 k(s) = 262*s**2 + 20465*s - 26193931. Let v(j) = 412*j**2 + 30697*j - 39290897. Let x(f) = 11*k(f) - 7*v(f). Factor x(u).
-2*(u - 2559)**2
Let z(o) be the first derivative of 4*o**3/27 - 3320*o**2/9 - 6644*o/9 + 9865. Factor z(v).
4*(v - 1661)*(v + 1)/9
Let y(x) = x**2 - 39*x - 35. Let d be y(-1). Let f(w) be the third derivative of 0 - 1/45*w**d + 0*w**3 - 11*w**2 - 2/9*w**4 + 0*w. Factor f(b).
-4*b*(b + 4)/3
Let g(u) be the first derivative of u**5/60 - u**4/24 + u**3/36 + 49*u + 59. Let w(h) be the first derivative of g(h). Let w(p) = 0. What is p?
0, 1/2, 1
Let h(m) be the second derivative of m**8/560 - m**7/56 + 7*m**6/120 - 3*m**5/40 + 71*m**3/6 + 3*m - 10. Let b(p) be the second derivative of h(p). Factor b(a).
3*a*(a - 3)*(a - 1)**2
Let r(s) be the second derivative of 2/3*s**6 - 19 - 5/42*s**7 + 0*s**2 - 5/2*s**4 - s - 1/4*s**5 + 0*s**3. Suppose r(i) = 0. What is i?
-1, 0, 2, 3
Let n(x) = 3*x**3 + 39*x**2 - 202*x - 882. Let o(g) = -3*g**3 - 39*g**2 + 204*g + 891. Let w(s) = 3*n(s) + 2*o(s). Factor w(t).
3*(t - 6)*(t + 3)*(t + 16)
Let a(c) = 7*c - 5 - 62*c**2 - 55*c**2 + 12 - 2*c. Let i(s) = 59*s**2 - 3*s - 4. Let y(x) = -4*a(x) - 7*i(x). Factor y(j).
j*(55*j + 1)
Let o be (748/88)/(714/24). Factor -2/7*t**2 - o*t + 0.
-2*t*(t + 1)/7
Let k = 25466 + -101861/4. Let i(b) be the first derivative of 2*b**3 + 1/2*b**6 + 0*b**2 + 0*b - 18 - 6/5*b**5 - k*b**4. Factor i(v).
3*v**2*(v - 2)*(v - 1)*(v + 1)
Suppose 4*n = p + 9, -1418*n + 1417*n + 18 = 5*p. Let q(i) be the first derivative of -3*i**2 - 34 + 3/10*i**5 - 9/2*i + 3/2*i**4 + i**p. Solve q(j) = 0.
-3, -1, 1
Let x(c) = 310*c**2 + 35400*c - 186000. Let u(d) = -5*d**2 - 571*d + 3000. Let k(z) = -125*u(z) - 2*x(z). Find q, given that k(q) = 0.
-120, 5
Let h = 280462 + -280460. Factor -30/7 - 2/7*w**h - 32/7*w.
-2*(w + 1)*(w + 15)/7
Let b(o) be the first derivative of -14*o**3/9 + 334*o**2/3 + 64*o + 212. Solve b(v) = 0 for v.
-2/7, 48
Let u(z) be the first derivative of 5*z**4/4 + 5*z**3/3 - 115*z**2 + 400*z - 8926. Solve u(j) = 0.
-8, 2, 5
Let t(v) be the first derivative of -3*v**5/20 + 3*v**4/4 - v**3 + 358. Suppose t(l) = 0. What is l?
0, 2
Let n = -4147 + 4147. Let c(g) be the third derivative of -1/30*g**6 - 1/3*g**4 + 0*g**3 + 12*g**2 + 0 - 1/5*g**5 + n*g. Factor c(i).
-4*i*(i + 1)*(i + 2)
Let l = -272821 + 272821. Find t, given that -2/9*t**2 + 28/9*t + l = 0.
0, 14
Let y(d) be the first derivative of d**6/39 - 54*d**5/65 + 75*d**4/26 - 146*d**3/39 + 24*d**2/13 - 1239. Factor y(s).
2*s*(s - 24)*(s - 1)**3/13
Let f(w) be the second derivative of -w**7/840 - w**6/40 + 2*w**5/5 + 26*w**4/3 + 13*w. Let t(j) be the third derivative of f(j). Find b such that t(b) = 0.
-8, 2
Suppose -1099*w = -1082*w - 833. Let p be 5 + (1512/w)/(-8). Solve -8/7*m - 6/7 + 2/7*m**4 + 4/7*m**2 + p*m**3 = 0 for m.
