 -16*n**2 + 79*n. Suppose -u + 22 = 2*t + 10, 5*t - 3*u - 52 = 0. Let w(g) = t*q(g) - 5*c(g). Find f such that w(f) = 0.
0, 14
Let f(j) be the second derivative of -1369/3*j**4 - 32*j**2 + 149*j + 592/3*j**3 + 0. Factor f(m).
-4*(37*m - 4)**2
Let m = -190 - -250. Solve m*x + 12*x**2 + 369 - 10*x**2 - 183 + 264 = 0.
-15
Suppose -4767*d**2 - 8 + 8 + 825*d + 4772*d**2 = 0. What is d?
-165, 0
Suppose -50*o - 40 = -46*o. Let c be 15/(-25)*o/8. Determine t, given that -c*t**3 + 0*t + 3/2*t**4 + 0 - 3/4*t**5 + 0*t**2 = 0.
0, 1
Suppose 2801 = -793*v + 5180. Factor 0*n**v + 4/7*n - 2/7*n**4 + 6/7*n**2 + 0.
-2*n*(n - 2)*(n + 1)**2/7
Find u such that 5/3*u**5 + 56/3*u**2 + u**3 - 28/3*u**4 + 20/3*u + 0 = 0.
-1, -2/5, 0, 2, 5
Let t(x) = 8*x + 9. Let g be t(-5). Let z = 39 + g. Solve 9*u**2 + 2 + 28*u - 9*u - 16*u - z = 0.
-1, 2/3
Let t = 314 + -308. Let a(j) = -j**2 - 2*j + 39. Let y(x) = 2. Let r(k) = t*y(k) - 3*a(k). Find l, given that r(l) = 0.
-7, 5
Let k(j) = -4*j + 14. Let x be k(3). Let o(g) = 5*g - 67. Let i be o(14). Suppose -2*t**4 + 5*t**x - i*t**3 - 9*t**2 + 9*t**3 = 0. Calculate t.
0, 1, 2
Suppose -30/11*u**4 + 0 + 30/11*u**2 - 2/11*u**5 + 52/11*u - 50/11*u**3 = 0. What is u?
-13, -2, -1, 0, 1
Factor 4185*j**2 - 35*j**3 + 108588195 + 91*j**3 + 1167615*j - 51*j**3.
5*(j + 279)**3
Let r = -2/271453 + 271459/814359. Find a such that -35/6 + r*a + 1/6*a**2 = 0.
-7, 5
Let k(l) = 212*l**2 - l - 1. Let u(q) = -1268*q**2 + 194*q + 534. Let c(h) = 6*k(h) + u(h). Factor c(i).
4*(i + 3)*(i + 44)
Let l be ((-2)/(-5))/((-38)/(-10)). Let w be (((-128)/152)/(-16))/((-10)/(-80)). What is i in 8/19 - l*i**2 + w*i - 2/19*i**3 = 0?
-2, -1, 2
Solve -28 + 16/3*b**2 + 2/9*b**3 + 202/9*b = 0.
-18, -7, 1
Let d(s) = s**2 + 2703*s + 116998. Let j be d(-44). Find t such that -18/13*t**j + 4/13*t + 0 = 0.
0, 2/9
Solve 2/11*w**4 - 16/11*w**3 - 32/11 + 52/11*w - 6/11*w**2 = 0.
-2, 1, 8
Factor 8 + 27 - 5*u**2 + 85*u - 118 - 127.
-5*(u - 14)*(u - 3)
Suppose -11783*t = -11999*t + 1080. Factor -1/3*g**t + 4/3*g**2 + 4/3*g**4 - 1/3*g - 2*g**3 + 0.
-g*(g - 1)**4/3
Factor 174/7*p + 360/7*p**2 + 26*p**3 - 4/7.
2*(p + 1)**2*(91*p - 2)/7
Find f such that 4/7*f**2 + 32/7*f - 80/7 = 0.
-10, 2
Let r(u) = -5*u - 13. Let k be r(-4). Let s be (-1 + -1)/(((-42)/k)/18). Factor -20 + s*g + 2*g**2 + 12 + 1 + 11.
2*(g + 1)*(g + 2)
Factor 10320*f**3 + 5154*f**2 + 2*f**4 + 30*f**4 - 3561*f + 4205*f.
2*f*(f + 322)*(4*f + 1)**2
Let n be (138/92)/(((-3)/1988)/(-1)). What is o in -n*o + o**2 - 14 - 988*o + 1995*o = 0?
-14, 1
Let g(p) be the first derivative of 0*p + 3*p**5 + 19 - 1/2*p**6 - 27/4*p**4 + 7*p**3 - 3*p**2. Factor g(b).
-3*b*(b - 2)*(b - 1)**3
Solve 0 - 16/13*a**4 - 16/13*a**3 + 288/13*a + 2/13*a**5 + 192/13*a**2 = 0 for a.
