t 4303 - v**2 - 12835 + 4450 + 4509 + 426*v = 0.
-1, 427
Let h(o) be the first derivative of -o**6/150 + o**5/50 - o**4/60 + 73*o**2/2 + 4. Let a(b) be the second derivative of h(b). Determine t so that a(t) = 0.
0, 1/2, 1
Let a(n) = -55*n**4 + 16*n**3 + 128*n**2 + 43*n + 28. Let u(r) = 18*r**4 - 6*r**3 - 42*r**2 - 14*r - 8. Let z(c) = -4*a(c) - 14*u(c). Factor z(l).
-4*l*(l - 2)*(l + 1)*(8*l + 3)
Let n(v) be the third derivative of -1/525*v**7 + 0*v**3 + 0 + 0*v - 171*v**2 + 1/12*v**6 - 47/150*v**5 + 23/60*v**4. Determine i, given that n(i) = 0.
0, 1, 23
Let s(x) be the third derivative of x**7/105 - 29*x**6/60 + 41*x**5/10 + 337*x**4/12 + 184*x**3/3 + 8470*x**2. Factor s(h).
2*(h - 23)*(h - 8)*(h + 1)**2
Suppose -232/3*z**2 + 112/3*z**3 + 26/3*z**4 - 2/3*z**5 + 512/3 - 416/3*z = 0. Calculate z.
-4, -2, 1, 2, 16
Suppose 0 = 516*f - 494*f. Factor 14/3*r**3 + f*r**2 + 0 + 0*r - 4*r**4 - 2/3*r**5.
-2*r**3*(r - 1)*(r + 7)/3
Let h(y) = 1 - 4*y**4 + 2 - 2*y**3 + 1358*y**2 - 1353*y**2. Let o(f) = -7*f**4 - 3*f**3 + 9*f**2 + 5. Let i(z) = 10*h(z) - 6*o(z). Factor i(c).
2*c**2*(c - 2)*(c + 1)
Suppose -116 = -l - 4*z, -5*l + 3*z + 2*z + 630 = 0. Suppose -l - 559 - 5*q**2 + 290*q - 224 - 3298 = 0. Calculate q.
29
Let u = -460659 + 2303301/5. Find f, given that 4/5*f**4 + u*f**5 + 4/5 - 12/5*f**3 + 6/5*f - 8/5*f**2 = 0.
-1, -2/3, 1
Let l(r) = -r**3 - 222*r**2 - 866*r + 1331. Let c be l(-218). Suppose c*z**2 - 1225/3 + 385*z + 1/3*z**3 = 0. What is z?
-35, 1
Let w(a) be the third derivative of -a**7/630 - a**6/240 - 5*a**4 - 65*a**2. Let b(z) be the second derivative of w(z). Determine s, given that b(s) = 0.
-3/4, 0
Let t be -9 + 385/66 - (-22)/6. Find u, given that t*u**2 + 7/4*u - 1/4*u**3 + 1 = 0.
-1, 4
Let a be (-1273)/(-1140) - (11 - (-2261)/(-204)). Factor a*t**2 - 3/5*t**3 + 12/5*t - 24/5.
-3*(t - 2)**2*(t + 2)/5
Let d(a) = -a**2 - 3. Let l(b) = -8*b**2 - 1480*b - 273818. Let r(p) = 6*d(p) - l(p). Factor r(v).
2*(v + 370)**2
Let q(j) be the second derivative of -7*j**5/180 - 19*j**4/18 - 80*j**3/9 - 64*j**2/9 - 6256*j. Factor q(c).
-(c + 8)**2*(7*c + 2)/9
Let o(x) = -2*x**2 + 15*x + 110. Let c be o(12). Let b(g) be the third derivative of 1/30*g**5 - 34*g**c + 0*g + 0 + 4/3*g**3 - 1/3*g**4. Factor b(n).
2*(n - 2)**2
Suppose n + 1 = -2*m, 3*n + m - 1 = -3*m. Suppose n*p - 3 - 3 = 0. Factor 0*h**2 + 17*h - h**p - 17*h.
-h**2
Let j(w) = -11*w**3 + 84*w**2 - 27*w + 2. Let g(d) = 4*d**3 + 2*d**2 - d - 1. Let n(f) = 10*g(f) + 5*j(f). Factor n(m).
-5*m*(m - 29)*(3*m - 1)
Let d(v) be the third derivative of 0 - 3/2*v**4 + 0*v + 1/15*v**5 + 28/3*v**3 + 70*v**2. Find f, given that d(f) = 0.
2, 7
Factor 9279*h**2 - 216*h**4 + 0*h**5 - 4*h**5 + 3934*h**2 - 3888*h**3 - 3667*h**2 - 32874*h**2.
