Find z, given that 0 + 2/3*z**2 - 1/6*z**4 + 5/3*z**3 - 1/6*z**5 - 4*z = 0.
-3, -2, 0, 2
Factor 30*r - 3*r**3 + 73*r + 30 - 64*r - 3*r**2 + 9*r**2.
-3*(r - 5)*(r + 1)*(r + 2)
Suppose 9 + 42 = 3*p. Suppose -p*t + 149 = -21. Determine m, given that -1/8*m**5 - t*m - 10*m**2 - 4 - 5*m**3 - 5/4*m**4 = 0.
-2
Factor -56/5 + 18*l - 34/5*l**2.
-2*(l - 1)*(17*l - 28)/5
Let v(f) be the second derivative of f**5/120 - 14*f**4/9 + 784*f**3/9 - 3*f - 75. Factor v(x).
x*(x - 56)**2/6
Let t(u) be the third derivative of 0*u**4 - 1/336*u**8 + 58*u**2 + 1/35*u**7 + 0*u**3 + 0*u + 1/15*u**5 + 0 - 3/40*u**6. Determine i so that t(i) = 0.
0, 1, 4
Let l(p) = 25*p**3 + p**2 - 280*p - 448. Let g(i) = 71*i**3 - i**2 - 839*i - 1344. Let b(t) = 6*g(t) - 17*l(t). Let b(z) = 0. What is z?
-7, -2, 32
Let a(v) = 46*v + 601. Let q be 330/(-15) - 1*-9. Let m be a(q). Factor 1/9*l**5 + 0 - 1/3*l**4 + 1/9*l**m - 2/9*l + 1/3*l**2.
l*(l - 2)*(l - 1)**2*(l + 1)/9
Let y be 33 - (47 - 1491/105). Find i such that 9/5*i - i**3 + 3/5*i**2 + y*i**4 + 0 = 0.
-1, 0, 3
Let h(q) = 2*q**3 - 17*q**2 - 12*q + 27. Let u be h(9). Let f(j) be the second derivative of u*j**3 - 5/12*j**4 + 0 + 4*j + 0*j**2. Factor f(v).
-5*v**2
Let k(q) = 288*q**2 - 442*q - 40. Let f(b) = 115*b**2 - 177*b - 13. Let j(r) = 12*f(r) - 5*k(r). Let j(c) = 0. Calculate c.
-2/5, 11/6
Let w(f) be the third derivative of 0 + 11/105*f**5 - 2*f - 1/420*f**6 - 8/7*f**4 - 59*f**2 - 96/7*f**3. Factor w(s).
-2*(s - 12)**2*(s + 2)/7
Let x(g) be the first derivative of 5/4*g**4 + 250*g**2 - 264 + 140/3*g**3 + 480*g. Find d such that x(d) = 0.
-24, -2
Let s be (-80)/(-7)*(45/6 - 4). Suppose 9*t = -11*t + s. Determine j, given that -3/2 + 3/2*j**t + 0*j = 0.
-1, 1
Factor -14*d**4 + 16*d**4 + 94*d**3 + 281 - 281 - 520*d**2.
2*d**2*(d - 5)*(d + 52)
Let u(l) be the third derivative of 3*l**8/28 - 31*l**6/30 - 6*l**5/5 + 2*l**4 + 16*l**3/3 + 4986*l**2. Find p, given that u(p) = 0.
-1, -2/3, 2/3, 2
Let b(c) = c**2 - 8*c - 3. Let m(z) = 9*z**2 - 807*z - 144. Let j(d) = 2*b(d) + m(d). Factor j(a).
(a - 75)*(11*a + 2)
Let 26*r**3 - 4*r**5 - 82*r**2 - 59*r**2 + 166*r**2 + 26*r**3 - 8*r**4 - 65*r**2 = 0. What is r?
-5, 0, 1, 2
Let z(j) = 2*j - 14. Let f be z(7). Suppose f = 2*v - 0*m + 2*m + 2, -19 = -2*v + 5*m. Suppose 7 - 11 + 6*x + 10*x - 24 + 12*x**v = 0. What is x?
-7/3, 1
Suppose 5*t - n = 20 + 40, 0 = 2*t - 3*n - 24. Factor -6785 + 6785 + t*l - 4*l**2.
-4*l*(l - 3)
Suppose 4*i + 5*b - 48 = 0, -i - 2*b - b + 19 = 0. Suppose 5*l = 78 + i. Find z, given that 175*z + 55*z**2 + 0*z**2 - l + 38 + 104 + 5*z**3 = 0.
-5, -1
Let x = -76 - -76. Suppose 4*b = -5*l - 2, 5*l + 3*b = -x*b + 1. Factor 2/3*p**3 - l*p + 0*p**2 + 4/3.
