 + 42 = 2*h - 5*f. Let r = h + 25. Determine o, given that -2*o - 2*o**2 + 2 - o - r*o**2 + 6*o**2 = 0.
1, 2
Let p(h) be the second derivative of 0 + 4/5*h**5 - 2/3*h**3 + h**4 + 0*h**2 - 40*h. Determine o, given that p(o) = 0.
-1, 0, 1/4
Let 0 - 24/7*a**4 + 0*a - 36/7*a**3 - 4/7*a**5 - 16/7*a**2 = 0. Calculate a.
-4, -1, 0
Let x = -21 + 21. Suppose 2*r - r - 3 = x. Factor 10*v**2 + 21*v + 23*v**2 + 17*v**r - v**3 + 3 - v**3.
3*(v + 1)**2*(5*v + 1)
Let h(d) be the first derivative of d**8/3780 + d**7/1890 - d**6/405 + 10*d**3/3 - 4. Let x(z) be the third derivative of h(z). Factor x(j).
4*j**2*(j - 1)*(j + 2)/9
Factor -6*a**2 + 4*a**2 + 1089 + 0*a**2 + 3*a**2 + 66*a.
(a + 33)**2
Factor 1 + 0*i**4 + 48*i + 10*i**2 + 31 + 6*i**2 - i**5 - 6*i**4 - 8*i**3.
-(i - 2)*(i + 2)**4
Let i be 15/6*4/5. Let x(l) be the first derivative of 1/9*l**i - 2/27*l**3 + 0*l + 2. Factor x(y).
-2*y*(y - 1)/9
Let f(a) be the third derivative of -a**8/112 - 9*a**7/175 - 3*a**6/25 - 7*a**5/50 - 3*a**4/40 - 2*a**2 - 291*a. Determine j, given that f(j) = 0.
-1, -3/5, 0
What is l in 405*l + 3*l**4 + 110*l**2 + 131*l**2 + 177 + 180 + 39*l**3 - 33 - 52*l**2 = 0?
-4, -3
Let z = -77 + 74. Let q be (-567)/(-385) - z/(-15). Let 32/11 - q*m**2 + 2/11*m**3 + 16/11*m = 0. Calculate m.
-1, 4
Let r = 58 - 58. Factor 0*t**3 + 2*t**2 + 0*t - 1/2*t**4 + r.
-t**2*(t - 2)*(t + 2)/2
Let g = 2/38077 + -14964269/152308. Let o = -98 - g. Factor -2*i**2 + o*i**5 + 3*i**3 + 0*i + 0 - 3/2*i**4.
i**2*(i - 2)**3/4
Let h(a) be the first derivative of 1/9*a**4 + a**3 + 0*a**2 - 1/45*a**5 + 5 + 0*a + 1/540*a**6. Let c(o) be the third derivative of h(o). Solve c(u) = 0 for u.
2
Let g(w) be the second derivative of w**4/48 - 7*w**3/24 + 5*w**2/4 + 43*w. Factor g(d).
(d - 5)*(d - 2)/4
Let m = -3003/20 - -907/5. Let a = -31 + m. Factor -1/2 - 3/4*q - a*q**2.
-(q + 1)*(q + 2)/4
Let p(c) be the third derivative of -4*c**5/5 - 3*c**4 - 9*c**3/2 - 44*c**2 - 2*c. Factor p(n).
-3*(4*n + 3)**2
Let z(p) be the first derivative of -p**6/75 + p**5/25 + p**4/10 + p - 7. Let h(q) be the first derivative of z(q). Factor h(g).
-2*g**2*(g - 3)*(g + 1)/5
Suppose 12 = 38*j - 62*j + 84. Find b, given that 0*b - 1 + 3/4*b**2 - 1/4*b**j = 0.
-1, 2
Let q(g) be the third derivative of g**6/180 - 7*g**3/2 + 17*g**2. Let b(x) be the first derivative of q(x). Let b(a) = 0. Calculate a.
0
Let c(k) be the first derivative of 1/16*k**5 - 6*k + 19/48*k**4 - 1/2*k**2 - 3 + 2/3*k**3. Let x(h) be the first derivative of c(h). Let x(v) = 0. Calculate v.
-2, 1/5
Let h(d) be the third derivative of 1/72*d**4 + 0*d + 0 + 6*d**2 - 1/360*d**5 - 1/36*d**3. Factor h(l).
-(l - 1)**2/6
Let w = 7 + -293/42. Let j(y) be the second derivative of w*y**4 + 2/7*y**2 + 0 - 1/7*y**3 + 9*y. Factor j(p).
