- 11 + 11. Let j(g) be the second derivative of g + 1/10*g**5 - 8/45*g**6 + 0*g**3 + 16/189*g**7 + 0 + f*g**2 - 1/54*g**4. Factor j(a).
2*a**2*(a - 1)*(4*a - 1)**2/9
Let 4*k - 146*k**3 + 6*k**3 + 61*k**2 + 75*k**2 + 4 - 4 = 0. Calculate k.
-1/35, 0, 1
Suppose -59 = -5*m + 61. Suppose -m = -4*k - t, -5*k + 2*k + 27 = 3*t. Suppose 4*v**2 - 2*v**2 - k*v**2 - 2*v**3 - v**3 = 0. What is v?
-1, 0
Let x(d) be the second derivative of d**8/168 - 2*d**7/35 + d**6/5 - 4*d**5/15 - 21*d**2/2 - 8*d. Let n(q) be the first derivative of x(q). Factor n(g).
2*g**2*(g - 2)**3
Let i(t) = 3*t**2 + 40*t + 80. Suppose -3*h + 7*h - 4 = 0, -15 = -5*z - 5*h. Let m(o) = -35*o**2 - 480*o - 960. Let g(c) = z*m(c) + 25*i(c). Factor g(q).
5*(q + 4)**2
Let p(i) be the third derivative of i**5/12 + 305*i**4/24 + 3*i**2 + 30. Factor p(o).
5*o*(o + 61)
Let d(p) = 4*p**5 + 12*p**4 + 4*p**3 - 12*p**2 + 8*p. Let h(y) = -y**5 - y**4 + y**2 - y. Let o(z) = d(z) + 8*h(z). Solve o(f) = 0 for f.
-1, 0, 1
Let x(g) be the second derivative of 3*g**7/70 - g**6/8 - 4*g**5/5 + 3*g**4/2 + 2*g**2 - 5*g. Let r(q) be the first derivative of x(q). Factor r(a).
3*a*(a - 3)*(a + 2)*(3*a - 2)
Let q(m) = -2*m**2 + 113*m + 3367. Let o(c) = 3*c**2 - 227*c - 6733. Let h(z) = 3*o(z) + 5*q(z). Suppose h(r) = 0. What is r?
-58
Let f(n) = -42*n**2 + 366*n + 1626. Let h(d) = 5*d**2 - 46*d - 203. Let y(s) = -4*f(s) - 33*h(s). Determine r so that y(r) = 0.
-13, -5
Let m(b) = 4*b - 24. Let n be m(9). Factor 5*h + 7 + 5*h**2 - h**3 - 8*h**2 + n*h**2 - 20*h.
-(h - 7)*(h - 1)**2
Let g(r) = -2*r**2 - 167*r + 6751. Let i(p) = -3*p**2 - 168*p + 6760. Let z(w) = 4*g(w) - 3*i(w). Find f such that z(f) = 0.
82
Let p = 656 + -654. Let w(s) be the third derivative of 0*s - 10*s**p + 1/78*s**4 - 1/39*s**3 + 0 - 1/390*s**5. Factor w(a).
-2*(a - 1)**2/13
Let w be (-2)/(-9) + (-77)/((-847)/66). Determine s so that -98/9*s**3 + w*s**2 - 8/9*s + 0 = 0.
0, 2/7
Let g(h) be the second derivative of -1/3*h**4 + 20/3*h**3 - 13*h + 0 - 50*h**2. Solve g(y) = 0.
5
Let p(h) be the first derivative of 45/2*h**4 + h**5 + 10 + 485/3*h**3 + 360*h**2 + 320*h. Solve p(w) = 0 for w.
-8, -1
Let h(p) be the third derivative of -p**8/10080 - 41*p**4/24 - 44*p**2. Let c(m) be the second derivative of h(m). Factor c(n).
-2*n**3/3
Let g(s) be the second derivative of -3*s**5/100 - s**4/20 + 3*s**3/5 + 3*s - 2. Factor g(z).
-3*z*(z - 2)*(z + 3)/5
Let q(l) be the third derivative of -4/3*l**3 - 1/2*l**5 - 7/12*l**6 - 2*l**2 + 11/21*l**7 + 0 + 0*l - 1/8*l**8 + 5/3*l**4. Determine n, given that q(n) = 0.
-2/3, 2/7, 1
Let r = 22 + -32. Let s = r + 13. Factor -4 + 4 + s*z - 2*z**2 - z**2.
-3*z*(z - 1)
Let v be 1/5 + (-2107)/35. Let s = 60 + v. Determine y so that -1/3*y**3 + 0*y**2 + s*y + 1/2*y**4 - 1/6*y**5 + 0 = 0.
