4
Let i(v) = -v**3 + 9*v**2 + 5*v - 7. Let l be i(7). Factor -999*q**2 + 20*q - 71*q + l + 1002*q**2.
3*(q - 14)*(q - 3)
Factor 0 + 2/3*x**2 + 128/3*x.
2*x*(x + 64)/3
Factor -800/13 + 98/13*l**3 + 462/13*l**2 + 240/13*l.
2*(l - 1)*(7*l + 20)**2/13
Let f be 2724/(-105) + 32/(-160). Let a = f + 79/3. Determine n, given that 2/7*n**5 + a*n - 22/21*n**4 + 10/7*n**3 + 0 - 6/7*n**2 = 0.
0, 2/3, 1
Factor -185/3 + 554/3*h + h**2.
(h + 185)*(3*h - 1)/3
Let s = 18557 + -18554. Factor -12/11 - 8/11*n**s - 50/11*n - 56/11*n**2.
-2*(n + 6)*(2*n + 1)**2/11
Let f = -1071 - -1073. Let c(p) be the first derivative of -1/3*p**6 + 1/2*p**4 + 0*p + 3 + 6/5*p**5 - 2*p**3 + 0*p**f. What is k in c(k) = 0?
-1, 0, 1, 3
Let w(g) be the third derivative of g**8/168 + 2*g**7/105 - 7*g**6/20 + 3*g**5/5 + 1129*g**2. Let w(u) = 0. What is u?
-6, 0, 1, 3
What is l in 34/9*l**3 + 0*l - 2/9*l**4 - 44/3*l**2 + 0 = 0?
0, 6, 11
Let f(j) = -39*j**3 - 2658*j**2 + 5373*j - 2712. Let p(k) = -55*k**3 - 3721*k**2 + 7522*k - 3797. Let g(z) = -17*f(z) + 12*p(z). Suppose g(a) = 0. Calculate a.
-180, 1
Suppose -3*w - 23 = -8*d, 30*d + 4*w = 32*d + 4. Solve -9/5*b + d + 1/5*b**2 = 0 for b.
4, 5
Factor -3/7*g**2 + 138/7*g - 135/7.
-3*(g - 45)*(g - 1)/7
Let q be 116/10 - ((-63)/35)/(-3). Determine v, given that -192 - 4*v**2 + 3*v + 2*v**2 - q*v + 186 = 0.
-3, -1
Let z(p) = p**2 - 140*p + 1302. Let b be z(10). Let m(q) be the second derivative of -6*q**2 - b*q**3 + 10*q - 1/4*q**4 + 0. Suppose m(s) = 0. Calculate s.
-2
Let b = -131 + 135. Suppose 15*v - 33 = b*v. Determine c, given that 3*c**5 + 9*c + 8*c**2 - 3 - 3 - 24*c**3 - 2*c**2 + 12*c**v = 0.
-2, -1, 1
Suppose -2*g + 36*g = 102. Factor 1 + 43*d**2 - 8*d**5 - 15*d + 36*d**4 + 5 - d**g - 4 - 57*d**3.
-(d - 2)*(d - 1)*(2*d - 1)**3
Solve -4096 - 2944/3*k + 2/3*k**3 - 160/3*k**2 = 0.
-8, 96
Let d(b) = b**2 - 9*b - 25. Let l be d(12). Let r be 552/253 + (-2)/l. Let -4*s**r + s**2 - 4 - s**2 - 3*s - 5*s = 0. Calculate s.
-1
Find l such that 34*l**2 - 115*l**2 - 3 + 137697*l**3 - 27*l - 137778*l**3 = 0.
-1/3
What is t in -36*t**3 + 49*t**5 + 77*t**2 - 47*t**5 + 3*t**4 - 17*t**4 - 44*t**3 + 123*t**2 = 0?
-5, 0, 2, 10
What is m in 136/11*m**2 + 138/11*m + 0 - 2/11*m**3 = 0?
-1, 0, 69
Let b(c) = -c**3 - 3*c**2 + 7*c + 4. Let l be b(0). Factor -14*z**2 + 0 - 24/5*z - 66/5*z**3 - 18/5*z**l + 2/5*z**5.
2*z*(z - 12)*(z + 1)**3/5
Let h(a) be the second derivative of -a**5/30 + 1067*a**4/6 - 1138489*a**3/3 + 1214767763*a**2/3 + 1018*a. Find w such that h(w) = 0.
1067
Let p(c) be the second derivative of -c**5/5 + 11*c**4/3 + 80*c**3/3 + 56*c**2 + 66*c + 11. Find j, given that p(j) = 0.
-2, -1, 14
Factor 35369*u**2 + 318*u + 35351*u**2 - 70226*u**2 - 90 + 90*u**3 - 810 - 2*u**4.
