 -2/9
Let x = -2554 + 2558. Find r such that -10*r**5 + 8/5*r + 8*r**2 + 42/5*r**3 + 0 - 8*r**x = 0.
-1, -2/5, 0, 1
Let d(u) be the third derivative of u**10/20160 - u**8/2240 + u**6/480 + u**4/12 + u**2. Let f(n) be the second derivative of d(n). Let f(v) = 0. What is v?
-1, 0, 1
Let g(q) be the second derivative of q**5/4 + 5*q**4 + 35*q**3/2 + 25*q**2 + 2*q - 14. Factor g(f).
5*(f + 1)**2*(f + 10)
Let x(w) be the first derivative of -w**6/3 + 2*w**4 - 4*w**3/3 - 3*w**2 + 4*w - 112. Suppose x(d) = 0. Calculate d.
-2, -1, 1
Let r(a) be the second derivative of -8*a**7/15 + 94*a**6/25 - 199*a**5/25 + 27*a**4/5 + 22*a**3/15 - 12*a**2/5 - 2*a + 58. Let r(t) = 0. What is t?
-1/4, 2/7, 1, 3
Let z(c) be the first derivative of -c**6/8 - 8*c**5/5 - 5*c**4/4 - 277. Factor z(h).
-h**3*(h + 10)*(3*h + 2)/4
Let -12 - b + 1/2*b**2 = 0. What is b?
-4, 6
Let f be (19 + -22)*(1 + (-6)/4). Factor -f*x**2 - 6 - 6*x.
-3*(x + 2)**2/2
Let j(h) be the first derivative of -1/3*h**3 - h**2 - 25 + 0*h + 1/4*h**4. Find o such that j(o) = 0.
-1, 0, 2
Suppose 10 + 2 = 6*c. Suppose i - f = f + 8, c*i + 8 = -4*f. Factor 2/5*z**i + 0*z - 1/5*z**4 - 1/5 + 0*z**3.
-(z - 1)**2*(z + 1)**2/5
Let n(a) be the first derivative of a**4/10 - 22*a**3/15 - 5*a**2 - 26*a/5 + 74. Factor n(y).
2*(y - 13)*(y + 1)**2/5
Let o(r) = -4*r**3 - 5*r**2 - 4*r - 6. Let p be o(-3). Find b, given that -46*b**4 + 80*b**3 + 66*b**2 + 147*b**4 + 18*b - p*b**4 = 0.
-1, -3/4, 0
Let t(j) be the third derivative of -1/10*j**5 - 1/6*j**3 + 0*j - 3*j**2 + 0 + 1/6*j**4 - 1/210*j**7 + 1/30*j**6. Factor t(x).
-(x - 1)**4
Let u be -6*(22/(-4) - -3). Let x = -12 + u. Factor x*p**2 + 34*p**4 - 6*p + 36*p**3 - 13*p**4 + 3*p**2 + 3*p**2.
3*p*(p + 1)**2*(7*p - 2)
What is y in 1/3*y - 1/3*y**2 + 2/3 = 0?
-1, 2
Let g(j) be the first derivative of 3/4*j**4 + 0*j**3 + 0*j + 0*j**2 + 7. What is d in g(d) = 0?
0
Let p(i) be the first derivative of 4*i**5/35 - 2*i**4/7 - 20*i**3/7 - 298. Factor p(x).
4*x**2*(x - 5)*(x + 3)/7
Let c(h) be the second derivative of -h**4/8 + 5*h**3 + 98*h. Suppose c(p) = 0. Calculate p.
0, 20
Suppose 8*l - 22 - 18 = 0. What is p in 8*p - 139*p**4 + 71*p**3 - 48*p**2 + 5*p**5 + 3*p**l + 97*p**4 + 3*p**3 = 0?
0, 1/4, 1, 2
Let l = -7705/2 + 3855. Suppose -l*k + 3 - 1/2*k**2 = 0. Calculate k.
-6, 1
Factor 36*i**3 + 345*i**4 + 876*i**2 + 1058 - 343*i**4 + 52*i**3 - 2024*i.
2*(i - 1)**2*(i + 23)**2
Let f(c) be the third derivative of c**5/66 + 29*c**4/132 - 2*c**3/11 + 39*c**2. Factor f(w).
2*(w + 6)*(5*w - 1)/11
Let j(c) = c**2 - c + 3. Let t(v) = -2*v**2 - 19*v + 51. Let w(s) = j(s) - t(s). Factor w(r).
3*(r - 2)*(r + 8)
Let s(n) be the first derivative of n**4/16 + n**3/12 - 5*n**2/8 + 3*n/4 - 478. Factor s(y).
