 0.
-1, 1, 3
Let f(s) = 2*s**2 - 269*s + 1172. Let p be f(130). Determine x, given that -6*x**3 + 3/2*x**p + 0*x + 0 = 0.
0, 1/4
Factor t**2 + 45 - 8*t + 14*t - 26*t**2 + 2*t + 7*t + 5*t**3.
5*(t - 3)**2*(t + 1)
Suppose -3*i + 14 = 2*g, -g = 2*i + i - 13. Let p = g + 1. Factor 0 - 1/3*l**3 + 0*l + 1/3*l**p.
-l**2*(l - 1)/3
Let y(x) be the second derivative of x**8/336 + x**7/120 + x**6/240 - x**5/240 - x**2 - 5*x. Let t(o) be the first derivative of y(o). Let t(q) = 0. What is q?
-1, 0, 1/4
Let j be -27*(-12)/18*((-12)/(-9) + -1). Factor 135/2*h**4 + 0 - 75/2*h**5 + j*h**2 - 36*h**3 + 0*h.
-3*h**2*(h - 1)*(5*h - 2)**2/2
Suppose 4*o = -5*b + 14, -4 = 4*b + 5*o - 8. Suppose -6 = 5*l - 2*y, 0*y - 2*y = 2*l - b. Factor 2/17*d**3 + 4/17*d**2 + 0*d + l.
2*d**2*(d + 2)/17
Let j(o) = -5*o**3 - 23*o**2 - 67*o - 64. Let d(y) = -9*y**3 - 45*y**2 - 133*y - 128. Let s(v) = 3*d(v) - 5*j(v). Let s(q) = 0. What is q?
-4, -2
Factor -2 + 2*l**2 - 2/3*l + 2/3*l**3.
2*(l - 1)*(l + 1)*(l + 3)/3
Let d(l) be the first derivative of -3*l**4/4 - 3*l**3 + 67. Factor d(s).
-3*s**2*(s + 3)
Let v = 16 + -11. Suppose -d + v*d = 12. Suppose d*r**2 + r + 2*r + 0*r = 0. What is r?
-1, 0
Let m(v) be the second derivative of v**6/60 - v**5/24 - v**4/18 + v**3/9 + 6*v - 8. Factor m(i).
i*(i - 2)*(i + 1)*(3*i - 2)/6
Let h(l) = 4*l**2 - 28*l - 3. Let b(w) = w**2 + w + 1. Let n(u) = -b(u) - h(u). Let g(f) = 60*f**2 - 325*f - 25. Let r(c) = -2*g(c) - 25*n(c). Factor r(s).
5*s*(s - 5)
Suppose 4*n - 20 = 0, -2*a + 11*n = 10*n - 3. Suppose 48/7*p**a + 20/7*p**5 - 16/7*p - 48/7*p**2 + 0 - 4/7*p**3 = 0. What is p?
-2, -1, -2/5, 0, 1
Let a(h) = 8*h**3 + 20*h**2 + 29*h. Let t(g) = 7*g**3 + 19*g**2 + 30*g. Let o(x) = 6*a(x) - 7*t(x). Factor o(v).
-v*(v + 4)*(v + 9)
Let m(t) = -44*t**3 + 138*t**2 - 130*t + 16. Let x(v) = v**3 + v + 1. Let j(n) = m(n) + 4*x(n). What is l in j(l) = 0?
1/5, 5/4, 2
Factor 2*c**3 - 9*c**2 - 1 - 3*c**2 + 11 - 2 + 4*c**2 - 2*c.
2*(c - 4)*(c - 1)*(c + 1)
Let -180/7 - 2/7*a**2 + 6*a = 0. What is a?
6, 15
Let n be (15/45*-3)/((-10)/4). Factor 1/5*h**5 + 1/5*h**4 - n*h**2 + 1/5 + 1/5*h - 2/5*h**3.
(h - 1)**2*(h + 1)**3/5
Factor u**3 + 3/4 - 1/4*u**4 - 1/2*u**2 - u.
-(u - 3)*(u - 1)**2*(u + 1)/4
Let s(n) be the second derivative of -n**7/21 - 11*n**6/24 - n**5 + 15*n**4/8 + 9*n**2/2 + 7*n. Let j(t) be the first derivative of s(t). Factor j(p).
-5*p*(p + 3)**2*(2*p - 1)
Let g be ((-4)/(-30))/((-106)/(-424)*(-8)/(-10)). Factor -g*p**5 + 8*p**2 - 26/3*p**3 + 0 + 4*p**4 - 8/3*p.
-2*p*(p - 2)**2*(p - 1)**2/3
Suppose -24/5 + 84/5*a + 6/5*a**2 - 21/5*a**3 = 0. Calculate a.