2*(p - 1)**2*(p + 2)/3
Let n(g) = -3*g**2 + 178*g + 134. Let a(d) = -d - 3. Let w(i) = 6*a(i) + n(i). Factor w(z).
-(z - 58)*(3*z + 2)
Let g(x) be the third derivative of x**5/210 + 9*x**4/28 - 30*x**3 - 5980*x**2. Find u, given that g(u) = 0.
-42, 15
Let a(o) = 2*o**2 - 7*o + 41. Let c(k) = 3*k - 7. Let n(t) = -13*t + 29. Let h(r) = -18*c(r) - 4*n(r). Let v(x) = 2*a(x) - 9*h(x). Factor v(b).
4*(b - 1)*(b + 2)
Let m(o) be the third derivative of -o**6/1080 - 251*o**5/108 + 285*o**2 - 17*o. Find i such that m(i) = 0.
-1255, 0
Let d(s) be the second derivative of -101*s - 7*s**2 - 1/42*s**4 + 2/3*s**3 + 0. Factor d(t).
-2*(t - 7)**2/7
Let j(o) = -o**3 - 14*o**2 + 42. Let x be j(-14). Suppose x*v**3 + 0*v**4 - 58*v**3 + 12*v**4 + 4*v**5 = 0. Calculate v.
-4, 0, 1
Let v(s) = 5*s**3 + 3*s**2 - s. Let w be v(1). Suppose w*k = -10 + 31. Factor 1 - 3 - 5*g**4 + 10*g**2 + 0 - k.
-5*(g - 1)**2*(g + 1)**2
Suppose 4*s + 4*d - 20 = 4, s - 5*d + 18 = 0. Let b(t) = -4*t - t**s + 3*t + 2 - 4*t. Let n(g) = g**2 + g - 1. Let w(f) = -b(f) - 2*n(f). Factor w(y).
-y*(y - 3)
Let m(y) be the second derivative of -3*y**4/8 + 323*y**3 + 1293*y**2/4 + 431*y - 2. Determine z, given that m(z) = 0.
-1/3, 431
Let o(v) = 4*v**3 - 4*v**2 + 8. Let z = 67 + -68. Let f(p) = -p + 15 + 23 - 39. Let b(i) = z*o(i) - 8*f(i). Factor b(y).
-4*y*(y - 2)*(y + 1)
Let h be -7 - (-7 - 1036/1015). Let b = h + -18/29. Solve -6/5*k**4 - b*k**5 + 4/5*k**3 + 24/5*k**2 + 0 + 16/5*k = 0 for k.
-2, -1, 0, 2
Let n(s) = -4*s**3 + 88*s**2 + 132*s. Let d(k) = k. Let c(f) = -f**3 + 29*f**2 + 43*f. Let v(p) = -c(p) - d(p). Let b(m) = 3*n(m) + 10*v(m). Factor b(o).
-2*o*(o + 2)*(o + 11)
Let d(w) = -4*w - 1 - 2 - 7. Let g be d(-3). Find s, given that -s - 3*s + 6*s - 4*s**4 + 128*s**2 - 124*s**2 - g*s**3 = 0.
-1, -1/2, 0, 1
Suppose -2*p = 12*u - 15*u + 326, 3*u + p - 332 = 0. Suppose 61 = 2*f - 19. Factor -126*q**2 + 21*q + u*q**3 + 5*q**5 - f*q**4 - 14*q**2 - 19*q + 83*q - 20.
5*(q - 4)*(q - 1)**4
Let t(x) be the third derivative of -x**5/4 - 139*x**4/24 + 29*x**3/3 + 3376*x**2. Solve t(d) = 0 for d.
-29/3, 2/5
Let g(j) be the first derivative of -j**4 - 44/3*j**3 + 12/5*j**5 - 24*j**2 - 16*j + 2/3*j**6 + 78. Factor g(f).
4*(f - 2)*(f + 1)**3*(f + 2)
Suppose -108*n + 1399 = 2*t - 103*n, 0 = -t + 3*n + 716. Factor 10*x**2 + 7*x**3 - t*x**4 - 2 - x**5 + 1 + 1 + 703*x**4.
-x**2*(x - 2)*(x + 1)*(x + 5)
Let q(d) be the second derivative of -d**5/60 + d**4/2 - 71*d**3/18 - 15*d**2 - 1014*d. Factor q(x).
-(x - 10)*(x - 9)*(x + 1)/3
Let j(u) be the second derivative of u**4/3 + 716*u**3/3 + 64082*u**2 - 1100*u. Determine y, given that j(y) = 0.
-179
Let l(a) = -32*a + 11. Let u be l(-2). Let d = u - 72. Determine n, given that -d*n**3 + 4*n**4 - 12*n - 1188 + 1180 + 46*n**2 - 30*n**3 + 3*n**4 = 0.