(y - 1)**2*(y + 3)/4
Suppose -8*v - 8 = -12*v. Suppose -5*x - 6 = -3*y, -6*x + v = -x + y. Factor 3/5*k**3 + x - 3/5*k + 0*k**2.
3*k*(k - 1)*(k + 1)/5
Let i(s) = 7*s**4 + 23 - 20*s - 5*s + 20*s**3 - 48*s**2 - 4*s**3. Let f(h) = -2*h**4 - 4*h**3 + 12*h**2 + 6*h - 6. Let k(w) = 9*f(w) + 2*i(w). Solve k(m) = 0.
-2, -1, 1
Let c(l) be the first derivative of -l**3/12 + 3*l**2/4 + 407. Suppose c(d) = 0. What is d?
0, 6
Suppose 2*q = 3*q - 2. Let t(k) = -k**3 + 4*k**2 - 3*k. Let v be t(q). Factor -2*r**4 + r**5 + 2*r**v - 4*r**5 + 4*r**5 + 3*r - 4*r.
r*(r - 1)**3*(r + 1)
Let t = 48 - 38. Factor 8*z - 2*z**2 - 8*z - t*z.
-2*z*(z + 5)
Let k(s) = -7*s**3 - 4*s**2 + 3*s. Let h(m) = 15*m**3 + 8*m**2 - 7*m. Suppose -14*q = -9*q - 30. Let y(r) = q*h(r) + 13*k(r). Factor y(n).
-n*(n + 1)*(n + 3)
Suppose -86*v + 19*v + 134 = 0. Find c such that 15/2*c**4 - 15/2*c**v - 9/2*c**5 + 0 + 15/2*c**3 - 3*c = 0.
-1, -1/3, 0, 1, 2
Let l(t) be the first derivative of -t**6/27 + 8*t**5/45 + t**4/9 - 16*t**3/27 - t**2/9 + 8*t/9 - 138. Let l(z) = 0. Calculate z.
-1, 1, 4
Let y(a) = a**3 + 7*a**2 - 9*a - 4. Let w be y(-8). Suppose -4*c + w*z + 16 = 0, -z + 7 = c - 1. Solve -4*p**2 + c*p**3 - 2*p**4 - 74*p + 68*p + 6*p**2 = 0.
-1, 0, 1, 3
Suppose 620*u + 8 - 19220*u**2 - 19 + 5 + 1 = 0. What is u?
1/62
Let v be (3*-11 - -1)*5/(-10). Suppose 2*g - v = -5*n - 0*g, 5*g = n + 13. Factor -2/5*y - 2*y**n + 2/5 - 6/5*y**3.
-2*(y + 1)**2*(3*y - 1)/5
Let i(o) be the third derivative of o**8/15120 - o**6/540 + 2*o**5/15 + 19*o**2. Let m(r) be the third derivative of i(r). Determine y so that m(y) = 0.
-1, 1
Suppose -5*t + 3*j + 14 = 0, 0 = -2*t - 13*j + 17*j. Let l(z) be the second derivative of 5*z + 1/28*z**t + 1/7*z**3 - 9/14*z**2 + 0. Factor l(n).
3*(n - 1)*(n + 3)/7
Let x = 427 - 424. Let n(t) be the second derivative of -5/3*t**x - 2/3*t**4 + 0 - t**2 + 5*t. Suppose n(w) = 0. What is w?
-1, -1/4
Let b = -1/8 - -21/40. Let h(p) be the first derivative of 0*p**3 - 2*p**2 + p**4 + 2*p + 2 - b*p**5. Factor h(n).
-2*(n - 1)**3*(n + 1)
Let r(d) be the second derivative of 5/2*d**2 + 1/36*d**3 - 1/360*d**5 - 2*d + 0*d**4 + 0. Let y(i) be the first derivative of r(i). Factor y(b).
-(b - 1)*(b + 1)/6
Let h(r) be the second derivative of -r**4/72 - 7*r**3/36 + 2*r**2/3 + r - 5. Determine q so that h(q) = 0.
-8, 1
Let d(t) = -2*t**4 - t**2 + t - 1. Let c(m) = m**5 + 7*m**4 - 5*m**3 - 44*m**2 - m + 109. Let q(f) = -2*c(f) - 2*d(f). Let q(h) = 0. Calculate h.
-3, 2
Factor 14/9 + 16/9*u + 2/9*u**2.
2*(u + 1)*(u + 7)/9
Let t(b) be the third derivative of 1/245*b**7 - 1/105*b**6 + 0 + 0*b**3 + 1/42*b**4 - 1/210*b**5 + 0*b + 18*b**2. Determine v, given that t(v) = 0.
