56*s**4. Determine m so that d(m) = 0.
-2, -1/2
Let m(q) be the third derivative of 0 - q**2 - 1/33*q**4 + 1/330*q**5 + 0*q + 1/11*q**3. Factor m(a).
2*(a - 3)*(a - 1)/11
Determine n so that 183*n + 21 - 10*n**2 - 93 - 16*n**3 - 94*n**2 = 0.
-8, 3/4
Let u(l) be the second derivative of l**7/126 - l**5/30 + l**3/18 + 9*l + 2. Find q, given that u(q) = 0.
-1, 0, 1
Find h such that -4/9*h**2 - 26896/9 + 656/9*h = 0.
82
Let x(l) = 2*l**2 - 4*l - 2. Let r be x(-1). Factor 5*i + 0*i - r*i - 2*i**4 + 2*i**2 - i**5.
-i*(i - 1)*(i + 1)**3
Let v(a) = a**2 + 45*a + 503. Let y be v(-20). Factor 2/3*m**4 + 0*m + 2/3*m**y + 0 - 4/3*m**2.
2*m**2*(m - 1)*(m + 2)/3
Let m = 507 - 504. Let w(s) be the third derivative of 0*s + 0 - 1/30*s**4 + 0*s**m + 4/75*s**5 - 7*s**2 - 1/50*s**6. Determine p so that w(p) = 0.
0, 1/3, 1
Let c be -1 - 1*(1 - 4). Let k be -2*((-112)/98)/8. Factor k*p**3 - 8/7*p + 0 + 0*p**c.
2*p*(p - 2)*(p + 2)/7
Let p(o) be the third derivative of -o**5/20 + 17*o**4/4 + 36*o**3 + 102*o**2. Factor p(v).
-3*(v - 36)*(v + 2)
Let f(x) = -x + 14. Let o be f(2). Let q be 5/o - (-6)/18. Factor 1/2*v + 1/4*v**5 + 1/4*v**2 - 1/4*v**4 - q*v**3 + 0.
v*(v - 2)*(v - 1)*(v + 1)**2/4
Suppose -64*g + 38*g = 0. Let 0*q**3 - 4/3*q**5 + 0*q**2 + 2/3*q**4 + 0 + g*q = 0. What is q?
0, 1/2
Suppose -2*j = 5*r - 10, 0*r = 4*j + 3*r - 6. Let x(y) be the second derivative of -2/5*y**3 + 1/20*y**4 + 5*y + j + 6/5*y**2. Factor x(u).
3*(u - 2)**2/5
Let d(s) be the first derivative of s**6/6 - 6*s**5/5 + 9*s**4/4 + 4*s**3/3 - 6*s**2 - 326. Suppose d(k) = 0. What is k?
-1, 0, 2, 3
Let i(u) = -20*u**4 + 20*u**3 + 3*u**2 - 3*u - 17. Let z(m) = -6 - 26*m**3 - 7*m**4 + m**2 - m + 15*m**3 + 18*m**3. Let b(o) = -6*i(o) + 17*z(o). Factor b(r).
r*(r - 1)**2*(r + 1)
Suppose 5*c - 21 = w + w, -c - 3 = -4*w. Let -26*i**3 - 4*i - w*i**4 + 25*i**2 - 3 - 1 + 2*i**2 + 9*i**4 = 0. Calculate i.
-2/7, 1, 2
Let p(q) be the first derivative of -4/5*q + 2/5*q**2 - 1/15*q**3 - 6. Factor p(l).
-(l - 2)**2/5
Suppose -5*m = -2*g - 2, 0 = -4*m - 5*g + 37 - 9. Determine h so that -3*h**m - 3/4*h**4 - 3/2*h - 5/2*h**3 - 1/4 = 0.
-1, -1/3
Let z be 4/240*10 - (-50)/396*3. Suppose 0 + 2/11*t**4 - z*t**2 + 0*t**3 + 4/11*t = 0. What is t?
-2, 0, 1
Let g(l) = l + 6. Let m be g(3). Solve -12*s**3 + m*s**4 + 4*s**5 + 28*s - s**5 - 28*s = 0.
-4, 0, 1
Let u = -50 + 52. Let 79 - 48*x + 112 - x**2 - 47 + 5*x**u = 0. What is x?
6
Find x such that 2/11*x**4 + 8/11 - 8/11*x - 6/11*x**2 + 4/11*x**3 = 0.
-2, 1
Suppose -7*b = -6*b - 30. Let -16 + 21*n**2 - 78*n + 30*n - 12*n**3 - 35*n**2 - b*n**2 = 0. What is n?
-2, -1, -2/3
Let n(r) be the third derivative of r**5/420 + 2*r**4/21 - 201*r**2. Let n(f) = 0. Calculate f.