-4*h**2*(h + 18)**3
Let u(b) be the third derivative of 0*b**3 + 7/160*b**6 + 1/20*b**7 + 0*b**4 + 5/448*b**8 + 4*b - 22*b**2 + 0 - 1/40*b**5. What is g in u(g) = 0?
-2, -1, 0, 1/5
Let y be (2 - (-94)/(-8))/(12/(-32)). Suppose 12*b + 129*b**3 + 98*b**2 + 110*b**4 - 20*b**4 - y*b**2 + 21*b**5 = 0. What is b?
-2, -1, -2/7, 0
Suppose -208*a = -210*a + 4*i + 68, -74 = -5*a + 4*i. What is m in 0*m + 0 - 3/2*m**3 - 4/3*m**a - 1/6*m**4 = 0?
-8, -1, 0
Let c = -2942/3 - -981. Let f(m) be the second derivative of -c*m**4 - 32/3*m**2 + 0 - 1/60*m**5 + 2*m - 8/3*m**3. Factor f(z).
-(z + 4)**3/3
Let v(r) be the first derivative of -57 - r**4 + 0*r + 2*r**2 + 2/3*r**3 - 2/5*r**5. Factor v(y).
-2*y*(y - 1)*(y + 1)*(y + 2)
Let s = 2974/10395 - 4/10395. Let o(g) be the first derivative of 26 - 1/14*g**4 + s*g + 1/7*g**2 - 2/21*g**3. Determine n, given that o(n) = 0.
-1, 1
Let w(t) be the second derivative of 9*t**5/20 + 121*t**4/4 + 236*t**3/3 + 78*t**2 - 2577*t. Factor w(k).
(k + 39)*(3*k + 2)**2
Let l(n) = -n**2 + n + 2. Let r(o) = 3*o**2 - 3*o - 12. Suppose -8 = 4*s - j, -2*s - 4*j + 2 = -3*j. Let i(u) = s*r(u) - 6*l(u). Factor i(a).
3*a*(a - 1)
Let c = -9185 - -9187. Let x(l) be the third derivative of 0*l - 1/2*l**4 - 4*l**3 - 1/40*l**5 + 24*l**c + 0. Factor x(o).
-3*(o + 4)**2/2
Let m(b) = 6*b**3 - 12*b**2 + 12*b - 6. Let k = -351 + 347. Let x(w) = 7*w**3 - 13*w**2 + 13*w - 7. Let v(a) = k*m(a) + 3*x(a). Solve v(n) = 0.
1
Let x be 612/110 + 30402/18579. Factor 324/5 + 1/5*i**2 - x*i.
(i - 18)**2/5
Let c(b) be the second derivative of -3*b**2 - 42*b - 9/20*b**5 + 1/10*b**6 + 1/4*b**4 + 3/2*b**3 - 2. Factor c(o).
3*(o - 2)*(o - 1)**2*(o + 1)
Suppose 2*i - p + 95 = 1662, 0 = 5*i - 3*p - 3915. Suppose -429 - i = -5*o. Factor o + 240 - 12*a**2 - 3*a - 483.
-3*a*(4*a + 1)
Let p(x) be the third derivative of -x**8/224 + 4*x**7/105 + 47*x**6/120 + 2*x**5/5 - 9*x**4/16 + 11575*x**2 + 2. Let p(m) = 0. What is m?
-3, -1, 0, 1/3, 9
Suppose 0*v + t = -v + 3, 2*t = v + 6. Suppose v*l - l + 2 = 0. Solve -2022*f - f**l + 1 + 2022*f = 0 for f.
-1, 1
Let o(u) be the first derivative of -2*u**5/25 - 7*u**4/5 - 88*u**3/15 - 8*u**2 - 5361. Let o(n) = 0. What is n?
-10, -2, 0
Let d(v) = -v**3 - 32*v**2 - 60*v + 2. Let b be d(-30). Find t such that 12*t**4 - 33*t**2 + t**5 + 9*t**b - 57*t**3 + 74*t**2 + 2*t**5 - 8*t**2 = 0.
-7, 0, 1, 2
Let a be (0*8/32)/(2 - 4). Let b(h) be the second derivative of -1/10*h**6 - 1/2*h**3 - 3*h**2 + 14*h + a + 3/20*h**5 + 3/4*h**4. Find g such that b(g) = 0.
-1, 1, 2
Let f(k) be the third derivative of -1/42*k**7 + 0 + 0*k**3 + 57*k + 1/24*k**6 + 1/12*k**5 - 5/24*k**4 + k**2. Factor f(x).