-2, 0, 6
Suppose 5*d = -4*c + 32, -4*c + 21*d + 16 = 22*d. Let t(a) be the first derivative of 25 + 1/12*a**c - 5/8*a**2 + 3/2*a. Determine h so that t(h) = 0.
2, 3
Let p(a) be the first derivative of -162*a**4 + 48 + 52*a**2 + 8*a - 571*a**4 - 61*a**2 + 544*a**3 - 117*a**2 - 19*a**4. Factor p(j).
-4*(4*j - 1)**2*(47*j - 2)
Suppose -2718/7 + 3/7*b**2 + 435/7*b = 0. Calculate b.
-151, 6
Let d(l) = -l**3 - 14*l**2 - 27*l - 29. Let u be d(-12). Suppose 14 = -u*z + 14*z. Solve 18*s - 9 + 3 - 4 - 6*s**z - 2*s**3 = 0.
-5, 1
Let g(y) be the second derivative of -21*y**2 + 3/20*y**5 - 128*y + 29/2*y**3 + 0 - 4*y**4. Let g(w) = 0. What is w?
1, 14
Let -6*l**3 - 55*l**3 - 296*l - 11 + 145*l**3 - 10*l**3 - 4*l**2 + 27 = 0. What is l?
-2, 2/37, 2
Let n(a) = 13*a**3 - 228*a**2 - 1301*a - 1951. Let o(k) = -k**3 + 2*k**2 + k - 1. Let f(v) = -2*n(v) - 22*o(v). What is d in f(d) = 0?
-3, 109
Let f(b) be the third derivative of -b**8/60480 + b**7/7560 - b**6/3240 + b**4/3 - 9*b**2 - 3*b. Let q(j) be the second derivative of f(j). Factor q(p).
-p*(p - 2)*(p - 1)/9
Let f(i) = 19*i + 965. Let c be f(-50). Let d(k) = -4*k**2 - 7*k. Let j(g) = -3 + 2 + 2. Let n(x) = c*j(x) - 5*d(x). Factor n(l).
5*(l + 1)*(4*l + 3)
Let i(x) = 3*x**3 + 267*x**2 - 1989*x - 2292. Let w(o) = -o**3 - 270*o**2 + 1989*o + 2284. Let p(g) = -2*i(g) - 3*w(g). Factor p(r).
-3*(r - 84)*(r - 9)*(r + 1)
Let u(x) = -4*x**4 + 2*x**3 - 15*x**2 - 7*x - 4. Let w(i) = -i**4 - 4*i**2 - 2*i - 1. Let p(m) = 2*u(m) - 9*w(m). Determine z, given that p(z) = 0.
-1
Let r(p) be the third derivative of -1/40*p**6 + 0*p + 27*p**2 + 33/20*p**5 + 2 - 63/8*p**4 + 31/2*p**3. Factor r(g).
-3*(g - 31)*(g - 1)**2
Let f(g) = g**3 + 16*g**2 + 18*g + 65. Let y be f(-15). Suppose -148 = -14*u + y. Determine q so that u*q + 15/2*q**2 + 6 + 3/2*q**3 = 0.
-2, -1
Let x = -56 - -60. Let u be 1143/3048 - (-2)/15*(-582)/(-32). What is g in -8*g + 2/5*g**x + 16/5 + 36/5*g**2 - u*g**3 = 0?
1, 2
Factor 0 + 16*q + 4/3*q**4 + 12*q**3 + 80/3*q**2.
4*q*(q + 1)*(q + 2)*(q + 6)/3
Solve 19/2*w**3 + 17/2*w**2 + 1/2*w**4 - 9 - 19/2*w = 0.
-18, -1, 1
Let t be 5*(-3)/105*(22 - 37). Suppose 1/7*p**3 + 6/7*p**2 + 8/7 - t*p = 0. What is p?
-8, 1
Let i(c) be the first derivative of -3*c**6/2 - 6*c**5 + 87*c**4/4 + 16*c**3 - 30*c**2 + 879. Find n, given that i(n) = 0.
-5, -1, 0, 2/3, 2
Solve 35 + 61/2*j - 5*j**2 - 1/2*j**3 = 0 for j.
-14, -1, 5
Let d(j) = -2*j**3 - j + 8. Let m(q) = 28*q**3 + 48*q**2 + 32*q - 320. Let w(t) = -16*d(t) - m(t). Factor w(x).
4*(x - 12)*(x - 2)*(x + 2)
Let m(h) = 18*h - 2. Let q be m(4). Let l = 72 - q. Factor -2*c**4 - c**2 - 3*c**4 + 3*c**4 + 3*c**l.
-2*c**2*(c - 1)*(c + 1)
Suppose 388*p + 7232 = 372*p. Let a = p - -454. Let 10*n - 5/2 - 15/2*n**a = 0. What is n?
