2)*(i + 1)/10
Determine b, given that 3/2*b**4 + 57/4*b**2 - 6*b - 81/8*b**3 + 3/8*b**5 + 0 = 0.
-8, 0, 1, 2
Solve -4/7*h**4 - 60/7 + 152/7*h + 40/7*h**3 - 128/7*h**2 = 0 for h.
1, 3, 5
Suppose 169*w = 4*w + 330. Factor 0 - 2/11*h**w + 4/11*h**3 + 2/11*h**4 - 4/11*h.
2*h*(h - 1)*(h + 1)*(h + 2)/11
Let z be (39/(-65))/(1/115). Let v = 72 + z. Factor -v*i - i**2 + 122 - i - 125.
-(i + 1)*(i + 3)
Let s = -1295054/3 + 431716. Solve 62*j**3 + 130/3*j**2 + 28/3*j + 10/3*j**5 + s*j**4 + 0 = 0 for j.
-7, -1, -2/5, 0
Let s = -89 + 91. Suppose -c - 5*n = -0*n - 25, n - 5 = -s*c. Factor -16/19*v**3 + 32/19*v**4 + 2/19*v**2 + 0 + c*v.
2*v**2*(4*v - 1)**2/19
Suppose 5 = 10*d - 9*d. Suppose -2*g - 21 = -d*y, -11 - 2 = -y - 4*g. Factor 3*p**5 - y*p**3 - 6*p**4 - 3*p**5 + 2*p**5 + 9*p**3.
2*p**3*(p - 2)*(p - 1)
Let m(r) be the second derivative of r**6/30 - r**5/10 - r**4/12 + r**3/3 - 18*r + 2. Let m(a) = 0. Calculate a.
-1, 0, 1, 2
Suppose -4*l + 5*g + 220 = 0, g = -9*l + 7*l + 96. Factor -51*a**2 - 20*a - 9*a - 6 + 36*a + l*a.
-3*(a - 1)*(17*a - 2)
Let n be ((-99)/(-55))/((-5)/225). Let u be n*8*174/(-2436). Factor 4/7*c**2 + u - 72/7*c.
4*(c - 9)**2/7
Let g(n) = -n**3 - n**2 - 1. Let r(j) = -11*j**3 + 297*j**2 - 354*j + 62. Let k(y) = -4*g(y) + 2*r(y). Factor k(c).
-2*(c - 32)*(c - 1)*(9*c - 2)
Let k(b) be the second derivative of 1/3*b**4 - 1/42*b**7 - 42 + 0*b**2 + 2*b - 1/30*b**6 - 4/3*b**3 + 3/10*b**5. Determine q so that k(q) = 0.
-2, 0, 1, 2
Let g(k) be the second derivative of k**4/21 - 4*k**3/3 - 352*k**2/7 - 2821*k. Determine j so that g(j) = 0.
-8, 22
Factor 1649 - 51*s - 796 + s**2 - 755.
(s - 49)*(s - 2)
Let s(p) = -4*p + 20. Let n be s(4). Suppose -16 = -n*r - 8. Solve d**4 + 4*d**4 - 22*d**3 - 4*d**4 - d + 3*d**r + 19*d**3 = 0 for d.
0, 1
Suppose -t = 4*t + 2*v, t + 4*v + 18 = 0. Suppose 1 = 2*x + t*w - 1, 3*w = 4*x - 18. Factor 11*l**3 - 8*l**2 - 5*l**5 + l**x + l**5.
-4*l**2*(l - 1)**2*(l + 2)
What is h in -1/3*h**2 + 0 + 46*h = 0?
0, 138
Let c = -7721 - -7723. Let t(m) be the first derivative of 5/6*m**6 - 5/3*m**3 + 5*m**5 + 35/4*m**4 - 20*m + 3 - 20*m**c. What is l in t(l) = 0?
-2, -1, 1
Determine x so that 48*x**2 + 145*x**5 + 135*x**5 + 56*x**4 + 136*x**5 + 100*x**3 - 412*x**5 = 0.
-12, -1, 0
Let x(u) = -u**3 + 2*u**2 + 6*u - 7. Let k be x(3). Factor -338*g + 9*g - 133*g + 17787 + 0*g**k + 3*g**2.
3*(g - 77)**2
Let p = -785050 - -785053. Suppose 180/11 + 96/11*a + 17/11*a**2 + 1/11*a**p = 0. What is a?
-6, -5
Let m be (-8)/32 - (-33)/4. Suppose m = 11*z - 7*z. Factor 11/4*i**4 + 1/4*i + 0 - 9/4*i**3 + 1/4*i**z - i**5.
-i*(i - 1)**3*(4*i + 1)/4
Let z(n) be the first derivative of n**4/10 + 52*n**3/15 + 71*n**2/5 + 92*n/5 + 129. Determine o, given that z(o) = 0.
