 so that w(q) = 0.
3, 18
Let f(m) = 9*m + 1. Let y be f(3). Solve 6*x**2 + 2*x**2 + y*x**3 - 4*x**4 - 24*x**3 = 0 for x.
-1, 0, 2
Suppose -2*u - 12 + 36 = 0. Let z be 1/6 + 1/u. Factor z*l**4 + 0 + 0*l - 1/4*l**2 + 0*l**3.
l**2*(l - 1)*(l + 1)/4
Let o(h) be the first derivative of h**5/120 - h**4/72 - 14*h - 2. Let k(s) be the first derivative of o(s). Factor k(c).
c**2*(c - 1)/6
Let q be 6 - (3 + -3 - -2). Let y be 2/q + (-4)/56. Factor y*m**2 - 2/7 - 1/7*m**3 - 1/7*m**4 + 1/7*m.
-(m - 1)**2*(m + 1)*(m + 2)/7
Let j be (64/72 - 2/2)*-1. Let q(n) be the first derivative of -j*n**6 + 1/3*n**4 - 1/3*n**2 + 2/15*n**5 + 2/3*n - 4/9*n**3 + 6. Solve q(s) = 0.
-1, 1
Suppose -5*u - 4*v - 328 = 0, -3*v + 5*v = -u - 62. Let y = u + 71. Let -16/3*k + 0 + 32/3*k**2 + 20/3*k**y = 0. Calculate k.
-2, 0, 2/5
Let q(l) = 115 + l - l**3 - 10*l**2 + 15*l - 76 + 27*l**2. Let r be q(18). Factor -s + 5/2*s**2 + 1/2*s**4 - 2*s**r + 0.
s*(s - 2)*(s - 1)**2/2
Let i be (-16)/64 - (-2661)/4. Find o, given that -641*o + 3*o**2 + o**2 - o**2 + i*o = 0.
-8, 0
Let -2*r + 6 - 8/9*r**4 - 26/3*r**2 + 50/9*r**3 = 0. What is r?
-3/4, 1, 3
Let v(g) be the second derivative of -5*g**4/12 + 10*g**3/3 + 41*g. What is m in v(m) = 0?
0, 4
Let h(x) be the second derivative of 5*x**4/12 - 65*x**3/6 - 75*x**2 + 16*x - 1. Suppose h(i) = 0. What is i?
-2, 15
Let t = -71 - -46. Let n = 28 + t. Factor 1/5*y**4 + 3/5*y**n - 4/5*y + 0 + 0*y**2.
y*(y - 1)*(y + 2)**2/5
Let y = -363 + 368. Let w(f) be the second derivative of -f**2 - 1/12*f**4 - 1/2*f**3 - y*f + 0. What is q in w(q) = 0?
-2, -1
Let t(u) = -5*u**3 - 41*u**2 - 86*u - 60. Let s(o) = 5*o**3 + 40*o**2 + 85*o + 60. Let c(n) = -6*s(n) - 5*t(n). Find d such that c(d) = 0.
-3, -2
Let a(u) be the second derivative of u - 1/78*u**4 + 44 + 1/13*u**3 + 4/13*u**2. Factor a(f).
-2*(f - 4)*(f + 1)/13
Let c(t) be the second derivative of t**5/35 + t**4/21 - 13*t - 2. Solve c(b) = 0.
-1, 0
Suppose 0 = -2*z + 2*f + 10, -284*z + 286*z + 5*f - 3 = 0. Factor 48/13*n**2 + 0 - 18/13*n**3 - 32/13*n + 2/13*n**z.
2*n*(n - 4)**2*(n - 1)/13
Let r(q) be the second derivative of -q**2 + 0 + 1/24*q**4 - 7*q + 1/3*q**3 - 1/40*q**5. Factor r(t).
-(t - 2)*(t - 1)*(t + 2)/2
Let d(g) be the first derivative of g**9/504 - g**8/224 + g**7/560 + 19*g**3/3 - 28. Let l(f) be the third derivative of d(f). Factor l(i).
3*i**3*(i - 1)*(4*i - 1)/2
Let r = 2119/110 - 189/10. Suppose 6/11*p**3 + 0 - 28/11*p**4 + r*p + 18/11*p**2 = 0. Calculate p.
-1/2, -2/7, 0, 1
Let v(p) = 11*p**3 + 23*p**2 + 7*p. Let o(z) be the second derivative of -17*z**5/20 - 35*z**4/12 - 5*z**3/3 + 2*z. Let w(g) = -5*o(g) - 8*v(g). Factor w(d).
-3*d*(d + 1)*(d + 2)
What is c in -131 - 20*c**5 + 1500*c**2 - 360*c + 242 - 190*c**3 - 111 - 195*c**4 = 0?
