 17 - r. Factor 4/7*n**3 - 2/7*n**4 + 0 + 2/7*n**o - 4/7*n.
-2*n*(n - 2)*(n - 1)*(n + 1)/7
Let t(g) be the third derivative of -1/42*g**7 + 1 + 42*g**2 - 5/24*g**6 + 0*g**4 + 0*g + 0*g**5 + 0*g**3. Factor t(y).
-5*y**3*(y + 5)
Let j = -1404/7 - -151. Let t = -49 - j. Solve 16/7 - 16/7*x + t*x**2 = 0 for x.
2
Suppose -5*a - 38 = 2*c - 5*c, 2*a = -5*c + 53. Suppose 9*s**4 - 50*s + 20*s**3 - c*s**4 + 35*s**2 - 3*s**4 = 0. Calculate s.
-2, 0, 1, 5
Let y = -117/665 - -8/35. Let g = 52/95 + y. Factor -6/5*f**3 + 6/5*f + 0*f**2 + g*f**4 - 3/5.
3*(f - 1)**3*(f + 1)/5
Let b(v) = 2*v**2 + 37*v + 83. Let o(u) = -7*u**2 - 112*u - 248. Suppose t = -4*t - 40. Let l(q) = t*b(q) - 3*o(q). Factor l(f).
5*(f + 4)**2
Let b = -447 - -450. Let s(u) be the third derivative of 0*u + 1/40*u**6 + 0*u**3 - b*u**2 - 1/36*u**4 + 0 - 7/180*u**5. Factor s(k).
k*(k - 1)*(9*k + 2)/3
Let s = -61/1950 + 2/39. Let t(w) be the second derivative of 1/105*w**7 - 1/30*w**4 + 3*w + 0*w**3 + 0 + 1/75*w**6 - s*w**5 + 0*w**2. Factor t(o).
2*o**2*(o - 1)*(o + 1)**2/5
Let b(j) be the second derivative of -j**8/1680 + j**6/360 - 8*j**3/3 - 22*j. Let y(o) be the second derivative of b(o). Factor y(r).
-r**2*(r - 1)*(r + 1)
Let r(m) be the first derivative of 2*m**5/15 + m**4/3 - 2*m**2/3 - 2*m/3 + 533. Factor r(d).
2*(d - 1)*(d + 1)**3/3
Let p be 33/77 + (-9618)/(-196). Determine j, given that -1 - 157/4*j**2 - p*j**3 - 81/4*j**4 - 11*j = 0.
-1, -2/9
Let h(v) be the first derivative of 3/80*v**5 + 3*v + 0*v**2 - 1/8*v**4 + 1/8*v**3 + 2. Let m(r) be the first derivative of h(r). Factor m(d).
3*d*(d - 1)**2/4
Suppose 974*p**3 - 975*p**3 - 4*p**2 + 4*p + 0*p**2 + p**2 = 0. What is p?
-4, 0, 1
Let i(g) be the second derivative of -g**6/15 - g**5 + 4*g**4 + 256*g**3/3 - 512*g**2 + 465*g. Factor i(s).
-2*(s - 4)*(s - 2)*(s + 8)**2
Let x(a) be the first derivative of a**4/32 + 11*a**3/24 - 11. Solve x(t) = 0 for t.
-11, 0
Let c(f) be the first derivative of 2*f**6/45 + f**5/5 + f**4/3 + 2*f**3/9 - 7*f + 16. Let a(q) be the first derivative of c(q). Find j such that a(j) = 0.
-1, 0
Factor q**3 + 9*q**2 + 7*q**2 - 18*q**2.
q**2*(q - 2)
Let l be (276/(-184))/(((-4)/(-160))/(3/(-6))). Factor -50/3*b**4 - 8/3*b - 16*b**2 + 0 - l*b**3.
-2*b*(b + 1)*(5*b + 2)**2/3
Let q(b) = b**2 - b - 4. Let p be q(3). Let k = 5 - p. What is z in 6*z**3 + k*z**3 - 10*z**3 + 4*z**3 = 0?
0
Suppose 2*k = -h - 2 + 5, -3*h - 5*k + 10 = 0. Let o be (2 + 0)*(h - 3). Determine a so that 21 + o*a**3 - 8*a**3 + 29 - 20*a**2 - 14 - 12*a = 0.
-3, 1
Let x(i) be the third derivative of -i**6/108 + 2*i**5/45 + i**4/3 - 16*i**3/27 + 226*i**2. Factor x(g).
-2*(g - 4)*(g + 2)*(5*g - 2)/9
Let n(w) = -2*w**2 + w - 3. Let c(g) = g**5 - 2*g**4 - 20*g**2 + 10*g - 33. Let x(z) = 2*c(z) - 22*n(z). Find k, given that x(k) = 0.