-23, -2, -1
Let h(l) be the second derivative of l**8/4200 + l**7/6300 - l**6/450 - l**5/300 + 101*l**4/12 - 30*l. Let r(j) be the third derivative of h(j). Factor r(p).
2*(p - 1)*(p + 1)*(4*p + 1)/5
Let k(u) = 4*u**2 - 4. Suppose 24 - 26 = -n. Let x(o) = o**3 + 16*o**2 - o - 16. Let g(y) = n*x(y) - 9*k(y). Factor g(i).
2*(i - 2)*(i - 1)*(i + 1)
Determine f, given that 63/4 - 31/2*f - 1/4*f**2 = 0.
-63, 1
Let a(v) be the first derivative of 13/16*v**4 - 182 + 5/3*v**3 + 1/8*v**2 - 3/2*v. Factor a(r).
(r + 1)**2*(13*r - 6)/4
Suppose -17*z - 4 = -18*z. Let u = 1366 - 1363. Find q such that -q**z + 0 + 1/2*q**5 + 3/2*q - 2*q**u + q**2 = 0.
-1, 0, 1, 3
Let a(v) be the first derivative of v**4/28 + 3*v**3/7 - v**2/14 - 15*v - 757. Find l such that a(l) = 0.
-7, -5, 3
Let o(m) = -2*m**3 - 81*m**2 + 585*m - 1397. Let w(d) = 21*d**3 + 815*d**2 - 5850*d + 13969. Let t(f) = 62*o(f) + 6*w(f). Let t(r) = 0. Calculate r.
5, 56
Factor m**2 + 29/3 + 88/3*m.
(m + 29)*(3*m + 1)/3
Let c = -214438/11 + 19495. Let y(g) be the first derivative of -4/11*g + 2/3*g**3 - 7/22*g**4 + c*g**2 - 18/55*g**5 + 10. Find x such that y(x) = 0.
-1, 2/9, 1
Let z(m) be the first derivative of -m**4 + 916*m**3/3 - 910*m**2 + 908*m - 1148. Factor z(y).
-4*(y - 227)*(y - 1)**2
Let x(c) = 4*c**3 - 50*c**2 + 3*c + 3. Let f(q) be the first derivative of -3*q**4 + 152*q**3/3 - 4*q**2 - 8*q + 11. Let s(w) = -3*f(w) - 8*x(w). Factor s(g).
4*g**2*(g - 14)
Let j(a) = a**3 + 8*a**2 + 4*a - 8. Let t be j(-4). Suppose 0 = -4*d - q + 5*q + t, -5*d = 2*q - 36. Factor -8*s**3 - 8*s**3 - d*s**2 - 40 + 16*s - 4*s**4 + 52.
-4*(s - 1)*(s + 1)**2*(s + 3)
Let w(k) be the third derivative of -3*k**6/100 - 7*k**5/20 - 22*k**4/15 - 32*k**3/15 + 4*k**2 + 774*k. Factor w(t).
-(2*t + 1)*(3*t + 8)**2/5
Let o(f) be the first derivative of f**6/6 - 4*f**5 - f**4/4 + 20*f**3/3 + 1686. Factor o(p).
p**2*(p - 20)*(p - 1)*(p + 1)
Let o be (664/44 + -15)/((-4)/(-272)). Solve -10/11 + o*y - 136/11*y**2 + 60/11*y**3 + 18/11*y**4 = 0 for y.
-5, 1/3, 1
Let c(l) be the third derivative of -l**6/600 - 26*l**5/75 - 338*l**4/15 - 2*l**2 - 3*l + 184. Factor c(x).
-x*(x + 52)**2/5
Let q(h) be the second derivative of -h**9/756 - h**8/420 + 113*h**3/3 - 40*h + 1. Let t(x) be the second derivative of q(x). Factor t(s).
-4*s**4*(s + 1)
Factor -44*b - 9 + 25/4*b**3 - 205/4*b**2.
(b - 9)*(5*b + 2)**2/4
Suppose -31*x + 53200 = 49*x. Let v = 665 - x. Factor 1/2*g**5 + v*g**2 + 0*g + 0 - 3/2*g**4 + g**3.
g**3*(g - 2)*(g - 1)/2
Let m(v) = 55*v**3 + 7715*v**2 - 15*v - 7735. Let h(d) = 8*d**3 + 1102*d**2 - 2*d - 1105. Let s(a) = 20*h(a) - 3*m(a). Let s(o) = 0. Calculate o.
-221, -1, 1
Suppose 981*m - 182 = -182. Solve 2/3*t**4 - 22/3*t**2 - 16/3 + m*t**3 - 12*t = 0.