1/3, 1
Let w(d) be the third derivative of -5*d**8/336 - 8*d**7/21 - 2665*d**2. Find y, given that w(y) = 0.
-16, 0
Let a(b) be the third derivative of -1/80*b**5 - 1/12*b**3 - 1/480*b**6 + 1/840*b**7 + 5/96*b**4 + 2*b**2 + 7*b + 0. Factor a(w).
(w - 1)**3*(w + 2)/4
Let b = 343 + -337. Let j(c) = c**2 - c - 28. Let u be j(b). Suppose -6/7*l + 0 + 2/7*l**3 - 4/7*l**u = 0. What is l?
-1, 0, 3
Suppose -39646*n = -39698*n + 1639 + 2105. Determine a so that -81/7*a**2 + 3/7*a**3 + 84 + n*a = 0.
-1, 14
Factor -637888512*w + 35473680794 - 4512*w**3 + 1010315*w**2 + 24487839334 + 3*w**4 + 1534453*w**2.
3*(w - 376)**4
Factor -3*j**3 + 0*j**2 - 7/2*j**4 + 3/2*j**5 + 0*j + 0.
j**3*(j - 3)*(3*j + 2)/2
Let z be (-646)/(-152) + 2/(-8). Suppose 0 = -z*p + 5*w - 13, -2*w = -5*p + p + 2. Determine m so that -14/5*m - 2*m**2 - 6/5 - 2/5*m**p = 0.
-3, -1
Let p(q) = -25431*q + 7. Let l be p(0). Factor l*o**3 + 4/3*o**4 + 4/3 + 8*o + 37/3*o**2.
(o + 1)*(o + 2)**2*(4*o + 1)/3
Suppose 3*l + 39*x - 13 = 38*x, -5*l + 4*x + 33 = 0. Suppose -l*o = -j - 5, 4*j - 31 = -5*o - 26. Factor j + 4/3*f**2 - 3*f**4 + 0*f + 0*f**3.
-f**2*(3*f - 2)*(3*f + 2)/3
Suppose -2*a = -5*m + 72, -2*a + 11 = 5*m - 77. Suppose o + 3*o = m. Factor 20*c**2 + 3*c**3 - 3*c**3 + 6*c**o - 3*c**3 - 26*c**2 + 3*c**5.
3*c**2*(c - 1)*(c + 1)*(c + 2)
Let k(a) be the second derivative of -4/7*a**3 + 0 + 24/7*a**2 + 34*a + 1/28*a**4. Factor k(g).
3*(g - 4)**2/7
Suppose 3*y - 29053 = -2*m, 6*y - m - 29038 = 3*y. Factor -y + 4*o**2 - 2*o**5 + 9681 + 8*o**4 - 10*o**3.
-2*o**2*(o - 2)*(o - 1)**2
Factor 15820 + 20*c - 31702 + 50*c**2 - 5*c**3 + 15682.
-5*(c - 10)*(c - 2)*(c + 2)
Factor 2/13*t**2 + 56/13 - 32/13*t.
2*(t - 14)*(t - 2)/13
Let v(t) be the first derivative of 81*t**3 - 918*t**2 + 3468*t + 285. Determine w, given that v(w) = 0.
34/9
Let k be (86/129)/(3/(-18)) - (2 + -8). Let g(p) be the third derivative of 1/12*p**4 + 1/60*p**5 + 0*p + 0 + 1/6*p**3 + 2*p**k. Factor g(w).
(w + 1)**2
Suppose 8*p - 1495 = 513. Solve p*t - 18 + 5*t**2 - 479*t + 271*t = 0 for t.
-9, 2/5
Let t be 27/(6/4 + 0) - 0. Suppose -2 = -h - 0*h - c, 0 = 4*h - c - t. Find d such that -37*d**5 + 22*d**5 + 2*d**4 - 6*d**3 + 5*d**4 + 14*d**h = 0.
0, 2/5, 1
Suppose 0 = -72*n + 78*n - 18. Let t(j) be the first derivative of 4/5*j**5 + 0*j**2 + 3*j**4 + 8/3*j**n + 10 + 0*j. Let t(q) = 0. What is q?
-2, -1, 0
Factor 583*h**3 - 1749*h**3 + 583*h**3 - 166*h - 192 + 582*h**3 - 37*h**2.
-(h + 2)*(h + 3)*(h + 32)
Let p(v) = -v**3 - v**2 - v + 6. Let q be p(0). Let r(i) = -q*i**2 - 11 - 9 + 16 - 4. Let d(k) = -2*k**2 - 3. Let g(t) = -8*d(t) + 3*r(t). Solve g(z) = 0.
0
Suppose -b + 4 = -3*t, 0 = -4*t + 1484*b - 1486*b + 8. Find f such that t - 58/7*f**2 - f**3 - 16/7*f = 0.
-8, -2