-16, 0
Let m(i) be the second derivative of -i**7/21 - 14*i**6/15 - 73*i**5/10 - 28*i**4 - 48*i**3 + 95*i. Factor m(k).
-2*k*(k + 3)**2*(k + 4)**2
Factor 8 - 33/2*w - 9*w**4 + 1/2*w**5 + w**2 + 16*w**3.
(w - 16)*(w - 1)**3*(w + 1)/2
Let o(y) be the first derivative of 10*y + 5/2*y**2 + 12 - 5/3*y**3. Factor o(j).
-5*(j - 2)*(j + 1)
Let t(w) be the third derivative of 0 + 0*w + 1/144*w**4 - 12*w**2 + 0*w**3 + 1/360*w**5. Factor t(h).
h*(h + 1)/6
Suppose 108 = 2*o + o. Factor i**4 + o*i**5 - 3*i**3 - 37*i**5 + 0*i**3 - i**2 - 4*i**4.
-i**2*(i + 1)**3
Let q be 16/((-2240)/42)*5/(-3). Find j such that -q*j**2 + 1 + 1/2*j = 0.
-1, 2
Suppose 15*s - 13*s - 8 = 0. Let c be 16/(-12) + s + (-4)/6. Suppose 1/6*f + 0 + 1/6*f**3 - 1/3*f**c = 0. What is f?
0, 1
Let i = 58 + -55. Solve -9 + t + 35*t**3 - 30*t**i + 15*t**2 - 6*t - 1 - 5*t**4 = 0 for t.
-1, 1, 2
Let f(p) be the third derivative of p**9/7560 - p**8/3360 - p**4/24 + 6*p**2. Let b(d) be the second derivative of f(d). Factor b(w).
2*w**3*(w - 1)
Let g = -407 + 411. Let o(x) be the second derivative of 3/20*x**5 + 15/2*x**3 + 27/2*x**2 + g*x + 7/4*x**4 + 0. Find p, given that o(p) = 0.
-3, -1
Let x(l) = -384 + 384 - 2*l. Let s be x(0). Factor 2/3*q**3 + s + 0*q**2 + 0*q**4 - 2/3*q**5 + 0*q.
-2*q**3*(q - 1)*(q + 1)/3
Let j be (-4)/10*(-3 + -2). Suppose -3*i + 4 = -j. Let -2*a**2 + 0*a**2 + i*a + 0*a = 0. Calculate a.
0, 1
Let t(p) be the first derivative of 4/5*p**5 - 8*p + 6*p**2 + 4/3*p**3 - 19 - 3*p**4. Factor t(j).
4*(j - 2)*(j - 1)**2*(j + 1)
Solve -219 + 178*j**3 - 17*j**4 + 251 - 59*j**4 - j**2 + 10*j**5 - 2*j - 135*j**2 - 6*j = 0.
-2/5, 1, 2, 4
Let t(o) be the first derivative of 4*o**3/3 - 38*o**2 + 280*o - 205. Factor t(p).
4*(p - 14)*(p - 5)
Let h(o) be the second derivative of o**7/2520 - o**6/360 - o**5/40 + o**4/12 - 2*o. Let b(a) be the third derivative of h(a). Factor b(x).
(x - 3)*(x + 1)
Let o be (-4)/(-24) + 95/(-48) - -2. Let v = 5/144 + o. Determine a so that -2/9*a**3 - v*a + 0 - 4/9*a**2 = 0.
-1, 0
Let t(f) be the second derivative of -3*f**4/2 + 2*f**3/3 - 22*f - 7. Factor t(o).
-2*o*(9*o - 2)
Let h(t) be the first derivative of t**7/126 + t**6/90 - t**5/60 - t**4/36 + 26*t - 27. Let i(s) be the first derivative of h(s). What is v in i(v) = 0?
-1, 0, 1
Factor -762 + 197*m + 331*m + 3*m**3 - 170*m - 738 + 242*m - 75*m**2.
3*(m - 10)**2*(m - 5)
Factor 2*d**4 - 4*d**2 - 10*d**3 + 110*d - 9*d**3 + 5*d**3 - 2*d**2 + 100.
2*(d - 5)**2*(d + 1)*(d + 2)
Factor -2/13*y**3 - 28/13 + 54/13*y - 24/13*y**2.
-2*(y - 1)**2*(y + 14)/13
Suppose 15*h - 13*h + 2 = 0. Let k be (4/(-12))/h*9. What is x in 0 - 15/2*x**4 + 3*x - 3/2*x**2 - 12*x**k = 0?
-1, 0, 2/5
Let q(w) = -35*w**3 - 5*w**2 - 40*w + 20. Let f(p) = p**3 - p**2 - p - 2. Let t(n) = -30*f(n) - q(n). Factor t(r).