2*(p - 2)*(p - 1)/7
Let j(s) be the second derivative of -5*s - 1/360*s**6 + 0*s**4 + 0*s**2 + 5/6*s**3 - 1/120*s**5 + 0. Let c(i) be the second derivative of j(i). Factor c(y).
-y*(y + 1)
Let c = -591/62 - -3203/310. What is f in 8/5*f**2 + 0 + 16/5*f**4 - 4*f**3 - c*f**5 + 0*f = 0?
0, 1, 2
Suppose -28 = -2*d - 5*d. Suppose d - 4 = -5*p. Factor 3/2*w**3 - 1/2*w**4 + p + 1/2*w - 3/2*w**2.
-w*(w - 1)**3/2
Let r be 4/(-1 + (0 - -3)). Let h be 10/r - (14 + -9). Factor h - 2/3*v + 1/3*v**2.
v*(v - 2)/3
Let f(m) be the second derivative of -m**7/4200 + m**6/900 + m**5/150 - m**4/15 - 7*m**3/2 + 27*m. Let z(t) be the second derivative of f(t). Factor z(y).
-(y - 2)**2*(y + 2)/5
Let p(o) be the third derivative of 1/6*o**4 + 4*o**2 - 1/180*o**5 + 0*o + 0 - 2*o**3. Find d such that p(d) = 0.
6
Let x(b) be the third derivative of b**7/315 + 4*b**6/45 + 32*b**5/45 - 290*b**2. Suppose x(c) = 0. Calculate c.
-8, 0
Let g(c) be the second derivative of c**5/10 - 16*c**4/3 - 4*c**3/3 + 128*c**2 - 35*c - 3. Factor g(u).
2*(u - 32)*(u - 2)*(u + 2)
Let c(k) be the third derivative of k**6/144 + 11*k**5/72 - 5*k**4/144 - 55*k**3/36 - 78*k**2 - k. What is p in c(p) = 0?
-11, -1, 1
Let z(j) = j**2 + 17*j + 46. Let b be z(-4). Let k be 5/(-20) - 15/b. Determine h, given that -9/4*h**3 - 3/4*h + 0 + 3/4*h**4 + k*h**2 = 0.
0, 1
Let f = -168/47 - -9119/2538. Let s(y) be the second derivative of -8*y + 0*y**2 + 0 - 1/27*y**3 - f*y**4. Find l such that s(l) = 0.
-1, 0
Suppose 2*z - 6 = g, z + z = 3*g + 2. Let u(n) be the first derivative of -6*n**z + 0*n + 0*n**2 - 4/3*n**3 - 9*n**5 - 5 - 25/6*n**6. Solve u(s) = 0.
-1, -2/5, 0
Suppose -24*g + k - 6 = -21*g, 4*g = 2*k - 12. Determine p, given that -p**2 + 1/2*p**3 + 0 + g*p = 0.
0, 2
Let i(p) be the first derivative of -1/2*p**4 + p + 18 + p**2 - 1/5*p**5 + 0*p**3. Factor i(s).
-(s - 1)*(s + 1)**3
Let h = 359 - 352. Let z(a) be the first derivative of -h + 5/2*a**2 - 2*a + 3/5*a**5 - 1/3*a**3 - 5/4*a**4. Solve z(c) = 0 for c.
-1, 2/3, 1
Factor -1/3*k**3 + 2*k + 0 + 5/3*k**2.
-k*(k - 6)*(k + 1)/3
What is t in -8 + 48*t**2 + 678*t - 666*t - 12*t**3 + 40*t**3 = 0?
-1, 2/7
Suppose -7*b - 3 = -4*b. Let o = 4 + b. Factor -2*t**o - t**3 - 2*t**2 - t**4 - t**4 - t**3.
-2*t**2*(t + 1)**2
Factor -362*h**2 + 66*h**3 - 300 - 242*h**2 - 3*h**4 + 181*h**2 + 660*h.
-3*(h - 10)**2*(h - 1)**2
Suppose 5*r - 4*o - 3 - 7 = 0, -r = 5*o - 2. Let v(j) = j**2. Let q(p) = -p**2 + 6*p + 5. Let w(g) = r*v(g) + q(g). Suppose w(n) = 0. Calculate n.
-5, -1
Let c be ((-5 - 0) + -7)*(-2)/12. Let z(m) be the second derivative of 4*m + 1/72*m**4 + 0*m**c + 0 - 1/36*m**3. Factor z(b).
b*(b - 1)/6
Let l = -7 + 4. Let m be l/(-2) - 2/(-4). Determine b so that 9*b - 3*b + 79*b**2 - 82*b**m = 0.