-1, 0, 1
Let a(i) be the first derivative of -1/12*i**3 - 17 + 0*i**2 + i. Determine h, given that a(h) = 0.
-2, 2
Suppose 14*o = 8 + 48. Let w(j) be the second derivative of j + 0*j**2 - 1/10*j**6 - 1/2*j**o + 9/20*j**5 + 0 + 0*j**3. What is k in w(k) = 0?
0, 1, 2
Let f be (-2)/5*(-12 - 3). Suppose -u - f = -3*u. Solve 3 + 8*o**2 - 1 - 5*o**u - 4*o + 3*o - 4 = 0 for o.
-2/5, 1
Factor 8*x**2 + 64 - 60 + 0*x**2 + 2*x**3 + 10*x.
2*(x + 1)**2*(x + 2)
Let y(v) be the third derivative of 19*v**2 + 0*v - 2*v**4 - 32*v**3 - 1/20*v**5 + 0. Factor y(a).
-3*(a + 8)**2
Let c be 4 - ((-8)/14)/((-180)/(-630)). Solve 37/4*q**2 + q**4 - c*q - 21/4*q**3 + 1 = 0 for q.
1/4, 1, 2
Let b(n) = 15*n**3 - 3*n**2 + 45*n + 13. Let q(y) = -7*y**3 + 2*y**2 - 22*y - 6. Let c(v) = 6*b(v) + 13*q(v). Factor c(s).
-s*(s - 4)**2
Suppose -11 = -3*p + 4. Suppose -p = j, 0*t + 1 = -t - j. Factor -f**2 + t*f**2 - 10 + 11 + 12*f + 11.
3*(f + 2)**2
Let c(u) be the second derivative of -8*u**7/21 + 334*u**6/105 - 132*u**5/35 - 17*u**4/21 + 20*u**3/21 + 22*u + 2. Let c(i) = 0. What is i?
-2/7, 0, 1/4, 1, 5
Let i(b) = 10*b**3 + 137*b**2 - 41*b + 22. Let l be i(-14). Find t, given that 8/3 - 6*t**2 - 14/3*t**3 + l*t = 0.
-2, -2/7, 1
Let n(g) be the third derivative of g**5/20 - 5*g**4/2 - 4*g**2 - 2*g. Factor n(y).
3*y*(y - 20)
Let y = 80 + -74. Suppose -3*p + 12 = 0, 2*b - p = -b + 11. Factor -3*i**4 - 3*i**2 + i**3 - 10*i**3 + y*i**4 + 3*i**b + 6*i.
3*i*(i - 1)**2*(i + 1)*(i + 2)
Let s(j) be the third derivative of j**5/180 + j**4/8 + 7*j**3/9 + j**2 - 3. Factor s(q).
(q + 2)*(q + 7)/3
Let k(g) be the first derivative of 3*g**4/4 - 42*g**3 - 3*g**2/2 + 126*g - 384. Factor k(o).
3*(o - 42)*(o - 1)*(o + 1)
Let a(i) = -i**3 + 25*i**2 - 23*i - 49. Let s be a(21). Let h be 1 + (-13)/11 - (-532)/s. Factor 0 - h*k - k**2 - 3/4*k**3.
-k*(k + 1)*(3*k + 1)/4
Let q be (4/(-36))/(140/(-540))*536/6. Find z, given that -q*z**3 + 222/7*z**4 + 86/7*z**2 + 24/7*z - 8/7 - 8*z**5 = 0.
-2/7, 1/4, 1, 2
Let t(a) be the third derivative of a**6/780 + a**5/78 + a**4/26 + 17*a**2 - a. Factor t(o).
2*o*(o + 2)*(o + 3)/13
Let u(j) be the first derivative of 0*j**3 - 1/4*j**4 - 1/20*j**5 + 4 - 2*j**2 + 0*j. Let c(m) be the second derivative of u(m). Factor c(b).
-3*b*(b + 2)
Suppose 61 = -8*n - 43. Let u be n*1/(-20) - (-2)/(-8). Determine h, given that -48/5*h - 18*h**4 + 8/5 + 10*h**5 + 82/5*h**2 - u*h**3 = 0.
-1, 2/5, 1
Let w(b) = b**3 - 5*b**2 - 17*b + 3. Let l be w(7). Let u be (-9)/(-2)*(-6)/l. Solve -1/2 + 1/2*i**3 + u*i - 3/2*i**2 = 0.
1
Let f(p) be the first derivative of -5*p**4/12 - 5*p**3/3 - 5*p**2/2 - 11*p + 16. Let r(n) be the first derivative of f(n). Suppose r(g) = 0. What is g?