-2/7, 1, 2
Let p(q) = 3*q - 62. Let r be p(22). Let 33*l**5 + 618*l**2 + 4745*l**3 + 58*l - 4988*l**3 - 72 - 334*l - 60*l**r = 0. Calculate l.
-3, -2/11, 1, 2
Let f(u) be the first derivative of u**6/10 - 14*u**5/5 + 129*u**4/10 - 68*u**3/5 - 101*u**2/10 + 114*u/5 - 2142. Solve f(p) = 0.
-2/3, 1, 3, 19
Let a = 43529 - 43526. Suppose -117/2*t - 135/2 - 33/2*t**2 - 3/2*t**a = 0. Calculate t.
-5, -3
Factor -162/19*n**2 - 680/19*n + 0 + 2/19*n**3.
2*n*(n - 85)*(n + 4)/19
Let u(x) be the first derivative of 2*x**6 + 0*x**2 - 81/5*x**5 - 30 + 0*x + 6*x**3 + 51/4*x**4. Suppose u(z) = 0. What is z?
-1/4, 0, 1, 6
Suppose 14*z - 1965 = 53839. Factor -3*n**2 + 486*n - z - 16702 + 1123 - 118.
-3*(n - 81)**2
Let i = -36562450/19 - -1923082. Let p = i + 1258. Determine a so that p*a + 2/19*a**2 - 12/19 = 0.
-6, 1
Let r be (40/(-14))/(80/(-280)). Find j, given that -2 + 22*j - 8 + 16 + 26*j**2 + r*j**3 = 0.
-1, -3/5
Suppose 236 + 247 = -7*g. Let z be (-28)/70 - g/60. Factor z*v**5 + 375/4*v - 1875/4 + 195/2*v**3 + 525/2*v**2 + 57/4*v**4.
3*(v - 1)*(v + 5)**4/4
Let a(l) be the third derivative of -91*l**2 + 5/12*l**4 + 0*l + 0 + 5/12*l**5 - 40/3*l**3. Factor a(v).
5*(v + 2)*(5*v - 8)
Suppose -207 = 32*y - 79. Let i be ((-6)/y)/(54/240). Let -i*r**3 + 2/3*r**4 + 74/3*r**2 - 40*r + 24 = 0. What is r?
2, 3
Suppose 41*h = 12*h + 41 + 17. Let j(m) be the first derivative of -1/21*m**3 - 1/7*m + 29 + 1/7*m**h. Let j(u) = 0. Calculate u.
1
Suppose -17*f + 14*f = -12. Solve 11*n - 7*n - 4*n - 14*n**2 + f*n = 0 for n.
0, 2/7
Suppose 583 = 228*o - 241 - 88. Let m(r) be the third derivative of -1/840*r**7 - 1/240*r**6 - 19*r**2 + 0*r**5 + 0*r + 0 + 0*r**3 + 0*r**o. Factor m(z).
-z**3*(z + 2)/4
Let b be (90/21)/(27/1953). Suppose b*s = 317*s. What is k in 16/3*k**3 - 22/3*k**2 - 2*k + 32/3*k**4 + s = 0?
-1, -1/4, 0, 3/4
Let w(n) = -n**3 - 2*n**2 - 3*n. Let t(p) = 6*p**3 - 2*p**3 + 4*p**2 - p**3 + 19*p - 11*p. Let l(s) = 6*t(s) + 15*w(s). Factor l(a).
3*a*(a - 1)**2
Let p(l) be the second derivative of 1/15*l**6 + 0*l**2 - 23/6*l**4 - 7 + 0*l**3 - 11/5*l**5 - 10*l. Factor p(g).
2*g**2*(g - 23)*(g + 1)
Factor -39/2*z - 3*z**2 + 15/2*z**3 - 9.
3*(z - 2)*(z + 1)*(5*z + 3)/2
Let x(j) be the second derivative of -20449*j**7/28 + 61919*j**6/20 - 63927*j**5/20 + 289*j**4/2 - 2*j**3 - 1286*j. Find u, given that x(u) = 0.
0, 2/143, 1, 2
Let a = -37941 - -37944. Determine q, given that -1800/11 - 120/11*q + 120/11*q**a + 2/11*q**4 + 1798/11*q**2 = 0.
-30, -1, 1
Let m(a) = -a**2 + 5*a + 9. Let o be m(9). Let k = 33 + o. Factor -4*q - 7*q + 5*q - k - 2*q**2 - 2*q.
-2*(q + 1)*(q + 3)
Let d be 8/12 - 1/(-6)*134. Suppose -15 + d = 4*o. Let -4*g**5 - 12*g**4 - 54*g**3 + 9*g + 8*g**o + 46*g**3 + 3*g + 4 = 0. What is g?
-1, 1
Let i be (-75)