irst derivative of -y**6/720 - 7*y**5/360 - y**4/9 - y**3/3 + 4*y**2 + 40. Let f(b) be the second derivative of w(b). Factor f(n).
-(n + 2)**2*(n + 3)/6
Let c(x) be the third derivative of x**8/336 - 13*x**7/105 + 7*x**6/5 + 13*x**5/30 - 169*x**4/24 + 139*x**2. Suppose c(v) = 0. What is v?
-1, 0, 1, 13
Factor 1/5*u**2 - 2/5*u - 3/5.
(u - 3)*(u + 1)/5
Let m(k) be the third derivative of -k**5/30 + k**4/30 + 78*k**2. What is j in m(j) = 0?
0, 2/5
Let g(o) = 12*o**4 - 144*o**3 + 220*o**2 - 56*o - 32. Let k(i) = -i**4 + 13*i**3 - 20*i**2 + 5*i + 3. Let z(r) = 3*g(r) + 32*k(r). Solve z(x) = 0.
0, 1, 2
Let w(d) = 5*d**4 + 75*d**3 + 5*d**2 + 5. Let s(u) = 5*u**4 + 76*u**3 + 6*u**2 + 6. Let r(j) = 5*s(j) - 6*w(j). Find h, given that r(h) = 0.
-14, 0
Let c(a) be the second derivative of 7*a**4/8 - 6*a**3 + 27*a**2/4 + 38*a. Let c(l) = 0. What is l?
3/7, 3
Find s such that -60*s**2 - 73*s + 290*s**4 + 28*s + 45*s**3 - 35*s + 35*s**5 - 230*s**2 = 0.
-8, -1, -2/7, 0, 1
Factor -3*l**2 - 2*l**2 - 20 - 4*l**2 - 7 - 81*l + 37*l**3 + 0*l**4 - 8*l**4.
-(l - 3)**2*(l + 1)*(8*l + 3)
What is i in 6*i**3 + 2*i**5 - 12*i + 0*i**3 + 4*i**3 - 10*i**2 + 10*i**4 = 0?
-3, -2, -1, 0, 1
Let w = 402 + -402. Let g(x) be the first derivative of 5/3*x**3 - 15/2*x**2 + w*x + 9. Factor g(k).
5*k*(k - 3)
Let k be 6 + (48/4)/(-2). Let b(r) be the second derivative of 3*r + 0 + k*r**2 - 1/12*r**4 - 1/6*r**3. Factor b(m).
-m*(m + 1)
Find g, given that -2016*g**2 - 64 - 10 + 2940*g**3 - 1029*g**4 + 528*g + 26 = 0.
2/7, 2
Suppose 0*n + 4*n = -3*k + 14, -k = -n. Suppose n*a = 5*g - 25, -10 = 2*a + 3*a - 2*g. Let 6/7*o**4 - 8/7*o**2 + a + 0*o - 8/7*o**3 = 0. Calculate o.
-2/3, 0, 2
Let f = -1593 - -11152/7. Let j(a) be the first derivative of f*a**2 - 3 - 3/7*a + 1/21*a**3. Factor j(d).
(d - 1)*(d + 3)/7
Let u be (115/(-15) - -11)*3/55. Let -4/11*b + 0 + u*b**2 = 0. What is b?
0, 2
Let g(t) be the first derivative of -2*t**6/9 - 34*t**5/15 - 22*t**4/3 - 100*t**3/9 - 26*t**2/3 - 10*t/3 - 218. Suppose g(a) = 0. Calculate a.
-5, -1, -1/2
Suppose -2*p = -33 + 27. Factor 0 + 12/7*y**4 - 3/7*y**5 - 15/7*y**p + 0*y + 6/7*y**2.
-3*y**2*(y - 2)*(y - 1)**2/7
Let c(r) be the third derivative of r**6/30 + 4*r**5/15 + 5*r**4/6 + 4*r**3/3 + 286*r**2. Factor c(j).
4*(j + 1)**2*(j + 2)
Suppose -17*t + 12*t = 4*p - 22, 4*p - 2 = 5*t. Let o(q) be the second derivative of 1/4*q**4 + 0 - 3/20*q**5 - 9*q - 6*q**t + 2*q**3. Factor o(b).
-3*(b - 2)*(b - 1)*(b + 2)
Let n = 2/16195 + 64774/48585. Let -n*o - 2/3*o**2 + 1/3*o**3 + 8/3 = 0. What is o?
-2, 2
Let k(y) be the second derivative of y**8/420 + y**7/210 - y**6/18 + y**5/10 + 13*y**3/6 + 30*y. Let j(h) be the second derivative of k(h). Factor j(m).
4*m*(m - 1)**2*(m + 3)
Let b = -57 - -59. Let k(m) be the third derivative of 7/144*m**4 + 0*m - 3*m**b + 1/18*m**3 + 1/72*m**5 + 0. Determine c so that k(c) = 0.