-1
Let p(u) = -79*u + 795. Let m be p(10). Let d(n) be the first derivative of 1/10*n**m + 3/4*n**4 + 0*n + 2*n**3 + 2*n**2 - 6. Factor d(l).
l*(l + 2)**3/2
Let h(f) = 32*f**2 - 390*f + 76. Let y be h(12). Factor -6/11*q**y + 0*q**2 - 2/11*q**3 + 8/11*q**5 + 0*q + 0.
2*q**3*(q - 1)*(4*q + 1)/11
Let s(b) be the second derivative of b**6/45 + b**5/270 - 6*b**2 - 30*b. Let c(i) be the first derivative of s(i). Factor c(q).
2*q**2*(12*q + 1)/9
Let f(v) = -v**3 - 25*v**2 - 47*v - 20. Let w be f(-23). Let z(p) be the first derivative of -2/9*p**w + 8/3*p**2 - 2 - 32/3*p. Find y such that z(y) = 0.
4
Let n(b) = 1. Let u(f) = -21*f**2 - 279*f - 83. Let a(i) = 5*n(i) + u(i). Factor a(v).
-3*(v + 13)*(7*v + 2)
Let d be (-10)/(-3 + ((-28)/4 - -8)). Factor 2/13*s**d + 0*s**3 + 4/13*s**2 + 0 - 4/13*s**4 - 2/13*s.
2*s*(s - 1)**3*(s + 1)/13
Determine q so that 1348/5*q - 16/5*q**2 - 336/5 = 0.
1/4, 84
Let h(q) = 4*q**2 - 98*q - 6. Let z(f) = -9*f**2 + 198*f + 13. Let g(y) = -13*h(y) - 6*z(y). Let g(n) = 0. Calculate n.
-43, 0
Factor -10*j**2 - 60*j + 6*j**2 - 48*j - 104.
-4*(j + 1)*(j + 26)
Let o(n) be the third derivative of -7*n**2 - 1/112*n**8 + 0 + 3/70*n**7 + 3/8*n**4 + 0*n - 1/10*n**5 - 1/20*n**6 - 1/2*n**3. Find j such that o(j) = 0.
-1, 1
Suppose 0 = 4*a + 2*v - 212, 3*v + 107 = 4*a - 85. Let x = a - 33. Let -3*z**4 + x*z**2 - 18*z**2 + 3*z**5 = 0. What is z?
0, 1
Let i(n) be the third derivative of 2*n**7/105 + n**6/30 - n**5/3 + n**4/2 + 129*n**2 + 1. Find a, given that i(a) = 0.
-3, 0, 1
Factor -982*r**2 - 15 + 1026*r**2 - 17 - 12*r**3 + 24*r.
-4*(r - 4)*(r + 1)*(3*r - 2)
Let o(k) be the first derivative of -k**4/2 + 2*k**3 + 4*k**2 - 113. Factor o(i).
-2*i*(i - 4)*(i + 1)
Let o be 6*(5 + (-8 + 7)*(-328)/(-66)). Factor 2/11*f**2 - 4/11 - o*f.
2*(f - 2)*(f + 1)/11
Let r be (-8)/(-18)*(83/80 - 1). Let g(a) be the second derivative of r*a**4 + 0 - 3*a + 0*a**2 + 0*a**3. Determine w, given that g(w) = 0.
0
Let j(z) = 2*z**4 + 38*z**3 + 147*z**2 - 861. Let h(p) = 2*p**4 + 36*p**3 + 146*p**2 - 862. Let g(q) = -6*h(q) + 4*j(q). Suppose g(m) = 0. Calculate m.
-6, 2
Let d = 363/70 - 49/10. Factor 0 + 0*t - d*t**2 + 4/7*t**3 - 2/7*t**4.
-2*t**2*(t - 1)**2/7
Let f(q) be the second derivative of -2*q + 0*q**2 + 1/24*q**3 - 1/32*q**4 + 1/160*q**5 - 6. Factor f(t).
t*(t - 2)*(t - 1)/8
Let g = 1445645/259476 - -1/37068. Solve -9/7*t**5 - g*t**4 - 24/7*t - 4/7 - 57/7*t**2 - 67/7*t**3 = 0 for t.
-1, -2/3
Let l = 3 + -1. Let s(d) = d**3 - 9*d**2 + 10*d - 12. Let a be s(8). What is b in -b**4 + 31*b - 31*b - b**a + 4*b**3 - l*b**2 = 0?
0, 1
Let d(h) be the first derivative of -h**5/5 - 3*h**4/4 + 4*h**3/3 - 196. Determine r so that d(r) = 0.
-4, 0, 1
Let v(s) be the second derivative of -s**7/63 - 11*s**6/45 + 3*s**