-5*x*(x - 1)**2*(x + 1)
Let p(r) = 9*r**4 - r**3 - r**2 - r. Let s(i) = 88*i**4 + 6*i**3 - 10*i**2 - 10*i. Let a(w) = -10*p(w) + s(w). Factor a(t).
-2*t**3*(t - 8)
Suppose 0 = 2*i - 8, q - 3*i + 36 = i. Let c be 3/((2 + 34/q)*2). Factor 4*b - 4*b**2 + c*b**3 - 6*b + 2*b**5 + 4*b**4 - 5*b**3.
2*b*(b - 1)*(b + 1)**3
Determine f so that -958*f - 289*f**2 - 40 - 243*f**2 - 231*f**2 + 811*f**2 = 0.
-1/24, 20
Let v(q) = -q**3 - 5*q**2 - 8*q - 3. Let f be v(-3). Let 21*l**2 - 49*l**2 + 3*l**f - 12*l + 28*l**2 = 0. What is l?
-2, 0, 2
Let i(o) be the first derivative of -6*o + o**4 - 2/5*o**5 + 2 + 8/3*o**3 - 2*o**2. Determine g, given that i(g) = 0.
-1, 1, 3
Let p be 3/6*0 - (-202 + -8). Factor p*q**2 + 18*q - 216*q**2 - 5 - 2*q**3 - 5.
-2*(q - 1)**2*(q + 5)
Let b(o) be the third derivative of -o**7/1155 - 17*o**6/330 - 31*o**5/330 + o**4/2 + 532*o**2 - o. Find t, given that b(t) = 0.
-33, -2, 0, 1
Let h = -12281 + 73975/6. Let u(l) be the first derivative of 0*l - 136/9*l**3 - 25 + 4/3*l**2 + h*l**4. Factor u(t).
2*t*(17*t - 2)**2/3
Let u(y) be the first derivative of 1 + 15/14*y**4 + 0*y - 6/35*y**5 + 0*y**2 - 8/7*y**3. Find n such that u(n) = 0.
0, 1, 4
Let f(t) be the second derivative of 75/14*t**2 - 12/7*t**3 - 1/28*t**4 + 28 + t. Factor f(d).
-3*(d - 1)*(d + 25)/7
Let g(n) be the second derivative of 37/2*n**2 - 8*n + 0*n**3 - 1/660*n**6 + 1/330*n**5 + 0 + 0*n**4. Let k(h) be the first derivative of g(h). Factor k(j).
-2*j**2*(j - 1)/11
Let c(j) = j**2 + 2. Let b(s) = 3*s**3 + 3998*s**2 + 1326672*s - 1330658. Let m(h) = b(h) - 5*c(h). Factor m(g).
3*(g - 1)*(g + 666)**2
Let p be (-742)/106 - (-4 - (-19)/(-6)). Suppose 5/6 - 2/3*l - p*l**2 = 0. Calculate l.
-5, 1
Let s(j) be the second derivative of j**4/8 + 1236*j**3 + 4583088*j**2 - 416*j + 17. Factor s(n).
3*(n + 2472)**2/2
Let h(i) be the first derivative of -i**6/18 + 8*i**5/15 + i**4/4 - 62*i**3/9 - 28*i**2/3 - 5420. Let h(w) = 0. What is w?
-2, -1, 0, 4, 7
Suppose 10 = -3*f - 5*c - 20, 6*f - 5*c - 30 = 0. Let m(i) be the second derivative of 0*i**2 + f + 19*i - 1/20*i**4 + 1/10*i**3. Solve m(q) = 0 for q.
0, 1
Let s(g) be the first derivative of -g**3/21 - g**2/14 + 30*g/7 - 308. Suppose s(x) = 0. What is x?
-6, 5
Let y(u) be the second derivative of -2*u + 1/255*u**6 + 4/17*u**2 - 1/85*u**5 - 14 + 4/51*u**3 - 1/34*u**4. Suppose y(l) = 0. Calculate l.
-1, 2
Suppose -21 = 3*i - 10*i. Suppose -p + 0 = i*b - 25, 55 = 5*b + 5*p. Suppose 33*o**2 + 4*o**3 + 49*o + b*o**2 + 51*o = 0. Calculate o.
-5, 0
Let b(d) be the third derivative of 0*d**3 + 0 - 11/24*d**6 + 0*d**7 + 5/336*d**8 - 78*d**2 + 3/2*d**5 + 0*d - 5/3*d**4. Determine u so that b(u) = 0.
-4, 0, 1, 2
Determine p, given that -447*p + 892*p + 64 - 461*p + p**2 = 0.
8
Suppose -4687*z = -4699*z + 168. Let m(n) be the first derivative of 7/13*n**2 + 40/39*n**3 - 12/13*n - z. Fac