0, 1, 2
Suppose -j = 2*j + 12, 2*j - 20 = -4*h. Suppose h*l = 13*l - 18. Let 0 - 1/5*u**4 + u**l - 8/5*u**2 + 4/5*u = 0. What is u?
0, 1, 2
Suppose -4*x + 8 = 0, 5*x = -5*g + 19 + 31. Let j = 10 - g. Determine a so that j*a**3 - a**4 - 6*a + 0 + 4*a**4 - 3 + 4*a**3 = 0.
-1, 1
Let t be (1 - 6) + (-1)/((-840)/4204). Let u(o) be the third derivative of 14*o**2 + 0*o**3 + 0*o**4 + t*o**7 + 0*o + 0 - 1/60*o**6 + 1/60*o**5. Solve u(r) = 0.
0, 1
Let w(z) be the second derivative of 36/5*z**2 + 0 + 1/30*z**4 - 8*z - 4/5*z**3. Suppose w(p) = 0. What is p?
6
Suppose -4*p + 106 = 3*q - 2*q, -2*p + 242 = 2*q. Let l = q + -123. Solve -i + 0 - 5/4*i**l - 2*i**2 - 1/4*i**4 = 0 for i.
-2, -1, 0
Let z be -13 - (-28 - 32472/168). Factor 3/7*k**4 + 648/7*k**2 - 2187/7 + z*k + 78/7*k**3.
3*(k - 1)*(k + 9)**3/7
Let h(x) = -16*x + 19. Let g be h(2). Let c be (-13 - g)/(0 - 1*-1). Find m, given that 2/5*m**2 + 0*m + c = 0.
0
Let p(k) = 4*k**2 + 2*k. Let g be p(2). Let t = g - 18. Factor -6 + 7*l - 10*l**5 - 18*l**3 + 6 + 26*l**4 - 3*l - t*l**2.
-2*l*(l - 1)**3*(5*l + 2)
Let j(t) be the second derivative of t**5/140 + t**4/7 + 8*t**3/7 + 32*t**2/7 + 2*t - 30. Determine d, given that j(d) = 0.
-4
Let v(n) = n - 1. Suppose 4*t = 3*t + 3. Let a be v(t). Factor -2*p + a*p**2 + 30 - 30.
2*p*(p - 1)
Let y = 2032 - 2030. Factor 2*p + y + 1/2*p**2.
(p + 2)**2/2
Factor -159*y**3 + 15*y**4 + 227131*y**2 - 226837*y**2 + 119*y + 25*y.
3*y*(y - 8)*(y - 3)*(5*y + 2)
Let q(x) be the third derivative of x**5/15 - 11*x**4/6 - 187*x**2. Factor q(l).
4*l*(l - 11)
Let v be (18705/473 - 41)*22/(-4). Find f such that -20/3*f - v*f**2 + 4/3 = 0.
-1, 1/6
Let l = -2144 - -2147. Factor -3/4*x**5 - 3/4*x**2 + 0 + 3/4*x**l + 3/4*x**4 + 0*x.
-3*x**2*(x - 1)**2*(x + 1)/4
Let c(f) be the first derivative of -2/3*f**2 - 2/3*f**3 + 1/3*f**4 + 0*f - 3. Solve c(l) = 0 for l.
-1/2, 0, 2
Let m = 3019/13464 - 3/1496. Suppose m + 0*n**3 + 2/9*n**4 + 0*n - 4/9*n**2 = 0. Calculate n.
-1, 1
Let h = 69 + -64. Let y(u) be the second derivative of 0*u**3 + 1/2*u**4 + 0*u**2 - 1/10*u**6 - 2*u - 3/20*u**h + 0. Factor y(n).
-3*n**2*(n - 1)*(n + 2)
Let p = -2/3069 + 98222/21483. Factor 20/7*o**2 + 4/7*o**3 + 16/7 + p*o.
4*(o + 1)*(o + 2)**2/7
Let j be (-56)/14 + 0 + 0. Let a be j/18 + (-1736)/(-36). Determine t so that 10*t - 2*t**3 - 46*t**2 + 5 + a*t**2 + 1 = 0.
-1, 3
Let v(r) be the second derivative of r**4/36 + 17*r**3/18 + 2*r - 41. Solve v(w) = 0.
-17, 0
Let d(y) be the first derivative of -1/3*y**3 + 0*y**2 - 1/540*y**5 - 1/3240*y**6 + 1/72*y**4 + 0*y + 4. Let j(b) be the third derivative of d(b). Factor j(c).
-(c - 1)*(c + 3)/9
Let v(x) be the third derivative of -x**8/1176 - x**7/735 + x**6/105 + 2*x**5/105 + 93*x**2. Solve v(a) = 0 for a.
