- y**2. Let k be u(5). Find b, given that 18/13 + 2/13*b**3 - 10/13*b**k + 6/13*b = 0.
-1, 3
Let -417*x**4 - 456 - 492*x**2 + 40*x**3 + 856*x + 50 + 1234*x**4 - 405*x**4 - 410*x**4 = 0. What is x?
-29, 1, 7
Let i(w) = -2 + 2*w**3 + 3*w - 3*w**3 - 2*w - 6*w**2 + 2*w**3. Let j be i(6). Let 12*g**2 + j*g**5 - 12*g**4 - 4*g**3 - 8*g**5 - g + 9*g = 0. Calculate g.
-2, -1, 0, 1
Factor -612/7 - 2/7*g**2 + 86/7*g.
-2*(g - 34)*(g - 9)/7
Let o(y) be the third derivative of -y**8/840 - y**7/210 + y**5/30 + y**4/12 + 37*y**3/2 - 2*y**2 - 24. Let l(x) be the first derivative of o(x). Factor l(v).
-2*(v - 1)*(v + 1)**3
Let v(w) be the second derivative of -w**6/65 - 419*w**5/130 - 139*w**4/39 + 14*w - 64. Factor v(l).
-2*l**2*(l + 139)*(3*l + 2)/13
Let q(m) = m**2 + 24*m + 43. Let d(v) = 5*v**2 + 118*v + 220. Let r(p) = 4*d(p) - 19*q(p). Let r(f) = 0. Calculate f.
-9, -7
Let r(a) = -5*a**2 + 3*a**3 + 7 + 0*a**3 + a**2 - 6*a - 2*a**3. Let d be r(5). Factor j + 2*j + 3*j - 2*j - 2*j**d.
-2*j*(j - 2)
Let s = 3742/41 + -11144/123. Suppose s*t + 2/9*t**2 - 80/9 = 0. What is t?
-8, 5
Let b(s) be the second derivative of 0*s**2 + 2/9*s**4 - 1/5*s**5 + 4/45*s**6 - 1/63*s**7 + 0 - 1/9*s**3 + 145*s. Let b(d) = 0. Calculate d.
0, 1
Let h(q) be the second derivative of -q**7/840 + 7*q**6/480 + q**5/30 - 52*q**2 + 108*q. Let g(f) be the first derivative of h(f). Factor g(k).
-k**2*(k - 8)*(k + 1)/4
Let l(q) = 7865*q + 188792. Let b be l(-24). Suppose -4/5*d**5 - 64*d - b*d**3 - 128/5 - 8*d**4 - 64*d**2 = 0. Calculate d.
-2
Let i = 1089 + -1085. Suppose h + 0 = 3. Determine g so that 10*g**3 - 8*g - 4 + 4*g**i + 4*g**h - 6*g**3 = 0.
-1, 1
Let h(p) = 110*p**2 - p - 3. Let y be h(3). Suppose 4*g + 204 = y. Factor g*b + 2*b**3 - 99*b - 96*b + 2*b**4.
2*b**3*(b + 1)
Let z be (-4)/14 + (-16)/(-7). Suppose 4*s = -8*y + y + 43, 0 = 5*y - 25. Let 0*i**2 + 6 + 3*i - 3*i**s + 0*i**2 + 0*i**z = 0. Calculate i.
-1, 2
Let z(x) be the second derivative of 35*x**4/12 - 835*x**3 - 2160*x**2 + 11751*x. Factor z(n).
5*(n - 144)*(7*n + 6)
Let a(z) = -z**2 + z + 7. Let n(m) = -9*m**2 + 863*m - 265. Let f(s) = -6*a(s) + 2*n(s). Let f(g) = 0. Calculate g.
1/3, 143
Suppose -2*y = q - 2, 7*q - 14 = -8*y + 6*q. Factor -d**3 - 5/3*d - 2*d**y - 1/2 - 1/6*d**4.
-(d + 1)**3*(d + 3)/6
Factor -17 + 100*g - 15 - 420*g**3 + 464*g**3 - 50*g**2 - 4*g**4 - 58*g**2.
-4*(g - 8)*(g - 1)**3
Let m be 932/120*12/40. Let l = -2/25 + m. Factor 3/8*n**4 - l*n**3 - 9/8 + 3/8*n**5 + 15/8*n + 3/4*n**2.
3*(n - 1)**3*(n + 1)*(n + 3)/8
Let f be (54/30)/((-3)/(-20)). Let d be (8/f)/((-2)/(-12)). What is p in -4*p + p**4 - 16*p**2 - 69*p**5 + 18*p**3 + 9*p**d + 6*p**2 + 55*p**5 = 0?
-1, -2/7, 0, 1
Let g(w) = 2*w**2 + 896*w + 8. Let c(i) = -10*i + 2. Let n(r) = 4*c(r) - g(r). Factor n(p).