-2*(u - 50)*(u - 1)*(u + 3)**2
Suppose 4 = 2*u - 5*r + 23, 2*u - 2*r + 10 = 0. Let d = u - -5. Let -4*f**2 + 4*f**5 - 2*f + 2*f**4 + 5*f**d + f**3 + 14*f**4 + 4*f**5 = 0. What is f?
-1, -1/2, 0, 1/2
Let o(u) be the second derivative of 1/2*u**3 - 18/7*u**2 - 1/28*u**4 - 15 - 2*u. Suppose o(l) = 0. What is l?
3, 4
Let w = -8/1431 - -20170/24327. Let 0*l - 2/17*l**3 + 0 + w*l**2 = 0. What is l?
0, 7
Suppose 3*x - 222 = g, 20*x - 315 = 16*x - 5*g. Let n be (-3*6/54)/((-20)/x). Suppose -17/4*z**3 + 19/4*z**2 + 0*z - 1 + n*z**5 - 3/4*z**4 = 0. Calculate z.
-2, -2/5, 1
Let z(o) = -o - 3. Let s(x) = -46*x**2 + 191*x - 7. Let t(v) = s(v) + 3*z(v). Solve t(l) = 0 for l.
2/23, 4
Suppose -13*o - 4*r + 98 = 0, 24 - 76 = -2*o + 4*r. Find s, given that 10*s**2 - 5/2*s**4 - o*s + 0 + 5/2*s**3 = 0.
-2, 0, 1, 2
Let r = -21514 - -129085/6. Let h(n) be the second derivative of 0 + 2/3*n**3 - r*n**4 + 0*n**2 + 23*n. Factor h(d).
-2*d*(d - 2)
Let b(d) be the third derivative of 1/84*d**8 + 25 - 2/7*d**7 + 21/10*d**6 + 0*d**3 - 49/15*d**5 + 0*d + 0*d**4 + 2*d**2. Determine z, given that b(z) = 0.
0, 1, 7
Let q(t) = -3*t. Let b(v) = v**3 - v**2 - 13*v + 16. Let r(x) = 2*b(x) + 2*q(x). Factor r(p).
2*(p - 4)*(p - 1)*(p + 4)
Let o(f) be the first derivative of 0*f + 0*f**4 + 7/3*f**3 + 0*f**2 + 7/72*f**6 - 1/12*f**5 - 13. Let n(w) be the third derivative of o(w). Factor n(c).
5*c*(7*c - 2)
Let j(y) be the first derivative of 3*y**5/10 + 3*y**4 + 10*y**3 + 12*y**2 + 992. Factor j(f).
3*f*(f + 2)**2*(f + 4)/2
Suppose 4*y - 7*y + 5*k = -328, 485 = 5*y + 4*k. What is n in -105 - 18*n**3 + 41 + y*n - 301*n - 168*n**2 = 0?
-8, -2/3
Let 784/5 - 6/5*y**3 - 756/5*y + 134/5*y**2 = 0. Calculate y.
4/3, 7, 14
Determine d so that 171*d**3 - 166*d**3 + 561*d**2 - 580*d**2 - 699*d**2 - 892*d**2 - 1615*d = 0.
-1, 0, 323
Let z(p) be the first derivative of -44*p**5 + 221*p**4/4 + 73*p**3 - 221*p**2/2 + p - 5678. Suppose z(m) = 0. Calculate m.
-1, 1/220, 1
Let x = -509 - -477. Let d = x - -34. Factor -2/7*s**3 + 8/7 - 8/7*s**d + 2/7*s.
-2*(s - 1)*(s + 1)*(s + 4)/7
Let c(x) be the second derivative of 17 - 4*x + 0*x**3 - 245/48*x**4 - 35/16*x**5 - 5/168*x**7 + 0*x**2 + 13/24*x**6. Factor c(u).
-5*u**2*(u - 7)**2*(u + 1)/4
Let a(t) be the third derivative of t**5/8 + 71*t**4/16 - 15*t**3 - 1849*t**2. Factor a(d).
3*(d + 15)*(5*d - 4)/2
Let v = 6851/2742 + 2/1371. Let b(f) be the second derivative of -3/10*f**5 + 9*f**2 - 11*f - 4/3*f**4 + 1/5*f**6 + 0 - 1/42*f**7 + v*f**3. Factor b(p).
-(p - 3)**2*(p - 2)*(p + 1)**2
Let b = -601631/5 + 601632/5. Determine n so that 12/5 + b*n**4 - 13/5*n**2 - 1/5*n**5 - 8/5*n + 9/5*n**3 = 0.
-3, -1, 1, 2
Solve -27*u - 120*u**2 + 2173*u**4 + 184*u**3 - 2157*u**4 - 53*u**3 = 0 for u.