5*(r + 1)*(r + 2)*(r + 4)
Let n = -9671/2 + 4837. Suppose -n*g - 1/2*g**2 + 0 = 0. What is g?
-3, 0
Let k(j) be the third derivative of j**6/660 + 19*j**5/330 + 10*j**4/11 + 84*j**3/11 - 3*j**2 + 4. Solve k(o) = 0.
-7, -6
Let g(t) = -t**2 + 6*t - 6. Let h = 8 + -4. Let f be g(h). Let 33*a**f + 3 - 3*a - 39*a**2 + 0*a = 0. Calculate a.
-1, 1/2
Let t(k) be the second derivative of 3*k**7/14 - 19*k**6/7 - 21*k**5/20 + 239*k**4/14 + 194*k**3/7 + 108*k**2/7 - 717*k. Suppose t(m) = 0. Calculate m.
-1, -2/3, -2/7, 2, 9
Let j(i) be the first derivative of 5*i**6/2 - 86*i**5 + 3215*i**4/4 - 1820*i**3/3 - 490*i**2 - 480. Determine t, given that j(t) = 0.
-1/3, 0, 1, 14
Factor -16*k**2 - 2*k**2 - 9 + 8*k**2 + 2*k**2 + 5*k**2 + 12*k.
-3*(k - 3)*(k - 1)
Let c(q) = 14*q**4 + 5*q**3 - 46*q**2 + 49*q + 6. Let p(u) = u**4 - u**3 + u**2 + u + 2. Let v(h) = 5*c(h) - 35*p(h). Suppose v(k) = 0. What is k?
-4, 2/7, 1
Let o(j) = -5*j**2 + 50*j + 90. Let l(a) = 3*a**2 - 52*a - 92. Let n(m) = -5*l(m) - 4*o(m). Determine y so that n(y) = 0.
-10, -2
Let b be (-2)/15*(-370 - -367). Factor 0 - 4/5*z + b*z**2.
2*z*(z - 2)/5
Factor -1/3*x**3 + 0 + 0*x**2 + 1/6*x**4 + 1/6*x**5 + 0*x.
x**3*(x - 1)*(x + 2)/6
Let a(q) = 34*q - 1970. Let y be a(58). Let 2/3 + 1/6*p**y - 2/3*p = 0. What is p?
2
Let o(v) be the second derivative of -5*v**4/12 + 5*v**3/3 + 20*v + 11. Suppose o(y) = 0. Calculate y.
0, 2
Suppose -2*n + 576 = 570. Determine y, given that 0*y**n - 3/2*y**4 + 3*y**2 + 0*y - 3/2 = 0.
-1, 1
Let k = -2193 - -13159/6. Suppose -1/6*b**2 + 0*b + k = 0. What is b?
-1, 1
Factor -28 + 36*x**3 - 5*x**2 - 116 - 5*x**2 + 24 - 100*x - 31*x**3.
5*(x - 6)*(x + 2)**2
Let 261 - 24*d - 89 - 24*d**2 - 81 - 44*d - 79 = 0. What is d?
-3, 1/6
Let w(l) be the first derivative of l**9/4536 - l**8/1260 + l**6/270 - l**5/180 + 4*l**3/3 - 10. Let j(a) be the third derivative of w(a). Factor j(n).
2*n*(n - 1)**3*(n + 1)/3
Let c(y) = y**2 + 4*y + 4. Let v be c(-4). Factor 2*q + 22 + v*q**2 - 26 - 2*q.
4*(q - 1)*(q + 1)
Let y = -44 - -46. Let q be (y + -1)*-3 + (-144)/(-42). Suppose -6/7 + q*m + 3/7*m**2 = 0. What is m?
-2, 1
Let p = -1/74115 + -4166909/74115. Let l = p - -6668/117. Solve 0*d + 6/13*d**3 + 4/13*d**2 - l*d**4 + 0 = 0.
-2/5, 0, 1
Let b(m) be the first derivative of -m**3/15 - m**2/2 + 6*m/5 - 63. Suppose b(u) = 0. Calculate u.
-6, 1
Let u(s) be the first derivative of -5*s**5 - 20*s**4 - 8*s**3 + 32*s**2 - 16*s + 252. Solve u(i) = 0.
-2, 2/5
Let g(j) be the second derivative of j**6/105 - j**5/10 + 11*j**4/42 - 5*j**3/21 - 134*j. Let g(i) = 0. Calculate i.
0, 1, 5
Let l(c) be the second derivative of c**4/126 - c**3/9 + 85*c. Solve l(h) = 0 for h.
0, 7
Let c(a) = 4*a - 1. Let g be c(4). Suppose g = -0*l + 2*l - 3*u, 2*l = -3*