-2, 2/7, 2
Let r(z) = -z**2 + 0*z**3 - 6*z**3 + 0 + 7*z**3 - 1. Let g(u) = -3*u**3 - u**2 + 1. Suppose 3*l - 6 = -3. Let t(d) = l*r(d) + g(d). Solve t(b) = 0.
-1, 0
Let d(q) = -23*q**3 - 168*q**2 + 153*q + 42. Let x(t) = -93*t**3 - 672*t**2 + 612*t + 168. Let f(b) = -15*d(b) + 4*x(b). Let f(w) = 0. What is w?
-7, -2/9, 1
Factor 40*n**4 + 1104*n**3 + 1005*n + 2*n**5 + 3311*n**2 + 577*n**2 - 204*n**3 + 723*n + 33*n**4.
n*(n + 12)**3*(2*n + 1)
Let k = 19 - 8. Let r(f) = f - 8. Let p be r(k). Factor -1 - p*j + 4*j - 5*j + 4*j**3 + j**2.
(j - 1)*(j + 1)*(4*j + 1)
Let r(z) be the second derivative of 1/27*z**4 - 2/9*z**2 + 0 - 6*z + 1/27*z**3 - 1/90*z**5. Factor r(c).
-2*(c - 2)*(c - 1)*(c + 1)/9
Let q(g) = 21*g**4 - 33*g**3 + 33*g**2 + 33*g + 18. Let u(t) = -t**4 + t**3 - 2*t**2 - t - 1. Let j(c) = -q(c) - 18*u(c). Find h, given that j(h) = 0.
-1, 0, 1, 5
Let p(q) be the first derivative of -3*q**4/4 - 9*q**3 - 30*q**2 - 36*q - 296. Solve p(k) = 0 for k.
-6, -2, -1
Let y be 12*2*3/(-9). Let x(h) = -h - 6. Let z be x(y). Determine u, given that u**2 + 5*u - u + z - 2*u - 1 = 0.
-1
Let u be 6/30 - ((-48)/(-30))/(-4). Let d(y) be the first derivative of -1/5*y - 6 + u*y**2 - 1/3*y**3. Factor d(s).
-(s - 1)*(5*s - 1)/5
Suppose -8 + 112 = 52*w. Let b(g) be the second derivative of -3/4*g**4 - 6*g - 3/20*g**5 + 0 - 3/2*g**3 - 3/2*g**w. Factor b(r).
-3*(r + 1)**3
Let n(y) be the first derivative of y**8/2940 - y**7/490 + y**6/315 - 19*y**3/3 - 19. Let u(a) be the third derivative of n(a). Let u(s) = 0. Calculate s.
0, 1, 2
Suppose -2*p - 13 = -h, 4*h + 25 = 26*p - 29*p. Let l be 3 - (-3 - p) - -1. Solve 12/7*a**3 - 4/7*a**4 + l + 4/7*a - 12/7*a**2 = 0 for a.
0, 1
Let a(k) be the third derivative of -k**8/420 + k**7/210 + 7*k**3/6 + 12*k**2. Let y(i) be the first derivative of a(i). Suppose y(c) = 0. What is c?
0, 1
Let x be (-61)/(-244) + (63/(-60))/(-7). Let -4/5 - 6/5*v - x*v**2 = 0. What is v?
-2, -1
Let j(o) be the third derivative of -o**8/840 - 3*o**7/175 - 7*o**6/75 - 6*o**5/25 - 4*o**4/15 - 152*o**2. What is w in j(w) = 0?
-4, -2, -1, 0
Suppose 5*z - 4 = 11. Let u(g) = g**2 - 3*g + 2. Let r be u(z). Factor -6*i + i**r + 4*i + i**2.
2*i*(i - 1)
Suppose -191*x = -106*x - 105*x + 80. Determine g so that 0*g + 32/3*g**2 - 2/3*g**5 - 14/3*g**x + 0 - 16/3*g**3 = 0.
-4, 0, 1
Let x(y) be the third derivative of -2*y**7/315 + 2*y**6/45 + y**5/3 - y**4 - y**2 - 843. Suppose x(b) = 0. Calculate b.
-3, 0, 1, 6
Suppose 0 = 3*b + 2*v - 101, 2*b = -2*v + 54 + 14. Find f, given that b*f**2 - 4*f**3 - 2*f - 8*f**3 - 2*f**5 + 8*f**4 - 25*f**2 = 0.
0, 1
Let l(t) be the third derivative of -5*t**8/336 - t**7/42 + t**6/6 + t**5/3 + 12*t**2 - 3. Determine y so that l(y) = 0.
-2, -1, 0, 2
Let v(s) be the second derivative of 9/10*s**6 + 0 - 16*s + 37/4*s**4 + 6*s**2 - 10*s**3 - 9/2*s**5. Suppose v(k) = 0. Calculate k.
2/3, 1
Let y be 900/16 + (-4)/16. Factor 2*j - y + 2*j**2 + 3*j + 53.