-1, -2/5
Let n(y) be the first derivative of 8*y**5/5 - 13*y**4/2 - 74*y**3/3 + 10*y**2 + 150. Solve n(w) = 0.
-2, 0, 1/4, 5
Let p(f) = -f**4 - f. Let m(d) = 4*d**4 - 18*d**3 + 16*d**2 + 2*d. Let c(u) = -2*m(u) - 4*p(u). Factor c(l).
-4*l**2*(l - 8)*(l - 1)
Let p(d) be the third derivative of 1/2*d**4 + 0 - 7/15*d**5 + 1/6*d**6 - 2/105*d**7 + 10*d**2 + 0*d + 0*d**3. Factor p(u).
-4*u*(u - 3)*(u - 1)**2
Let z(t) = -t**2 - 30*t - 102. Let q be z(-26). Find s such that 0*s**q + 0 + 3/8*s**5 + 3/8*s**3 + 0*s + 5/4*s**4 = 0.
-3, -1/3, 0
Let d(c) be the first derivative of 3*c**5/5 - 9*c**4/2 + 11*c**3 - 9*c**2 + 200. Determine t, given that d(t) = 0.
0, 1, 2, 3
Let x(z) = 8*z**3 + 1039*z**2 + 2033*z + 1002. Let l(k) = -28*k**3 - 3636*k**2 - 7116*k - 3508. Let n(s) = -7*l(s) - 24*x(s). Factor n(r).
4*(r + 1)**2*(r + 127)
Suppose -8 = -5*t + 3*g, 4*t - 2 = -2*g - 0*g. Suppose p - 4*p**2 + 5*p**3 - 4*p**3 + t - 2*p**3 + 3*p**2 = 0. Calculate p.
-1, 1
Let g(o) be the second derivative of -7/15*o**6 + 2/3*o**3 + 0 + 13*o + 0*o**2 - 6/5*o**5 - 1/2*o**4. Factor g(z).
-2*z*(z + 1)**2*(7*z - 2)
Let h = -2 - -12. Suppose -5 = h*d - 45. Solve 4/13*a + 0 + 2/13*a**d - 4/13*a**3 - 2/13*a**2 = 0 for a.
-1, 0, 1, 2
Let q(r) = -3*r + 13. Let g be q(3). Let o = -2 + g. Find p such that 2*p**o + 46*p + 2*p**2 - 62*p + 16 = 0.
2
Factor -36 + 18*m - 3*m**2 + 1/6*m**3.
(m - 6)**3/6
Let m(c) = -c**2 + 11*c - 23. Let s be m(7). What is t in 21*t**2 - 17*t**2 - t**s + 0*t**2 - 3*t**4 = 0?
-2, 0, 1
Let p = 202/3 - 9089/135. Let r(y) be the second derivative of -1/189*y**7 - 2*y + 0*y**4 + 0*y**2 + 0 + 0*y**3 - p*y**6 + 0*y**5. Factor r(m).
-2*m**4*(m + 1)/9
Let j(i) be the second derivative of -5*i**7/42 - 2*i**6/3 + i**5/4 + 5*i**4/3 + 271*i. Determine g, given that j(g) = 0.
-4, -1, 0, 1
Let w(p) be the second derivative of -p**6/180 + p**5/40 + p**4/8 - 3*p**3/4 - 403*p. Factor w(s).
-s*(s - 3)**2*(s + 3)/6
Let l(y) = -y - 1. Suppose 0 = 2*r + 1 + 5. Let v be l(r). Solve v*z + 0 - 7*z + 2 + 2*z**2 + z = 0 for z.
1
Let o(k) = -4*k**3 + 2*k**2 - 8*k + 5. Let x(f) = f**3 + f - 1. Let h(p) = -4*o(p) - 20*x(p). Suppose h(y) = 0. What is y?
-3, 0, 1
Factor 1 + 35*b**2 - 279*b**3 - 14*b + 0 + 257*b**3.
-(b - 1)*(2*b - 1)*(11*b - 1)
Let r(p) be the third derivative of 0 - 1/10*p**6 - 1/8*p**4 + 0*p + 6*p**2 + 1/4*p**5 + 0*p**3. Factor r(w).
-3*w*(w - 1)*(4*w - 1)
Let d(t) be the third derivative of t**8/50400 + t**7/3150 + t**6/600 + 7*t**4/12 + 8*t**2. Let f(v) be the second derivative of d(v). Factor f(s).
2*s*(s + 3)**2/15
Let r(t) = -3*t**4 - 18*t**3 - 11*t**2 + 2*t + 2. Let o(d) = -10*d**4 - 55*d**3 - 31*d**2 + 7*d + 7. Let s(f) = 6*o(f) - 21*r(f). Solve s(p) = 0.