0, 2
Let k(j) = -7*j**3 + 37*j**2 - 75*j + 45. Let g(u) = -50*u**3 + 260*u**2 - 525*u + 315. Let o(r) = -2*g(r) + 15*k(r). Factor o(w).
-5*(w - 3)**2*(w - 1)
Let v(z) be the first derivative of -z**4 + 32*z**3 - 332. Solve v(d) = 0.
0, 24
Let f = -2912 + 2915. Let t(m) be the first derivative of 1/5*m**5 + 0*m - 1 + 0*m**4 - 1/3*m**f + 0*m**2. Suppose t(n) = 0. What is n?
-1, 0, 1
Let d be 6/18 - (3 - 3). Let a(x) be the third derivative of -1/60*x**6 + 0*x + 0 + d*x**3 - 1/4*x**4 + 1/10*x**5 + 3*x**2. Factor a(u).
-2*(u - 1)**3
Let n be (-38420)/(-57120) - 2/(-48). Find w such that -n*w + 1/7*w**2 + 0 = 0.
0, 5
Let z(k) be the third derivative of 3*k**6/200 + 4*k**5/25 + k**4/8 - 6*k**2 + 5. Factor z(s).
3*s*(s + 5)*(3*s + 1)/5
Let r(t) = t**2 + 194*t + 1359. Let f(p) = 96*p + 680. Suppose 35 = 7*y - 14. Let c(k) = y*f(k) - 4*r(k). Factor c(i).
-4*(i + 13)**2
Suppose -10 = -5*h + f, 3*f - 20 = -3*h + 4. Let o(a) be the first derivative of 1/9*a**2 - 2 + 1/2*a**4 + 0*a + 8/45*a**5 + 4/9*a**h. Factor o(i).
2*i*(i + 1)**2*(4*i + 1)/9
Let n = 48569606/133 - 365183. Let l = n + -30/19. What is k in 6/7*k - 3/7*k**2 - l = 0?
1
Find j such that -3/5*j + 2/5*j**3 + 0 - j**2 = 0.
-1/2, 0, 3
Let d(h) = -h**4 - 4*h**3 + 2*h**2 + 3*h + 1. Let r(c) = c**4 - c**3 + c**2. Suppose -2*g + 3 = 7. Let t(n) = g*d(n) + 2*r(n). Factor t(x).
2*(x - 1)*(x + 1)**2*(2*x + 1)
Let z be (1322 + 7)/((-14)/6). Let d = 571 + z. Find t, given that -16/7 + 36/7*t**2 + 24/7*t + d*t**3 = 0.
-2, 2/5
Let f(n) be the second derivative of 6*n**2 - 1/10*n**5 + 0 - 11/3*n**3 + n**4 + 16*n. Let f(i) = 0. What is i?
1, 2, 3
Let y(g) = -g**2 - 8*g - 9. Let b be y(-5). Find n such that -n**2 + 0*n**2 - b*n**2 + 4*n**2 = 0.
0
Let v(f) be the first derivative of 5*f**8/336 - 2*f**7/21 + f**6/4 - f**5/3 + 5*f**4/24 - 7*f**2/2 - 2. Let q(w) be the second derivative of v(w). Factor q(j).
5*j*(j - 1)**4
Let l(m) = -2 + 0*m**3 + 3 - m + 2*m**3. Let w be l(1). Find p such that -18*p + 5*p - 4*p**w + 12 - 20*p - 5*p**2 = 0.
-4, 1/3
Let v(z) = -571*z + 1145. Let d be v(2). Factor 4/15*t**2 + 0*t + 0 - 2/15*t**d - 2/15*t**4.
-2*t**2*(t - 1)*(t + 2)/15
Let i(b) be the first derivative of 0*b + 0*b**3 + 0*b**4 - 3/20*b**5 + 4 + 0*b**2. Let i(u) = 0. Calculate u.
0
Let g(a) = a**2 + 3. Suppose -u - 2*u = 0. Let r be g(u). Factor -2*n**2 + 4*n**3 + r*n**4 - 5*n**4 + 0*n**2.
-2*n**2*(n - 1)**2
What is x in -3/2*x**5 - 312*x - 345/2*x**3 + 57/2*x**4 + 96 + 723/2*x**2 = 0?
1, 8
Let n(l) be the third derivative of l**5/30 - l**4/4 + 2*l**3/3 - 4*l**2 - 4*l. Factor n(b).
2*(b - 2)*(b - 1)
Let i = -32 - -34. Suppose 5*f + 2*u - 7 = 0, -2*u - 3*u = f + 17. Factor 14*z**3 + 28*z**4 + z**3 - 48*z**i + 21*z**f - 16*z.
4*z*(z - 1)*(z + 2)*(7*z 