-3, -1, 1
Suppose 0 = 6*l + 4*b - 32, -l + b + 130 = 133. Suppose -1/3 - 16/3*x**l - 8/3*x = 0. Calculate x.
-1/4
Suppose 2/19*a**3 + 28/19*a**2 + 32/19 - 62/19*a = 0. Calculate a.
-16, 1
Let z(y) be the first derivative of -4*y**3/9 - 968*y**2/3 + 1940*y/3 + 1509. Factor z(m).
-4*(m - 1)*(m + 485)/3
Factor 28/5*m**4 + 1628/5*m + 1/5*m**5 + 968/5 + 998/5*m**2 + 53*m**3.
(m + 2)**3*(m + 11)**2/5
Let l(s) = 2*s**2 + 37*s + 567. Let w(z) = -z**2 - 19*z - 283. Let d(v) = -4*l(v) - 9*w(v). Let k be d(-11). Factor k + 63/2*b + 3/2*b**3 - 18*b**2.
3*(b - 7)**2*(b + 2)/2
Factor 230*q**3 + q**4 + 423*q**3 + 456*q - 1109*q - q**2.
q*(q - 1)*(q + 1)*(q + 653)
Let q = 93190 - 93190. Factor 3/2*y**3 + q - 9/2*y**2 + 5/2*y + 1/2*y**4.
y*(y - 1)**2*(y + 5)/2
Let v(f) be the third derivative of -f**6/30 - 19*f**5/15 - 83*f**4/6 - 130*f**3/3 + 16*f**2 + 21*f. Factor v(s).
-4*(s + 1)*(s + 5)*(s + 13)
Suppose -19*d + 15*d + 36 = 0. Let v = -7 + d. Factor -5*x + 35*x + 2*x**2 + 3*x**v.
5*x*(x + 6)
Let g = 497 + -328. Factor -g*w**3 + 2600*w**2 - 7*w**3 + 2304*w + 4*w**5 - 2216*w**2 - 16*w**4.
4*w*(w - 6)**2*(w + 4)**2
Let 98*t**2 + 207 + t**5 - 106 - 50*t**4 - 101 - 2*t**5 - 47*t**3 = 0. What is t?
-49, -2, 0, 1
Let q = 2/2613915 - -8713048/2613915. Suppose -10/3*w + q*w**2 + 5/6*w**3 - 40/3 = 0. What is w?
-4, -2, 2
Factor -2/3*l**3 + 194*l**2 - 13410*l - 310814/3.
-2*(l - 149)**2*(l + 7)/3
Solve 2/11*y**2 + 342792/11 + 1656/11*y = 0 for y.
-414
Let b(d) = -2*d**2 + d + 1. Let u(i) = -5*i**2 - 21*i + 26. Let o(n) = 4*b(n) - 2*u(n). Let o(m) = 0. Calculate m.
-24, 1
Let q(j) be the second derivative of -j**6/180 + j**4/4 + 115*j**2 - 136*j. Let r(i) be the first derivative of q(i). Find a such that r(a) = 0.
-3, 0, 3
Let g(a) be the first derivative of -9/7*a + 10 + 1/7*a**3 + 3/7*a**2. Factor g(o).
3*(o - 1)*(o + 3)/7
Suppose -2*v = -3*i, -5*i - 70*v = -73*v. Suppose -3*l + 2*j = 0, 12*j - 17*j + 15 = i. Factor -2/5*h**3 + 0 - 8/5*h + 8/5*h**l.
-2*h*(h - 2)**2/5
Let g(v) be the first derivative of -4*v**3/27 - 308*v**2/9 + 620*v/9 + 192. Determine r so that g(r) = 0.
-155, 1
Let s(f) be the second derivative of -3*f**5/100 - 178*f**4/15 - 79*f**3/10 + 18*f - 37. Solve s(t) = 0.
-237, -1/3, 0
Let o = 507 - 499. Determine s so that 253*s**3 + o*s + 6*s**2 - 18 - 256*s**3 + 7*s = 0.
-2, 1, 3
Suppose 5*c = -4*r + 215, r + 217 - 24 = 4*c. Let m = c - 44. Solve 10*n**m - 18*n**5 - 3*n - 68*n**2 + 3*n - 6*n**4 + 66*n**2 = 0.
-1, 0, 1/3
Solve -442*h**3 + 1750*h**3 - 433*h**3 - 441*h**3 - 435*h**3 - 674*h + 139*h**2 + 536 = 0 for h.
1, 4, 134
Let o(n) be the second derivative of -n**4/8 + 113*n**3/4 + 345*n**2/2 + 7*n - 42. Factor o(q).