-2/3, 0, 1
Solve -39*i**3 - 20*i + 89*i**3 - 60 - 55*i**3 + 35*i**2 = 0.
-1, 2, 6
Suppose 2*f - 7 = 3*h + 11, -5 = -3*f - h. Factor 3/4*a - 15/8*a**2 + 3/2*a**f - 3/8*a**4 + 0.
-3*a*(a - 2)*(a - 1)**2/8
Let j(f) = -f**4 - f**3 + f**2 + f. Let y(i) = -i**5 + 17*i**4 - 33*i**3 + 31*i**2 - 14*i. Let q(b) = -3*j(b) - y(b). Factor q(l).
l*(l - 11)*(l - 1)**3
Let c(z) be the first derivative of -2*z**5/15 - 23*z**4/6 - 80*z**3/3 + 48*z**2 + 859. Find s such that c(s) = 0.
-12, 0, 1
Let t(r) be the third derivative of r**5/300 + r**4/30 + 2*r**3/15 + 14*r**2 - 5. What is u in t(u) = 0?
-2
Solve -7479 + 783 - 16015 - 18511 - 5*a**2 + 7602 + 820*a = 0.
82
Let w(y) be the first derivative of 1/30*y**3 - 3 - y**2 + 0*y - 1/300*y**5 + 0*y**4. Let s(b) be the second derivative of w(b). Factor s(h).
-(h - 1)*(h + 1)/5
Let m(f) be the third derivative of f**9/12096 + 7*f**3/6 - f**2. Let y(q) be the first derivative of m(q). Solve y(c) = 0 for c.
0
Let n be -12 - ((-462)/30 - -3). Let 2/5*i + n*i**2 - 2/5*i**3 - 2/5 = 0. What is i?
-1, 1
Let c(y) be the second derivative of y**4/8 + 2*y**3 + y + 4. Factor c(h).
3*h*(h + 8)/2
Let s(p) be the third derivative of p**5/30 - p**4/12 - 20*p**3/3 + p**2 + 15. Determine r so that s(r) = 0.
-4, 5
Let f(x) be the second derivative of -x**4/3 + 22*x**3/3 - 48*x**2 + 2*x - 127. Factor f(k).
-4*(k - 8)*(k - 3)
Let j(x) be the third derivative of 1/480*x**6 - 41*x**2 + 1/8*x**3 + 0 + 0*x - 1/80*x**5 - 1/96*x**4. Factor j(h).
(h - 3)*(h - 1)*(h + 1)/4
Let k be -7 + (-3 - -4)*1. Let t be (-6)/2*2/k. Let -5/2*l**2 + 9/2*l - t + 7/2*l**4 - 9/2*l**3 = 0. What is l?
-1, 2/7, 1
Let s(g) = g**5 + g**4 - 3*g**3 + 1. Let q(p) = -8*p**5 - 14*p**4 + 24*p**3 + 16*p**2 - 8*p - 10. Let w(k) = q(k) + 10*s(k). Factor w(c).
2*c*(c - 2)*(c - 1)**2*(c + 2)
Let y(h) = h**2 + 3*h + 12. Let i be y(-6). Factor 28 - 6*c + 0*c - 4*c**2 + i*c.
-4*(c - 7)*(c + 1)
Let w be (-2 + 4)/((-4)/(-4)). Suppose 8 + 22*a**2 + 17*a**2 - 41*a**w = 0. Calculate a.
-2, 2
Determine u so that -3/2*u**4 + 3*u**2 - 3/2*u**3 + 0*u + 0 = 0.
-2, 0, 1
Let p(i) be the first derivative of 5*i**3/3 + 150*i**2 + 4500*i + 39. Determine o, given that p(o) = 0.
-30
Let w(r) be the first derivative of r**4/28 - r**3/21 - 2*r**2/7 + 4*r/7 + 207. Factor w(b).
(b - 2)*(b - 1)*(b + 2)/7
Let g(s) = -s**3 - 9*s**2 - s - 5. Let y be g(-9). Factor 6*h**2 - y*h - 3*h**2 + 6*h - h**2.
2*h*(h + 1)
Let h(c) be the first derivative of -c**8/1512 + c**7/945 + c**6/90 - 17*c**2 + 25. Let t(i) be the second derivative of h(i). Factor t(j).
-2*j**3*(j - 3)*(j + 2)/9
Let l(i) be the first derivative of 2*i**3/3 + 77*i**2 - 156*i + 292. Factor l(m).
2*(m - 1)*(m + 78)
Let m(z) be the third derivative of -1/2700*z**6 - 1/900*z**5 + 0*z + 0*z**4 + 0 - 3*z**2 + 1/2*z**3. Let y(a) be the first derivative of m(a). Factor y(w).
-2*w*(