-2, -1, 0, 2
Let m(y) be the first derivative of -3/4*y**4 - 2*y**3 + 0*y - 4 + 9/2*y**2. Suppose m(g) = 0. Calculate g.
-3, 0, 1
Let u(t) be the second derivative of 0*t**3 + 0 - t - 1/2*t**2 + 1/12*t**4. Factor u(f).
(f - 1)*(f + 1)
Let m be -4 + 316/36 + (-4)/(-18). Let v(y) be the second derivative of 4*y + 0 + 0*y**2 - 3/50*y**m - 1/70*y**7 + 0*y**3 + 0*y**4 + 3/50*y**6. Factor v(r).
-3*r**3*(r - 2)*(r - 1)/5
Let b(x) = 3*x**3 + 3*x**2 + 15*x - 11. Suppose 10*c - 15 = 7*c. Let a(v) = -v**3 - v**2 - v + 1. Let h(d) = c*a(d) + b(d). Find s such that h(s) = 0.
-3, 1
Suppose 3*f - 3*y - 1 - 2 = 0, -5*y = -3*f + 1. Let i(w) be the first derivative of -3/8*w**f - 1/6*w**3 - 1/4*w + 9. What is s in i(s) = 0?
-1, -1/2
Let a(y) be the third derivative of y**7/350 + y**6/4 + 25*y**5/4 - 93*y**2. Suppose a(j) = 0. What is j?
-25, 0
Let -72/13*p - 648/13 - 2/13*p**2 = 0. Calculate p.
-18
Suppose -5*d = -m - 14, -4*d - 28 = -4*m - 20. Let c(k) be the first derivative of m + 0*k + 1/16*k**4 + 0*k**2 + 1/12*k**3. Factor c(t).
t**2*(t + 1)/4
Let r(t) be the second derivative of 9*t + 7/2*t**2 + 2/3*t**3 + 0 + 11/15*t**5 - t**4 - 1/5*t**6. Let h(u) be the first derivative of r(u). Factor h(v).
-4*(v - 1)*(2*v - 1)*(3*v - 1)
Let p = -1209 - -1211. Let b(a) be the first derivative of -3/2*a**p - 1/2*a**3 + 8 + 0*a. Factor b(t).
-3*t*(t + 2)/2
Let a be (27/(-567))/((-3)/18). Factor 8/7*y + 3/7*y**2 + 3/7 - a*y**3.
-(y - 3)*(y + 1)*(2*y + 1)/7
Let f = 333 + -329. Let p(c) be the second derivative of 1/6*c**3 + 1/48*c**f + 4*c + 0 + 1/2*c**2. Factor p(w).
(w + 2)**2/4
Suppose 0 = -9*j + 58 - 58. Let p(z) be the first derivative of 0*z**3 + j*z + 0*z**2 - 3 - 1/33*z**6 + 1/11*z**4 - 2/55*z**5. Let p(k) = 0. Calculate k.
-2, 0, 1
Solve 55/3*d**2 + 19/3*d**4 + 169/9*d**3 + 17/3*d - 2/9 = 0 for d.
-1, 2/57
Let v = 16438/13665 - 8/2733. Find p, given that v - 3/5*p**3 - 3*p + 12/5*p**2 = 0.
1, 2
Let y(w) be the third derivative of 7/80*w**5 - 1/16*w**4 + 7/80*w**6 - 10*w**2 + 0*w**3 + 1/56*w**7 + 0 + 0*w. Suppose y(p) = 0. What is p?
-2, -1, 0, 1/5
Suppose -w = w. Suppose -20*m = -53 - 34 + 47. Factor w - 2/3*b**m - b + 1/3*b**3.
b*(b - 3)*(b + 1)/3
Let z(f) = -f**2 + 20. Let m be z(4). Factor 0 + 1/4*b**m + 3/4*b**3 + 0*b + 1/2*b**2.
b**2*(b + 1)*(b + 2)/4
Let h(q) be the first derivative of 17161*q**3/8 + 393*q**2/4 + 3*q/2 - 65. Find d, given that h(d) = 0.
-2/131
Let k(v) be the second derivative of v**4/66 - 10*v**3/33 - v**2 + 119*v. Determine y, given that k(y) = 0.
-1, 11
Let g(n) be the third derivative of 121*n**6/30 + 22*n**5/3 - 43*n**4/24 + n**3/6 + 2*n**2 + 183. Factor g(t).
(t + 1)*(22*t - 1)**2
Let c be ((-4)/(-10))/((-1)/(-15)). Let v be (7*4/42)/(16/c). Find g, giv