b**8/112 - 8*b**7/315 + b**6/9 + b**5/18 - 31*b**4/72 + b**3/3 + 128*b**2. Suppose u(d) = 0. What is d?
-3, -1, 2/9, 1
Solve 7*u - 17*u**2 - 2*u + 8*u + 14*u**2 - 4*u = 0 for u.
0, 3
Suppose 3*j = -12 + 18. Suppose 3*p = -j*w + 8, w = -3*p + p + 5. Factor r - 1/2*r**p + 0.
-r*(r - 2)/2
Let f(o) be the third derivative of -o**8/20160 - o**7/5040 + 11*o**5/30 - 15*o**2. Let i(d) be the third derivative of f(d). Determine g, given that i(g) = 0.
-1, 0
Let l(f) = 30*f + 11. Let w(o) = -10*o - 4. Let i(t) = 6*l(t) + 17*w(t). Let z be i(1). Factor -2*v + z + 18*v**2 - 6*v**2 - v + 23*v.
4*(v + 1)*(3*v + 2)
Let o(d) = -d + 8. Let c be o(6). Let i be 1/((-4 + c)/(-6)). Factor -2*y + 4*y**2 - 3*y - 2 + i.
(y - 1)*(4*y - 1)
Let y(t) be the first derivative of -t**6/210 - t**5/105 + t**4/21 + t**2/2 - 7. Let u(b) be the second derivative of y(b). Let u(m) = 0. What is m?
-2, 0, 1
Suppose 5*m + 3*l - 13 = 0, m - 39*l + 35*l = -2. What is w in -1/2*w**3 - 3/2*w + 9/2 - 5/2*w**m = 0?
-3, 1
Factor -51766*z**3 + 284*z**2 - 4987*z + 4900 - 193*z + 51762*z**3.
-4*(z - 35)**2*(z - 1)
Let q be (-18)/(-63)*7 + 2. Let k(t) be the third derivative of 0*t + 1/72*t**q + 4*t**2 + 1/180*t**5 + 0*t**3 + 0. Find m such that k(m) = 0.
-1, 0
Suppose 318 = 2*s + 2*r, 0 = -0*s - 2*s - 5*r + 306. Let v = s - 159. Factor 1/2*j**2 + 0*j - 1/6*j**3 + 0 - 2/3*j**v.
-j**2*(j + 1)*(4*j - 3)/6
Suppose q = -2*n + 4, -138*n + 3*q = -135*n - 6. Factor -4/3 - 2/3*x + 2/3*x**n.
2*(x - 2)*(x + 1)/3
Let c(z) be the second derivative of z**6/150 - 3*z**5/100 - z**4/20 + 7*z**3/30 + 3*z**2/5 - 86*z. Factor c(d).
(d - 3)*(d - 2)*(d + 1)**2/5
Let u(t) = 15*t**2 - t - 23. Let h(o) = -8*o**2 + 12. Suppose 4*k = 4*i + 8, i + k = -9 + 3. Let j(l) = i*u(l) - 7*h(l). Factor j(f).
-4*(f - 2)*(f + 1)
Let i(u) be the third derivative of -u**2 + 0*u**3 + 0*u - 1/360*u**6 - 1/180*u**5 + 0*u**4 + 0. Factor i(s).
-s**2*(s + 1)/3
Let v(u) be the third derivative of u**6/60 + u**5/15 - 3*u**4/4 - 6*u**3 - 8*u**2 - 5. Suppose v(k) = 0. What is k?
-3, -2, 3
Let z be -1 + 3/405*123. Let x = 143/90 + z. Solve 0*s - x*s**4 + 0*s**3 + 0 + 3/2*s**2 = 0 for s.
-1, 0, 1
Let m(d) be the second derivative of -d**5/110 - 2*d**4/33 - d**3/11 - 124*d. Factor m(b).
-2*b*(b + 1)*(b + 3)/11
What is i in 1/2*i**2 + 9/2*i + 4 = 0?
-8, -1
Let a(t) be the third derivative of 3*t**6/10 - 79*t**5/15 + 18*t**4 + 56*t**3/3 + t**2 + 15*t. Factor a(w).
4*(w - 7)*(w - 2)*(9*w + 2)
Let q = 13 + -10. Suppose 5 - 6*h**2 - 10*h + 11*h**q - 1 + 8*h**4 - 17*h**3 + 22*h**3 = 0. Calculate h.
-2, -1, 1/2
Let d(w) be the second derivative of -w**6/6 + 6*w**5 - 125*w**4/2 + 500*w**3/3 + 1875*w**2/2 + 674*w. Determine g so that d(g) = 0.
-1, 5, 15
Let n(s) = s**4 + 61*s**3 - 145*s**2 + 83*s - 5. Let x(b) = -4*b**4 - 184*b**3 + 436*b**2 - 248*b + 16. Let m(k) = -16*n(k) - 5*x(k). Factor m(u).
4*u*(u - 11)*(u - 2)*(u - 1)
Let c(i) be the first derivative of -20*i**3/3 + 18*i**2 + 8*i + 82. Solve c(k) = 0.
-1/5, 2
Let i = 657 + -653. Solve -i*n**3 + 4/3 + 4/3*n**2 - 8/3*n**4 + 4*n = 0 for n.
-1, -1/2, 1
Let t(r) = 3*r**2 + 75*r - 82. Let j(p) = 24*p**2 + 600*p - 657. Let k(b) = 4*j(b) - 33*t(b). Factor k(n).
-3*(n - 1)*(n + 26)
Let q(u) be the first derivative of 3*u**5/5 - 9*u**4/2 + 12*u**3 - 15*u**2 + 9*u - 891. Suppose q(d) = 0. What is d?
1, 3
Suppose 2*n + n = -54. Let f be (-7)/(-28)*n*(-4)/6. Factor 0*j + 1/5*j**f - 1/5*j**5 + 0 + 1/5*j**4 - 1/5*j**2.
-j**2*(j - 1)**2*(j + 1)/5
Suppose 3*b = -2*s + 58, 3 = 2*s - 5*s. Factor -25*z**2 - b + 5*z**2 - 5*z**2 - 60*z.
-5*(z + 2)*(5*z + 2)
Let b(g) = g**2 + 5*g + 2. Let x(j) = -j - 1. Let d(t) = -t**2 - t + 1. Let s(q) = 2*d(q) + 6*x(q). Let c(n) = -7*b(n) - 4*s(n). Factor c(p).
(p - 2)*(p - 1)
Let o(b) be the first derivative of 5 + 0*b**3 - 5*b + 0*b**2 + 1/20*b**5 + 1/12*b**4. Let n(d) be the first derivative of o(d). What is a in n(a) = 0?
-1, 0
Let y = 59