(w) be the third derivative of -w**5/630 + 4*w**4/21 - 64*w**3/7 + 7*w**2 + w. Suppose p(l) = 0. Calculate l.
24
Solve 7*a**3 + 13 - 1/6*a**5 + 14/3*a**2 - 5/3*a**4 - 137/6*a = 0 for a.
-13, -2, 1, 3
Let d = -118 + 121. Factor 9*c + 4*c**2 + 242*c**3 - c - 246*c**d.
-4*c*(c - 2)*(c + 1)
Let m be (1 - 6) + 4 + 3. Factor -78*w**2 - 4*w + 150*w**2 - m - 74*w**2.
-2*(w + 1)**2
Factor 4*y - 7*y**2 - 1 + 8*y**2 + 9 - 5*y**2.
-4*(y - 2)*(y + 1)
Let l be (21/(-35))/((-2)/10). Suppose -8 = -l*a + q, 2*a + 5*q + 7 - 1 = 0. Let 2*r**3 - a*r**2 - 10*r**4 + 4*r**2 - 1 + 1 + 6*r**5 = 0. What is r?
-1/3, 0, 1
Let a(z) = 19*z**5 - 24*z**4 - 65*z**3 - 21*z**2 + 19*z + 9. Let h(u) = u**5 + u**3 - u**2 + u + 1. Let m(j) = a(j) - 3*h(j). Let m(y) = 0. What is y?
-1, -1/2, 1/2, 3
Factor 4*i - 3096*i**2 + 5 + 3097*i**2 + 4 + 2*i.
(i + 3)**2
Let q(j) be the third derivative of -j**8/13440 + j**6/480 + j**5/30 + 10*j**2. Let c(l) be the third derivative of q(l). Suppose c(z) = 0. What is z?
-1, 1
Let b(i) be the third derivative of i**7/735 + i**6/35 + i**5/7 + i**4/3 + 3*i**3/7 - 371*i**2 - 1. Factor b(g).
2*(g + 1)**3*(g + 9)/7
Suppose -i + h - 34 = -4*h, 0 = 2*i - 2*h + 84. Let l = -42 - i. Factor 1/5*z**4 + 1/5 - 4/5*z**3 - 4/5*z + 6/5*z**l.
(z - 1)**4/5
Let a(v) = 4*v**3 + 1. Let z be a(1). Let r(h) be the first derivative of 6*h + z*h**3 + 21/2*h**2 - 4. Factor r(k).
3*(k + 1)*(5*k + 2)
Let c(f) be the second derivative of -f**6/600 - 5*f**3/3 + 11*f. Let p(m) be the second derivative of c(m). Factor p(z).
-3*z**2/5
Factor -50*g**2 - 3005*g**3 + 3010*g**3 + 67*g + 13*g.
5*g*(g - 8)*(g - 2)
Let a(t) be the first derivative of 4/21*t**4 + 1/1260*t**6 + 0*t**2 + 4/3*t**3 + 2/105*t**5 + 1 + 0*t. Let u(w) be the third derivative of a(w). Factor u(v).
2*(v + 4)**2/7
Determine k, given that 1/3*k**4 - 107/3*k**2 - 8*k**3 - 56/3 - 46*k = 0.
-2, -1, 28
Suppose 0*l = -3*l. Suppose -4*j - 2*h + 0*h = -18, l = 4*h - 12. Factor -1 - 9*t**j + 1 + 7*t**3 + 2*t**5.
2*t**3*(t - 1)*(t + 1)
Let l(f) be the first derivative of -10/3*f + 8 - 14/9*f**3 + 1/6*f**4 + 11/3*f**2. Factor l(q).
2*(q - 5)*(q - 1)**2/3
Let x = 99 + -96. Factor -44*u - 65*u**3 - 88*u**x + 42*u**2 + 137*u**3 + 16 + 2*u**4.
2*(u - 4)*(u - 2)*(u - 1)**2
Let i be -3*(2 + (-78)/18). Let v(h) be the third derivative of 0*h + 2/105*h**i + 0 + 6*h**2 + 0*h**5 + 0*h**3 + 0*h**4 - 1/30*h**6. Factor v(s).
4*s**3*(s - 1)
Factor 0*x**2 + 5/4*x**3 - 5/4*x**5 + 0 + 0*x**4 + 0*x.
-5*x**3*(x - 1)*(x + 1)/4
Let s = 15/373 + 5923/1119. Suppose s*h + 2/3*h**4 - 4*h**2 + 0*h**3 - 2 = 0. Calculate h.
-3, 1
Let c(d) be the second derivative of -d**5/180 + 2*d**3/27 - 2*d - 8. Factor c(s).
-s*(s - 2)*(s + 2)/9
Find z such that z**4 + 5*z**2 - 1535*z - 2*z**4 - 3*z**2 + z**3 + 1535*z = 0.