-2, -1, 4
Let x(n) be the first derivative of -5*n**2 - 2*n - 25/6*n**3 - 167. Suppose x(p) = 0. Calculate p.
-2/5
Let m = 1150 - 518. Let a = -632 + m. Solve a + 1/4*o**2 + 1/4*o = 0 for o.
-1, 0
Let m = -6 - -11. Let h be (4 + (-1 - 2))*m. Solve -h*r**2 + r**4 + 3*r**2 - 22 + 23 = 0 for r.
-1, 1
Let j be 188/(-3290)*2695/(-22). Solve 1/3*i**3 + j*i**2 - 40/3 + 6*i = 0 for i.
-20, -2, 1
Let w be (162/1539 - 560/(-95))/((-63)/(-12)). Factor 0*s - 4/7*s**3 + 0*s**2 + 0 - 4/7*s**5 + w*s**4.
-4*s**3*(s - 1)**2/7
Let c be -1 + (-595)/(-315) + (-8)/9. What is x in 0*x + c - 1/2*x**2 = 0?
0
Let x be -7 - 415/(-83)*(-526)/(-375). Let d(t) be the second derivative of 0 + 1/50*t**5 - 1/15*t**3 + 0*t**2 + 47*t - x*t**6 + 1/30*t**4. Factor d(o).
-2*o*(o - 1)**2*(o + 1)/5
Let f be -1*(-1 + (7 - 5) + -4). Factor 13*g**3 - 9 + 23*g**f + 25*g - 11*g**3 - 1 + 70*g**2 + 10*g.
5*(g + 1)*(g + 2)*(5*g - 1)
Let y(x) = 2*x**2 + 2. Suppose 0 = -q + 2*o + 114, 0 = q - 3*o - 57 - 61. Let d = q + -104. Let l(g) = -g**2 - 3. Let h(m) = d*l(m) + 3*y(m). Factor h(w).
4*w**2
Let l(g) be the third derivative of -g**5/240 + 23*g**4/16 - 130*g**3/3 + 1173*g**2. Factor l(k).
-(k - 130)*(k - 8)/4
Let z(b) = 34*b**3 - 56*b**2 - 41*b - 2. Let f(h) = 99*h**3 - 167*h**2 - 123*h - 4. Let l(v) = 2*f(v) - 7*z(v). Find u such that l(u) = 0.
-3/10, -1/4, 2
Let x(s) = 26*s**3 - 272*s**2 + 8674*s + 39206. Let b(c) = 30*c**3 - 272*c**2 + 8673*c + 39207. Let g(k) = -6*b(k) + 7*x(k). Factor g(l).
2*(l - 70)**2*(l + 4)
Let p = 491 - 472. Suppose 2*i - 8 = 0, -3*i + p = 3*g - 2*i. Determine v so that -15/2*v**3 - 5/2*v**2 + g*v + 5/2*v**4 + 0 + 5/2*v**5 = 0.
-2, -1, 0, 1
Let s(b) be the second derivative of b**5/20 + 3*b**4/8 + 50*b**2 + 10*b + 1. Let z(v) be the first derivative of s(v). Suppose z(n) = 0. Calculate n.
-3, 0
Let z(t) = t**3 - 4*t**2 + 4*t - 3. Let l be z(2). Let i be l/(-9)*(2 - -7). Suppose -8*u + 17*u**2 - 4*u - 8*u**2 + i*u**3 = 0. Calculate u.
-4, 0, 1
Let y = 429985 + -429983. Factor 3/4 + 0*m - 3/4*m**y.
-3*(m - 1)*(m + 1)/4
Let c(g) be the third derivative of g**7/7560 - 7*g**6/2160 - g**5/45 + 37*g**4/24 - g**3/6 - 83*g**2. Let k(s) be the second derivative of c(s). Factor k(n).
(n - 8)*(n + 1)/3
Let r be ((-38)/(-95))/((-1)/(-35)). Find a such that -49*a - 28 + 10*a**2 + r + 9 + 7 - 61*a**2 = 0.
-1, 2/51
Let -188*m**3 + 61*m**3 + 244*m + 124*m**2 + 66*m**3 + 77*m**3 + 120 = 0. Calculate m.
-5, -2, -3/4
Let x(t) = -3*t**2 - 118*t + 60. Let z be x(-39). Factor -52*h**2 - z*h + 3*h**3 - 36*h - 8*h**2 - 463 + 486*h - 23.
3*(h - 9)**2*(h - 2)
Let g(p) = 4*p + 855. Let h be g(-213). What is l in -4*l**2 - 16/3 + 80/9*l + 4/9*l**h = 0?
1, 2, 6
Let l(h) be the first derivative of -3*h**7/770 + 13*h**6/660 - h**5/110 - 163*h**3/3 - 100. L