-2*p*(p + 468)
Let h be (-21)/(-14)*128/(-3). Let l be 2*2 + 65 + h. Factor -2/13 - 2/13*c**4 + 2/13*c**l + 4/13*c**2 - 4/13*c**3 + 2/13*c.
2*(c - 1)**3*(c + 1)**2/13
Suppose 8*z - 29 = -21. Let u be (-9)/162*-9 + z. What is v in -u*v + 6*v**4 + 0 + 15/2*v**2 - 12*v**3 = 0?
0, 1/2, 1
Factor -4581*n**3 - 4*n**4 + 3*n**4 + 4578*n**3.
-n**3*(n + 3)
Let d = -376353 + 752709/2. Factor -3 + 15/2*k**3 + 21/2*k - 27/2*k**2 - d*k**4.
-3*(k - 2)*(k - 1)**3/2
Factor -135*r + 69*r**2 + 600 + 75*r**2 - 207*r**2 + 66*r**2 - 468*r.
3*(r - 200)*(r - 1)
Let o(f) be the third derivative of 11*f**6/420 + 103*f**5/210 + 95*f**4/42 + 8*f**3/3 + 69*f**2 - 8*f. Suppose o(q) = 0. Calculate q.
-7, -2, -4/11
Let c(r) be the third derivative of -r**6/30 + 23*r**5/20 - 305*r**4/24 + 12*r**3 - 50*r**2. Determine u so that c(u) = 0.
1/4, 8, 9
Factor 159/4*m**2 + 43/4*m**3 + 21/4*m - 49/2 + 3/4*m**4.
(m + 1)*(m + 7)**2*(3*m - 2)/4
Let k(v) be the third derivative of v**6/1140 - 4*v**5/285 + v**4/12 - 4*v**3/19 - 1001*v**2. Factor k(g).
2*(g - 4)*(g - 3)*(g - 1)/19
Suppose -10*s + 5*s + 2*x = -15169, -5*s + x = -15167. Suppose 3024 - s = -9*j. Solve j - w**2 - 7/2*w + 7/2*w**3 = 0.
-1, 2/7, 1
Determine q so that 465/4*q - 15/4*q**5 + 33/2*q**2 + 159/4*q**4 - 225/2*q**3 - 225/4 = 0.
-1, 3/5, 1, 5
Solve 2/19*x**2 - 2960/19 + 582/19*x = 0.
-296, 5
Suppose w = 6*w + 130. Let k = 30 + w. Factor -k*c**2 + 4 + 534*c - 534*c.
-4*(c - 1)*(c + 1)
Let t(g) = 5*g**3 + 673*g**2 + 654*g. Let r(p) = -p**3 - 224*p**2 - 219*p. Let h(i) = 7*r(i) + 2*t(i). Find s such that h(s) = 0.
-1, 0, 75
Let a(w) = 3*w**2 + 2*w + 3. Let l(n) = 42*n**2 - 414*n - 396. Let f(c) = 15*a(c) - l(c). Factor f(t).
3*(t + 1)*(t + 147)
Let f(c) be the third derivative of c**5/60 + 39*c**4/4 - 236*c**3/3 + 13187*c**2. Factor f(x).
(x - 2)*(x + 236)
Let l(c) = -9*c**2 - 29 + 2*c + 6 - 52*c - 57. Let x(h) = -245*h**2 - 1350*h - 2160. Let r(w) = -55*l(w) + 2*x(w). Determine v, given that r(v) = 0.
-8, -2
Let b(g) be the second derivative of -27/2*g**2 + 3 - 9/2*g**3 - 3/4*g**4 - 6*g - 1/20*g**5. Factor b(a).
-(a + 3)**3
Suppose -5*k + 16 + 14 = 0. Let n(h) = h**3 - 6*h**2 + 10*h - 6. Let p be n(4). Factor 4*z**p + 8*z**4 + 14*z**3 + 4*z**3 - k*z**3.
4*z**2*(z + 1)*(2*z + 1)
Let m(k) = -2*k**4 - 2*k**3 - 2*k**2 + 2*k. Let q(j) = 23*j**4 + 433*j**3 + 787*j**2 - 1093*j - 138. Let y(z) = 3*m(z) + q(z). Let y(f) = 0. What is f?
-23, -3, -2/17, 1
Let i(a) = a**2 + 21*a - 41. Let w be i(-23). Suppose 12 = w*k + o, 4*k - 4*o - 58 = -34. Factor 1/3*z**k + 1/3*z + 0 - 2/3*z**2.
z*(z - 1)**2/3
Suppose 9*z + 3*i + 37 = 13*z, -i = 2*z - 1. Let l(d) be the first derivative of 4*d**5 + 28 - 8/3*d**3 + 6*d**z - 14*d**2 - 12*d + 2/3*d**6. Factor l(u).