-15, -1, 0
Let -2/5*n**2 + 0 - 26/5*n = 0. What is n?
-13, 0
Determine k so that 21*k**3 - 24*k - 4*k + 14*k**4 - 137*k**3 + 1397*k**2 - 1267*k**2 = 0.
0, 2/7, 1, 7
Let z be 2/(19/((-1330)/(-28))). Factor -36/5*b**4 + 6/5*b**3 + 0 + 12/5*b**2 - 3/5*b - 27/5*b**z.
-3*b*(b + 1)**2*(3*b - 1)**2/5
Let t(y) = 39*y - 388. Let k be t(10). Suppose 0*j**k + 1/5*j**3 + 0 - 1/5*j = 0. Calculate j.
-1, 0, 1
Suppose 0 = -0*u + 29*u - 4959. Let r = -853/5 + u. Let r*a**2 - 4/5 + 2/5*a = 0. Calculate a.
-2, 1
Let z(r) be the first derivative of 4/15*r**5 - 2/3*r - 5/6*r**2 + 1/18*r**6 + 24 - 2/9*r**3 + 1/3*r**4. Determine p, given that z(p) = 0.
-2, -1, 1
Find b, given that -16/3*b - 118/9*b**4 + 0 + 148/9*b**3 - 8/9*b**2 + 26/9*b**5 = 0.
-6/13, 0, 1, 2
Find c such that -1/3*c**3 + 0 + 29/3*c**2 + 0*c = 0.
0, 29
Factor 6 + 3*s**3 - 14*s - 12*s**3 + 4*s**3 + 10*s**2 + 3*s**3.
-2*(s - 3)*(s - 1)**2
Suppose -296 = 6*n - 587 + 291. Factor n*t + 20/3*t**3 - 4/3*t**4 + 0 - 4/3*t**5 - 4*t**2.
-4*t**2*(t - 1)**2*(t + 3)/3
Let d(i) be the first derivative of -2*i**5/15 - i**4 + 16*i**3/3 - 26*i**2/3 + 6*i + 65. Suppose d(x) = 0. What is x?
-9, 1
Let c(y) be the second derivative of y**9/4536 - y**8/630 + y**7/315 + 5*y**3/2 - 28*y. Let w(g) be the second derivative of c(g). What is z in w(z) = 0?
0, 2
Let l(x) be the third derivative of 0*x**3 + 1/720*x**6 + 0 + 20*x**2 - 1/144*x**4 + 0*x + 1/360*x**5 - 1/1260*x**7. Factor l(n).
-n*(n - 1)**2*(n + 1)/6
Let x = -228 + 228. Suppose x = -5*p - 5*y + 15, -3*p + 4*y - 17 = -5. Solve 1/2*d**5 + d**2 + p*d - 1/2*d**3 - d**4 + 0 = 0 for d.
-1, 0, 1, 2
Let -9/7*i - 3/7*i**4 + 17/7*i**3 + 0 - 3*i**2 = 0. What is i?
-1/3, 0, 3
Let t(g) = -4*g + 68. Let d be t(17). Let b be d/((-20)/(-5) + -5). Factor -2/5*v**3 + 0 + b*v + 2/5*v**2 - 2/5*v**4 + 2/5*v**5.
2*v**2*(v - 1)**2*(v + 1)/5
Let i = -546 + 546. Let r(j) be the second derivative of 5*j + 0 - 1/48*j**4 + 0*j**2 + i*j**3. Solve r(d) = 0.
0
Suppose 3*m = -44*b + 45*b - 5, 3*b - 15 = 4*m. Factor 1/4*f**3 + 0 + f**5 + 0*f + m*f**2 - 5/4*f**4.
f**3*(f - 1)*(4*f - 1)/4
Let c = 3233/2296 + -87/328. Factor c - 2/7*z - 5/7*z**2 - 1/7*z**3.
-(z - 1)*(z + 2)*(z + 4)/7
Factor -4*p**3 + 91 + 151 - 98 + 52*p**2 - 160*p.
-4*(p - 9)*(p - 2)**2
Let f be (-2)/(-8) - 361/(-76). Factor -f + 1 - 2*j**2 - 14*j + 8*j.
-2*(j + 1)*(j + 2)
Let q(x) be the first derivative of -1/5*x**5 + 51 + 0*x + 0*x**2 + 0*x**4 + 1/3*x**3. Factor q(m).
-m**2*(m - 1)*(m + 1)
Let t(z) be the third derivative of -z**8/168 + z**7/35 + 3*z**6/20 + z**5/6 - 47*z**2 + 3. Let t(a) = 0. What is a?
-1, 0, 5
Suppose -237 = -31*p - 113. Let m(f) be the second derivative of 13*f - 1/3*f**p - 1/10*f*