-6, 0, 1/4, 2
Factor 108/19 + 630/19*u**2 + 202/19*u**3 + 22/19*u**4 + 702/19*u.
2*(u + 3)**3*(11*u + 2)/19
Let f(l) = -8*l**2 + 10*l - 8. Let x be 1/2*-2*5. Let m(h) = 15*h**2 - 20*h + 15. Let n(d) = x*f(d) - 3*m(d). Factor n(q).
-5*(q - 1)**2
Let y(b) be the first derivative of -2/3*b**3 + 0*b - 2*b**2 + 4. Find m, given that y(m) = 0.
-2, 0
Let i be (-16)/784*-7 + 4/(-28) + 0. Determine d so that 4/5*d**3 + 0*d**2 - 2/15*d**4 + i - 64/15*d = 0.
-2, 0, 4
Let b = -493910657/1437072 - -5/110544. Let u = 344 + b. Determine p so that -u + 8/13*p**2 - 2/13*p**5 - 4/13*p**4 - 2/13*p + 4/13*p**3 = 0.
-2, -1, 1
Let x(n) be the first derivative of n**6/24 - 39*n**5/20 + 35*n**4/16 + 119*n**3/12 - 24*n**2 + 19*n + 881. Factor x(h).
(h - 38)*(h - 1)**3*(h + 2)/4
Factor 8/5*g + 8/15 + 26/15*g**2 + 4/5*g**3 + 2/15*g**4.
2*(g + 1)**2*(g + 2)**2/15
Let g(f) = -f**3 + 6*f**2 - 4*f - 4. Let q be g(4). Find a such that 6*a**2 + 3*a + 6 + q - 9*a**2 = 0.
-2, 3
Let f(t) = t**3 - t**2 + t. Let y be f(0). Let o = y + 6. Factor 0 - o*v**2 + 2*v + 3*v**2 + 1.
-(v - 1)*(3*v + 1)
Let w(h) be the third derivative of -h**7/630 - 7*h**6/360 - h**5/18 - 56*h**2. Determine t so that w(t) = 0.
-5, -2, 0
Solve -152/3*b**2 - 16*b + 14/3*b**4 + 20*b**3 + 0 = 0.
-6, -2/7, 0, 2
Let b(j) be the second derivative of 0*j**2 + 2/9*j**4 + 0 - 2/15*j**5 - 1/9*j**3 - 15*j. Let b(o) = 0. What is o?
0, 1/2
Let z(m) = 3*m**5 - 39*m**4 - 37*m**3 + 5*m**2 - 5*m. Let a(i) = -4*i**5 + 60*i**4 + 56*i**3 - 8*i**2 + 8*i. Let w(u) = -5*a(u) - 8*z(u). Factor w(c).
-4*c**3*(c - 4)*(c + 1)
What is y in 24/7 + 2*y**2 + 32/7*y + 2/7*y**3 = 0?
-3, -2
Let z(v) be the second derivative of -v**7/7 + 7*v**6/15 + 17*v**5/5 + 5*v**4 + v**3/3 - 5*v**2 - 330*v. Solve z(o) = 0 for o.
-1, 1/3, 5
Let l(v) be the first derivative of -v**5/60 + v**3/6 - 21*v**2/2 + 30. Let c(k) be the second derivative of l(k). Factor c(a).
-(a - 1)*(a + 1)
Let a = -23 - -27. Suppose 4*f = -f. Factor 2/3*y**2 - 4/3*y**3 + 0*y + f + 2/3*y**a.
2*y**2*(y - 1)**2/3
Let a = -73 + 229/3. Let o = a + -8/3. Determine i so that -o - 2*i**2 + 2/3*i**3 + 2*i = 0.
1
Suppose -16*y = 1615 - 1711. Let g(n) be the second derivative of 0*n**4 + 0*n**3 + 0*n**2 - 2*n + 0*n**5 + 0 - 1/10*n**y. Factor g(z).
-3*z**4
Let i(c) = -c**3 + 6*c**2 + c - 30. Let m be i(5). Let k(y) be the first derivative of -7 + 0*y**2 + 2/5*y**5 + 0*y - 2/3*y**3 + m*y**4. Factor k(x).
2*x**2*(x - 1)*(x + 1)
Let p(a) be the first derivative of -a**5/10 + 47*a**4/8 - 123*a**3/2 + 1053*a**2/4 - 513*a + 414. Solve p(y) = 0.
3, 38
Suppose -31*l = -30*l - 3. Suppose l*g + 8 = 7*g. Factor 8/3*t + 8/3 + 2/3*t**g.
2*(t + 2)**2/3
Find x, given that -3/2*x**2 + 0 + 21/2*x = 0.