-9, -3/16, 0, 1
Let w = -570 - -572. Factor 51*m + 184*m - 10*m + 2*m**w - 7*m**2 + 230.
-5*(m - 46)*(m + 1)
Factor -4/5*s**2 + 104 + 84/5*s.
-4*(s - 26)*(s + 5)/5
Let v be (332/24)/1 - (-20)/120. Find f such that 98*f + 77*f + 100 - 6*f**2 - v*f**3 - 65*f + 2*f**4 = 0.
-2, -1, 5
Let o = -11639/5 + 2328. Let x(y) be the first derivative of -1/5*y**2 + 1/30*y**6 + 1/20*y**4 + 3/25*y**5 - 2 + 0*y - o*y**3. Factor x(j).
j*(j - 1)*(j + 1)**2*(j + 2)/5
Let c(n) be the third derivative of -n**8/224 - n**7/70 + n**6/20 + n**5/20 - 3*n**4/16 - 2*n**2 + 725. Let c(y) = 0. Calculate y.
-3, -1, 0, 1
Let t(i) be the third derivative of -3*i**8/56 - 104*i**7/35 + 32*i**6/15 + 409*i**5/15 + 457*i**4/12 + 70*i**3/3 - 42*i**2. Determine q so that t(q) = 0.
-35, -1, -1/3, 2
Let j be (-2)/7 - (3 + (-204)/28). Let q = 12 - j. Factor 2*z**2 + q*z - 6*z**2 - 4*z - 12*z.
-4*z*(z + 2)
Factor -4418/5 - 1128/5*v - 72/5*v**2.
-2*(6*v + 47)**2/5
Let d(h) = -h**2 + 15*h + 11. Let s be d(15). Find a, given that -40 - 35 + 624*a - 4*a**2 - 692*a + s = 0.
-16, -1
Let s(m) be the second derivative of 0*m**2 - 10/21*m**3 - 2*m + 1/35*m**5 + 1 + 4/21*m**4. Factor s(v).
4*v*(v - 1)*(v + 5)/7
Let u = 552/95 - 324/95. Let -14*k - 44/5*k**4 - 116/5*k**3 - 6/5*k**5 - 136/5*k**2 - u = 0. What is k?
-3, -2, -1, -1/3
Let s(l) = l**2 + l - 1. Let c(w) = -19*w**4 - 1233*w**3 - 20551*w**2 - 17289*w + 2057. Let n(b) = -c(b) - 9*s(b). Factor n(a).
(a + 1)*(a + 32)**2*(19*a - 2)
Let d be (-2)/6*(12 - 1173/92). Let n(p) be the first derivative of -1/18*p**3 - 13 - d*p**2 - 1/3*p. Solve n(y) = 0 for y.
-2, -1
Factor 5104418 + 289815*a - a**3 + 8604749 - 2108641 + 2085*a**2 + 1827569 + 6*a**3.
5*(a + 139)**3
Suppose 66*a - 71*a + 25 = 0. What is h in -12*h - 170*h**2 + a*h**3 + 77*h + 59*h + 41*h = 0?
0, 1, 33
Let w(f) = -f**3 - 9*f**2 + 6*f + 4. Let v be w(-9). Let q be (v/(-15))/2*3. Factor 28*p**5 + 2*p**4 - 52*p**q + 3*p**2 + 27*p**5 - 5*p**4 - 3*p**3.
3*p**2*(p - 1)**2*(p + 1)
Let z(k) be the second derivative of k**4/48 + 155*k**3/12 + 921*k**2/8 + 644*k. Solve z(l) = 0.
-307, -3
Let d be (2/(-60))/((-33)/99). Let t(z) be the first derivative of 1/30*z**6 + 3/10*z**4 + 3 + 4/25*z**5 + d*z**2 + 4/15*z**3 + 0*z. Factor t(v).
v*(v + 1)**4/5
Let t(q) = -13*q**3 - 20*q**2 - 110*q + 122. Let b(j) = 18*j**3 + 18*j**2 + 112*j - 120. Let u(y) = 3*b(y) + 4*t(y). Factor u(a).
2*(a - 16)*(a - 1)*(a + 4)
Let p(r) be the second derivative of r**4/42 + 110*r**3/21 + 216*r**2/7 - 617*r. Find s such that p(s) = 0.
-108, -2
Suppose 5*i - 187 - 33 = 0. Let m = i + -42. Factor 11*b - 39*b**m + 16 + 30*b - 12*b**3 - 4 - 2*b.
-3*(b - 1)*(b + 4)*(4*b + 1)
Let y(d) be the third derivative of d**8/504 + 8*d**7/105 - 4*d**6/9 + d**5/3 + 79*d**4/36 - 6*d**3 - 11214*d**2. Find j