4*(u - 1)*(u + 1)**3*(u + 3)
Let n(u) = 43*u**2 + 526*u - 535. Let q(b) = -5*b**2 - 66*b + 67. Let o(r) = 6*n(r) + 51*q(r). Factor o(a).
3*(a - 69)*(a - 1)
Let l = 8921/3645 - 472/729. Factor 3/5*g**2 + 0 + l*g.
3*g*(g + 3)/5
Let v = 1/18 + -23/387. Let n = v - -3101/1290. Factor 0 + n*z**2 - 4/5*z**3 - 8/5*z.
-4*z*(z - 2)*(z - 1)/5
Let h(c) be the first derivative of -c**7/840 + c**6/360 + c**5/60 - 218*c**3/3 - 45. Let i(y) be the third derivative of h(y). Factor i(x).
-x*(x - 2)*(x + 1)
Let x(d) = d**4 - 25*d**3 + 287*d**2 - 493*d. Let w(c) = -6*c**4 + 75*c**3 - 862*c**2 + 1478*c. Let a(o) = 2*w(o) + 7*x(o). Factor a(h).
-5*h*(h - 3)**2*(h + 11)
Suppose -3*o = 39 - 36. Let u(v) = v**3 + v**2 - 2*v + 1. Let a(t) = t**4 + 11*t**3 + 37*t**2 + 50*t + 8. Let k(x) = o*a(x) - 5*u(x). What is s in k(s) = 0?
-13, -1
Let v(i) be the third derivative of 0*i**3 + 0*i**4 - 7/80*i**6 - 1/42*i**7 + 296*i**2 - 1/672*i**8 + 0 + 0*i**5 + 0*i. What is o in v(o) = 0?
-7, -3, 0
Let k(l) be the second derivative of l**8/112 + 9*l**7/35 + 81*l**6/40 - 271*l**2/2 - 189*l. Let f(x) be the first derivative of k(x). Solve f(i) = 0 for i.
-9, 0
Suppose l + 807 = 3*w, l + 9*w + 801 = 10*w. Let a be (-6)/57 - 312/l. Factor 4/7 + 2/7*r - a*r**2.
-2*(r - 2)*(r + 1)/7
Let t(r) be the second derivative of -r**7/6 - 43*r**6/30 + 57*r**5/20 + 107*r**4/12 + 7*r**3/3 + r + 131. Solve t(c) = 0 for c.
-7, -1, -1/7, 0, 2
Let b(w) = 73*w - 288. Let y be b(13). Let -y*r**2 + 1332*r**2 + 9*r - 665*r**2 + r**3 = 0. What is r?
-3, 0
Let h(k) be the second derivative of k**5/40 - 7*k**4/16 - 24*k**2 - 2*k - 37. Let a(j) be the first derivative of h(j). Determine f so that a(f) = 0.
0, 7
Let q(v) be the third derivative of -1/350*v**7 - 3/100*v**6 - 3/10*v**4 + 0 - 13/100*v**5 + 0*v - 2/5*v**3 - 41*v**2. Factor q(t).
-3*(t + 1)**2*(t + 2)**2/5
Let d(m) be the first derivative of 3*m**5/70 + 5*m**4/42 - 2*m**3/21 + 92*m + 74. Let q(h) be the first derivative of d(h). Factor q(x).
2*x*(x + 2)*(3*x - 1)/7
Let d be -3 + (2332/(-8) - 1). Let g = 302 + d. Solve 15/4*f + 1/2 + g*f**2 - 7*f**4 - 15/4*f**3 = 0.
-1, -2/7, -1/4, 1
Let l be (-12)/980*(-1071)/34. Let n(u) be the third derivative of 0*u + l*u**6 + 5/21*u**3 - 21*u**2 + 23/42*u**4 + 24/35*u**5 + 0 + 9/245*u**7. Factor n(s).
2*(s + 5)*(3*s + 1)**3/7
Let s(y) be the second derivative of -3*y**7/35 - 22*y**6 - 541*y**5/50 + 734*y**4/15 + 244*y**3/5 - 3*y - 236. Solve s(u) = 0 for u.
-183, -2/3, 0, 1
Let o(u) be the third derivative of -1/40*u**6 + 20*u**2 - u + 1/8*u**4 + 1/70*u**7 + 0 - 7/20*u**5 + 3*u**3. What is p in o(p) = 0?
-2, -1, 1, 3
Let i(z) = 41*z**2 + 67*z + 127. Let p(d) = -13*d**2 - 22*d - 43. Let w(g) = -6*i(g) - 19*p(g). What is h in w(h) = 0?
-11, -5
Let k(s)