-1, 0, 2
Let u = 9408 - 9408. Factor 0 - 4/3*q**3 - 22/3*q**4 + u*q + 0*q**2 + 26/3*q**5.
2*q**3*(q - 1)*(13*q + 2)/3
Let 37*t**4 - 12*t**4 - 11*t**4 - 32*t**2 - 6*t**4 + 12*t**3 - t**5 - 64*t - 4*t**4 = 0. What is t?
-2, 0, 4
Find r, given that 26 + 0*r**2 + 2*r**2 - 105*r - r**2 + 120*r = 0.
-13, -2
Let i be 15/(-24)*2 - 2/(-1). Let k(f) be the first derivative of 3*f**3 - 6 + 0*f - 3*f**2 - i*f**4. Factor k(n).
-3*n*(n - 2)*(n - 1)
Let z = 531 - 529. Let s(f) be the third derivative of 0*f**3 + 0*f + 1/120*f**5 + 1/24*f**4 + 0 + 7*f**z. Determine r, given that s(r) = 0.
-2, 0
Let y(z) be the second derivative of -5*z**7/42 - 2*z**6/3 - 3*z**5/2 - 5*z**4/3 - 5*z**3/6 + 49*z. What is w in y(w) = 0?
-1, 0
Factor -2/3*u**4 + 0 - 18*u**2 + 26/3*u + 10*u**3.
-2*u*(u - 13)*(u - 1)**2/3
Let w = -96 + 458. Suppose -w = -4*g + 110. Factor -2*u**2 - u**5 + u + 118*u**3 + 2*u**4 - g*u**3.
-u*(u - 1)**3*(u + 1)
Factor 1/7*h**2 + 12/7 + 13/7*h.
(h + 1)*(h + 12)/7
Let j = 11/375 - -673/2625. Factor -j*x**2 - 4/7*x + 0.
-2*x*(x + 2)/7
Let r be 84/14 - (0 - 1 - -4). Factor 1/8*u**5 + 0 + 0*u**r - 1/8*u - 1/4*u**4 + 1/4*u**2.
u*(u - 1)**3*(u + 1)/8
Factor -2*f**3 + f**4 - 5*f**4 + 22*f**3 - 32*f**2 + 4*f**3.
-4*f**2*(f - 4)*(f - 2)
Find a, given that 8/9 - 4/9*a**5 - 8/9*a**2 - 4/3*a + 16/9*a**3 + 0*a**4 = 0.
-2, -1, 1
Let p(m) be the second derivative of -3*m**5/40 + 5*m**4/4 - 13*m**3/4 - 18*m**2 - m - 6. Factor p(h).
-3*(h - 8)*(h - 3)*(h + 1)/2
Let l = -77/10 - -811/105. Let s(c) be the second derivative of 0 + l*c**4 + 9/7*c**2 - 2/7*c**3 + 2*c. Factor s(f).
2*(f - 3)**2/7
Factor -3*k - 3/2*k**4 - 6*k**3 - 15/2*k**2 + 0.
-3*k*(k + 1)**2*(k + 2)/2
Let h(j) be the second derivative of 5*j**4/12 + 10*j**3/3 - 64*j. Factor h(k).
5*k*(k + 4)
Factor y**3 - 2*y**4 - 219*y**5 + 221*y**5 + 2*y**2 - 3*y**3.
2*y**2*(y - 1)**2*(y + 1)
Let w(s) be the second derivative of 1/4*s**5 + 12*s + 0 + 0*s**2 + 10/3*s**3 - 5/3*s**4. Factor w(a).
5*a*(a - 2)**2
Let z(f) be the third derivative of f**6/90 - f**5/15 + 4*f**3/3 - 4*f**2. Let p(s) be the first derivative of z(s). Find o such that p(o) = 0.
0, 2
Let d be (7 - (-698)/(-104))/((-6)/(-32)). Factor -6/13*p**4 + 8/13*p + d*p**3 - 22/13*p**2 + 0.
-2*p*(p - 1)**2*(3*p - 4)/13
Let t(g) = -g**2. Suppose -3*y = 5*w - 1, 2*w - 7*w + 5*y - 15 = 0. Let k(m) = 8*m**2 - 9*m + 6. Let o(u) = w*k(u) - 5*t(u). Suppose o(j) = 0. Calculate j.
1, 2
Let a(b) be the third derivative of -b**8/672 - b**7/210 + b**5/60 + b**4/48 + 111*b**2. Suppose a(n) = 0. Calculate n.
-1, 0, 1
Let b(u) = 3*u - 10. Let p be b(5). Factor 64*x**3 + 2*x + 4*x**2 - 3*x**4 - 2*x**p - 65*x**3 + x**5 - x**2.
-x*(x - 1)*(x + 1)**2*(x + 2)
Let g(y) be the third derivative of -y**5/90 + 77*y**4/144 - 19*y**3/36 + 374*y**2. Factor g(s).