0, 7
Let y(w) = 4*w - 75. Let j be y(24). Let v(p) be the first derivative of 39*p**3 - 5 - j*p**2 + 609/8*p**4 - 147/2*p**5 - 12*p. Suppose v(r) = 0. Calculate r.
-2/7, 2/5, 1
Let q be (1 - 13) + 12 + 0. Factor -2/13*r**3 + q*r**2 + 0 + 2/13*r.
-2*r*(r - 1)*(r + 1)/13
Let b = 595/4 + -148. Let g(x) be the second derivative of 0 + 1/6*x**3 + 1/24*x**4 + 4*x - b*x**2. Find t, given that g(t) = 0.
-3, 1
Suppose 11/7*n**3 + 68/7*n + 1/7*n**4 + 6*n**2 + 40/7 = 0. Calculate n.
-5, -2
Let k(m) be the second derivative of 2*m**4/3 - 7*m**3/6 + 3*m**2 - 6*m. Let g(z) = z**2 - z + 1. Let w(y) = -35*g(y) + 5*k(y). Suppose w(x) = 0. What is x?
-1, 1
Let b(z) be the second derivative of -z**6/240 + 9*z**5/200 + z**4/12 - z**3/5 + 15*z**2/2 + 32*z. Let r(l) be the first derivative of b(l). Factor r(u).
-(u - 6)*(u + 1)*(5*u - 2)/10
Suppose 2*h = -2, 4*k + 0 = 3*h + 11. Solve -k*x**4 + 4*x**3 - 5*x**3 - 4*x**2 - 7*x**3 + 2*x**3 = 0 for x.
-2, -1, 0
Let v(t) be the first derivative of -t**6/3 - 4*t**5/5 - t**4/2 + 93. What is r in v(r) = 0?
-1, 0
Let n(u) be the third derivative of u**6/120 - 49*u**5/20 + 2401*u**4/8 - 117649*u**3/6 - 213*u**2. Factor n(i).
(i - 49)**3
Let n(j) be the second derivative of j**4/30 - 32*j**3/5 + 2304*j**2/5 + 8*j + 1. Determine d, given that n(d) = 0.
48
Suppose -128*d - 22578 + 3*d**5 + 22450 - 3*d**5 + 4*d**5 + 88*d**2 + 40*d**4 + 124*d**3 = 0. What is d?
-4, -2, -1, 1
Find w, given that -1/2*w**3 + 13/2*w + 0 - 6*w**2 = 0.
-13, 0, 1
Let b(d) be the second derivative of -3*d**5/20 - 3*d**4/2 + 18*d**3 - 60*d**2 - 68*d + 1. Factor b(l).
-3*(l - 2)**2*(l + 10)
Let x = 1453 + -1451. Let f(a) be the third derivative of 1/12*a**5 + 0*a + 0 - 5/2*a**3 + 2*a**x + 5/12*a**4. Factor f(n).
5*(n - 1)*(n + 3)
Let q(n) be the second derivative of n**4/24 + 47*n**3/6 + 2209*n**2/4 + 23*n + 2. Factor q(v).
(v + 47)**2/2
Let 2*y - 61 + 0*y**2 - 54*y + 4*y + 15 - 2*y**2 = 0. What is y?
-23, -1
Let r be ((-4)/(-6))/(5/60) + -4. Factor h**4 + 277*h**2 - 10*h**r - 254*h**2 - 6*h + 20*h**3.
-h*(h - 3)*(h + 1)*(9*h - 2)
Let i(y) = -y**3 - y**2 - y - 1. Suppose -w - 4 = 4. Let z(j) = -10*j**3 - 10*j**2. Let t(s) = w*i(s) + z(s). Factor t(x).
-2*(x - 2)*(x + 1)*(x + 2)
Let o(r) = -2*r**4 + 4*r**3 - 2*r**2 - r - 1. Let h(u) be the first derivative of -1/2*u**2 - u + 2. Let w(c) = h(c) - o(c). Solve w(i) = 0 for i.
0, 1
Let -104/5 + 2/5*n**3 - 2/5*n + 104/5*n**2 = 0. Calculate n.
-52, -1, 1
Let y be -9 - ((-22)/1 + 11). Factor 1/2*s**3 + 1/2*s**y - 1/2 - 1/2*s.
(s - 1)*(s + 1)**2/2
Factor 0 + 1/2*p**2 - 8*p.
p*(p - 16)/2
Let y(f) = -f**3 - f**2 - f + 1. Suppose -2*d - 3*j + 14 = -0*j, 3 = -d + j. Let v(k) = 3*k**3 + 9*k**2 - 3*k - 1. Let t(b) = d*v(b) + 4*y(b). Factor t(a).
-(a - 3)*(a - 1)**2
Suppose 9*i + 2*i = 22. Suppose -2