(j + 3)*(2*j - 1)
Let u = -5 - -9. Suppose -u = 3*l - 10. Suppose -l*w**3 + w**3 + 2*w**5 + 2*w**2 - 2*w**3 - 2*w**4 + w**3 = 0. What is w?
-1, 0, 1
Let m(k) be the second derivative of -16*k**7/231 - 8*k**6/55 - 9*k**5/110 + 3*k - 28. Let m(o) = 0. Calculate o.
-3/4, 0
Let k = 70030 - 2660925/38. Let b = -60/19 + k. Determine x so that 1/2*x**4 - 4 + 3*x**2 + b*x**3 - 2*x = 0.
-2, 1
Factor 47/7 - 6*r - 5/7*r**2.
-(r - 1)*(5*r + 47)/7
Suppose -3 = 3*k, -5*k = -4*a - 0 + 13. What is h in h - 35 + 4*h**a - 3*h - 2*h + 27 = 0?
-1, 2
Let x(k) = 2*k**2 - 4*k. Let i be x(6). Factor 4*m**4 - 5*m**2 + 41*m**2 + 6*m + 24*m**3 - 24*m - i + 2*m.
4*(m - 1)*(m + 2)**2*(m + 3)
Determine j so that 112/3*j + 0 + 2/3*j**3 - 10*j**2 = 0.
0, 7, 8
Let x = 8725/156 - 726/13. Let j(d) be the second derivative of 1/4*d**3 - x*d**4 - 7*d - 3/40*d**5 + 1/2*d**2 + 0. Factor j(b).
-(b - 1)*(b + 1)*(3*b + 2)/2
Let u be 0/(-9)*(4 - 2)/(-2). Let h(l) be the second derivative of 11*l + 4/15*l**4 + u + 8/75*l**6 + 0*l**2 + 6/25*l**5 + 2/15*l**3 + 2/105*l**7. Factor h(p).
4*p*(p + 1)**4/5
Factor 3/2*i + 2 + 1/4*i**2.
(i + 2)*(i + 4)/4
Find x such that 7 + 32*x**3 + 67 + 45*x**4 + 84*x**2 - 43*x**4 + 136*x - 10*x**3 + 6 = 0.
-5, -2
Suppose 3*z = 3*c - 27, 4*c - 8 = 3*z + 24. Suppose -2*n = -p, -3*p = 5*n - 17 - c. Factor 2/9*g**2 + 4/3*g + n.
2*(g + 3)**2/9
Let v(t) be the second derivative of -t**4/48 - 17*t**3/6 - 289*t**2/2 - 4*t - 2. Suppose v(c) = 0. What is c?
-34
Let l(s) be the third derivative of s**8/672 + 13*s**7/840 + s**6/20 - s**5/30 - 2*s**4/3 - 2*s**3 - 5*s**2 + 1. Determine n, given that l(n) = 0.
-2, 3/2
Factor -7/4*z**2 + 25/4*z - 3.
-(z - 3)*(7*z - 4)/4
Let a(s) be the second derivative of -s**5/5 + s**4 - 2*s**3 + 2*s**2 + 19*s - 1. Let a(p) = 0. What is p?
1
Let x = -119 - -121. Let p = -223/3 + 75. Factor 2/3*s + 2/3 - 2/3*s**3 - p*s**x.
-2*(s - 1)*(s + 1)**2/3
Suppose -17*n = -24174 + 24089. Solve 0*o**3 - 6/5 - 9/5*o**n + 6*o**2 + 9/5*o - 24/5*o**4 = 0 for o.
-2, -1, 1/3, 1
Suppose -2*g - 210 = -17*g. Let -g*p**4 + 33*p**3 + 36*p**4 + 3*p**5 + 42*p**3 + 8*p**4 = 0. What is p?
-5, 0
Let z(s) = s**2 - 3*s - 52. Let m be z(9). Let q(h) be the second derivative of h**m + 1/6*h**3 - 1/20*h**5 - h - 1/6*h**4 + 0. Solve q(p) = 0 for p.
-2, -1, 1
Determine o, given that 1/6*o**5 + 0 + 3*o**3 - 8/3*o**2 - 4/3*o**4 + 5/6*o = 0.
0, 1, 5
Let n(r) be the second derivative of 0 + 3*r - 1/4*r**5 - 5/6*r**4 + 0*r**2 + 0*r**3. Factor n(g).
-5*g**2*(g + 2)
Let h(v) be the first derivative of -v**4/4 - v**3/3 + 2*v**2 + 4*v - 402. Factor h(a).
-(a - 2)*(a + 1)*(a + 2)
Suppose 2 + 6 = 4*o. Let 12*q - 4*q - 4*q**3 - 4*q**3 + 4*q**4 + 0*q**4 - 4*q**o = 0. What is q?
-1, 0, 1, 2