-3*(q - 115)*(q + 2)/2
Suppose -30*i + 140 = -16*i. Factor 35*s**2 + 42*s**4 - 126*s**4 - 2*s - 8*s + 49*s**4 + i*s**3.
-5*s*(s - 1)*(s + 1)*(7*s - 2)
Let n(o) = -9*o - 9. Let j be n(-3). Let b = j - 16. Factor -3*l**4 - 5*l + l + 11*l**2 - b - 11*l**3 + 3*l + 6*l**4.
(l - 2)*(l - 1)**2*(3*l + 1)
Factor 3/2*h**2 + 0 - 858*h.
3*h*(h - 572)/2
Determine l, given that 4/7*l**3 + 117128/7 - 960/7*l**2 + 56628/7*l = 0.
-2, 121
Suppose -4*q - 140 = -3*u - 18, 4*q = -5*u + 118. Let i(b) be the first derivative of 3/7*b**2 - 1/3*b**3 + 1/28*b**4 - u + 0*b. What is t in i(t) = 0?
0, 1, 6
Let q = 105/227 - 88/681. Determine n, given that -2/3*n - 11/6*n**3 + 3*n**2 - 4/3 + q*n**4 = 0.
-1/2, 2
Let m(v) be the third derivative of -9*v**8/224 - 59*v**7/140 - 14*v**6/9 - 37*v**5/30 + 8*v**4 + 256*v**3/9 - v**2 - 907*v. Suppose m(r) = 0. Calculate r.
-2, -16/9, 1
Let v(r) be the second derivative of -4*r + 0*r**2 + 4 - 1/35*r**5 + 1/210*r**6 - 1/21*r**3 + 5/84*r**4. Factor v(n).
n*(n - 2)*(n - 1)**2/7
Let b(v) be the third derivative of 1/10*v**5 + 0 - 10/19*v**4 - 7/1140*v**6 + 180*v**2 + 0*v + 16/57*v**3. Solve b(u) = 0 for u.
1/7, 4
Let i(l) be the first derivative of l**5/90 - l**4/27 - 7*l**3/27 - 4*l**2/9 - l - 27. Let c(j) be the first derivative of i(j). Suppose c(k) = 0. Calculate k.
-1, 4
Let u be (-33)/9*1788/(-3278). Factor -4/7*v**u - 252 - 24*v.
-4*(v + 21)**2/7
Factor 192/5*u - 816/5 + 3/5*u**2.
3*(u - 4)*(u + 68)/5
Let w(f) be the second derivative of -f**7/63 + 3*f**6/10 - 91*f**5/60 + 687*f. Suppose w(u) = 0. What is u?
0, 13/2, 7
Factor 1/2*a**2 - 237*a + 940.
(a - 470)*(a - 4)/2
Find w, given that -18*w - 12*w**3 - 27*w**3 + 46*w**3 - 65*w**2 - 14*w**3 = 0.
-9, -2/7, 0
Factor 9/2*n**2 + 1/2*n**4 + 0 + 6*n**3 - 11*n.
n*(n - 1)*(n + 2)*(n + 11)/2
Let n(o) = o**2 - 20*o + 95. Let i be n(13). Let l(c) = -c**2 - 13*c - 14. Let s be l(-11). Factor 192 + s*z**2 - 48*z - z**2 - i*z**2.
3*(z - 8)**2
Let y(o) be the second derivative of 1/8*o**4 + 0 - o**2 - 15*o + 1/60*o**6 - 1/10*o**5 + 1/3*o**3. Factor y(m).
(m - 2)**2*(m - 1)*(m + 1)/2
Let c be (-7)/(-1960)*3661 - 13. Let w(s) be the first derivative of -11 + 1/4*s**3 + 3/4*s**2 + c*s**5 - 9/8*s - 3/8*s**4. Find r such that w(r) = 0.
-1, 1, 3
Suppose 7*d = 6*d + 31*d. Let o(n) be the third derivative of n**2 + d - 1/6*n**3 - 1/120*n**6 - 1/8*n**4 + 0*n - 1/20*n**5. Factor o(c).
-(c + 1)**3
Let h(r) = r**3 + 7*r**2 + 2*r + 6. Let i be h(-6). Factor -27*u**2 + i*u**2 - 12*u - 7 - 8.
3*(u - 5)*(u + 1)
Let h(b) = -33*b - 294. Let x be h(-9). Suppose u = x*k - 3, -6*k - 4*u = -k + 12. Suppose k + 0*j - 1/3*j**2 = 0. Calculate j.
0
Let i be -6*(0 - -2)*(20/8)/(-5). Let q(n) be the first derivative of n**4 - 42 + 14/45*n**5 + 44/27*n**3 + 13/9*n