-(s - 19)*(4*s - 1)/6
Let s be (4 - 0/(-5)) + -4. Let l(u) be the third derivative of 0*u - 1/80*u**5 + 6*u**2 + 1/160*u**6 - 1/32*u**4 + s + 1/280*u**7 + 0*u**3. Factor l(b).
3*b*(b - 1)*(b + 1)**2/4
Let f = -246 - -249. Let x(z) be the first derivative of -z + 1/4*z**4 - z**f + 1 + 3/2*z**2. Factor x(h).
(h - 1)**3
Let r be (-2*1 - -6)*3. Suppose -181*h + 179*h + 41 = -5*t, -25 = h + 4*t. Factor -21/5*b**h + 54/5*b**2 + 24/5 + 3/5*b**4 - r*b.
3*(b - 2)**3*(b - 1)/5
Factor -3*w**2 + 8 + 16*w + 8 - 4 - 7*w.
-3*(w - 4)*(w + 1)
Let g(p) be the third derivative of -p**6/780 + 3*p**5/130 - 5*p**4/52 + 7*p**3/39 + 358*p**2. Factor g(s).
-2*(s - 7)*(s - 1)**2/13
Let h(f) be the third derivative of 7*f**5/330 + 17*f**4/132 - 4*f**3/11 + 49*f**2. Factor h(s).
2*(s + 3)*(7*s - 4)/11
Solve -2/17*u**3 + 30/17*u - 16/17 - 12/17*u**2 = 0 for u.
-8, 1
Let b(z) be the second derivative of -z**6/360 + z**4/6 - z**3/6 - 4*z. Let n(w) be the second derivative of b(w). Determine a so that n(a) = 0.
-2, 2
Suppose -5*l = 4*p + 8, 5*p + 4*l = 3*l - 31. Let a be p/(-6)*((-36)/(-14) + -2). Factor -2/3*w**3 + a*w + 2/3*w**2 - 2/3.
-2*(w - 1)**2*(w + 1)/3
Factor -5/3*j**2 + 85/3*j - 120.
-5*(j - 9)*(j - 8)/3
Let w = -2377 - -2379. Find l such that -2/5*l**w + 0 - 4/15*l**3 + 0*l = 0.
-3/2, 0
Let g be (3112/280 + -11)*55. Find b such that -52/7*b**4 - g*b + 8/7 + 44/7*b**2 + 4*b**3 + 16/7*b**5 = 0.
-1, 1/4, 1, 2
Let m(y) be the first derivative of y**3/3 - 7*y + 11. Let z be m(3). Factor 3*v**3 + 33*v**3 + 64*v**z - 23*v + 7*v.
4*v*(v + 2)*(9*v - 2)
What is a in 5/6*a**4 + 10/3*a**2 + 25/6*a**3 + 0*a + 0 = 0?
-4, -1, 0
Let n = -35293/5 + 7061. Suppose -4/5*u**3 - n*u + 4/5 + 12/5*u**2 = 0. What is u?
1
Factor -7/4*q**4 - 2 - 45/2*q**2 + 17*q + 43/4*q**3.
-(q - 2)**3*(7*q - 1)/4
Let n(q) be the second derivative of -13/36*q**4 + 8/3*q**3 - 6*q**2 + 0 + 1/60*q**5 + 3*q. Determine t so that n(t) = 0.
1, 6
Let x(t) be the second derivative of 1/3*t**4 + t**2 + t**3 + 2*t + 0. Suppose x(f) = 0. What is f?
-1, -1/2
Suppose 5*j + 4*t - 44 + 14 = 0, 0 = -4*j - 2*t + 18. Factor -3/5*q**j - 3/5 + 6/5*q.
-3*(q - 1)**2/5
Let i be (-42)/(-26)*194/291. Factor 32/13*d**3 + 0 - i*d**4 - 8/13*d**2 + 0*d.
-2*d**2*(d - 2)*(7*d - 2)/13
Let l(n) = -n**3 - 55*n**2 - 54*n + 1. Let z be l(-54). Suppose -1/4*s**3 + 0*s - 3/4*s**2 + z = 0. Calculate s.
-2, 1
Let w be (-132 + 150)/(2 - -4). Factor 0*d**2 + 0 - 6/5*d**w + 3/5*d + 3/5*d**5 + 0*d**4.
3*d*(d - 1)**2*(d + 1)**2/5
Let p = 2089 - 2089. Find z, given that 0*z**3 + 2/9 + 2/9*z**4 - 4/9*z**2 + p*z = 0.
-1, 1
Suppose -2967 - 1553 = -2*v. Suppose -2280 = -5*n - 5*y, 2*n - 5*y = -3*n + v. Factor -398*g**2 - 70*g - 900*g**2 + 362*g**