 1/2
Let i(q) = -8*q**3 + 32*q**2 + 8*q - 20. Let r(p) = p**4 + 15*p**3 - 63*p**2 - 15*p + 41. Let z(u) = -7*i(u) - 4*r(u). Let z(f) = 0. What is f?
-3, -1, 1, 2
Factor 1/4*m**3 + 272*m - 289 + 67/4*m**2.
(m - 1)*(m + 34)**2/4
Let w(k) be the second derivative of -9/16*k**3 + 0 + 3/8*k**2 + 3/32*k**4 + 3/40*k**5 - 22*k. Factor w(o).
3*(o - 1)*(o + 2)*(4*o - 1)/8
Let f be (-10)/35 - (-4)/(-30)*1248/(-112). Factor -f*w - 2/5*w**2 + 0.
-2*w*(w + 3)/5
Let h be (-40)/(-6)*(-24)/32*-2. Suppose h*d - 1 = -1. Factor 4/5*s - 6/5*s**2 + d + 2/5*s**3.
2*s*(s - 2)*(s - 1)/5
Let f be (-1)/((-10)/(-4) - (-75)/(-25)). Let d(y) be the first derivative of 0*y**f + 2/15*y**3 + 0*y - 1/5*y**4 - 6. Solve d(z) = 0.
0, 1/2
Let i(m) be the first derivative of m**3/3 - 11*m**2 + 121*m - 106. Factor i(s).
(s - 11)**2
Let v be 953/(-140) - -7 - (-2)/(-14). Let c(r) be the first derivative of 0*r + 0*r**3 + 1/10*r**2 + 2 - v*r**4. Factor c(w).
-w*(w - 1)*(w + 1)/5
Factor 625/4 + 102675/4*k**2 - 13875/4*k - 253265/4*k**3.
-5*(37*k - 5)**3/4
Let f(h) be the second derivative of -h**5/50 - h**4/5 - 4*h**3/5 - 8*h**2/5 - 229*h. Suppose f(t) = 0. What is t?
-2
Let o(q) be the third derivative of -q**5/240 - 25*q**4/48 + 17*q**3/8 - 283*q**2. Suppose o(v) = 0. What is v?
-51, 1
Let l be (32/40)/(18/15 - 1). Find y such that 2*y - 96*y**2 + l - 87*y**2 + 181*y**2 = 0.
-1, 2
Let q(l) = 5*l**3 + 31*l**2 - 77*l + 41. Let c(r) = -45*r**3 - 280*r**2 + 695*r - 370. Let j(d) = 6*c(d) + 55*q(d). Suppose j(v) = 0. What is v?
-7, 1
Let k(t) be the first derivative of 2*t**5/45 - t**4/9 + 2*t**3/27 + 112. Factor k(d).
2*d**2*(d - 1)**2/9
Let l(d) be the second derivative of d**6/180 - 3*d**5/20 + 4*d**4/9 - 779*d. Find i such that l(i) = 0.
0, 2, 16
Let u(h) be the third derivative of h**7/210 - h**6/360 - h**5/30 + h**4/24 + 4*h**3/3 - 11*h**2. Let s(l) be the first derivative of u(l). Factor s(g).
(g - 1)*(g + 1)*(4*g - 1)
Factor 6 - 27865*g + 2*g**2 + 27849*g + 18.
2*(g - 6)*(g - 2)
Let u = -2168/3 - -723. Let h(w) be the first derivative of 1/3*w + u*w**2 + 1/9*w**3 + 4. Factor h(b).
(b + 1)**2/3
Suppose 2*z - 2 = -0*z. Let m(d) = d**2 + d + 1. Let f(o) = o**2 + 23*o - 47. Let b(v) = z*f(v) - 3*m(v). Determine p, given that b(p) = 0.
5
Let a(b) be the second derivative of 4*b**6/15 + 13*b**5/5 - 10*b**4/3 - 14*b**3 - 11*b - 4. Let a(f) = 0. Calculate f.
-7, -1, 0, 3/2
Suppose -7*l + 10 = -5*l. Suppose -3*c = 2*c - 15, -4 = -l*k + 2*c. Determine b so that -3*b**4 + 4*b**2 - 12*b**3 + 3*b**3 + 6*b**3 - b**5 - 5*b**k = 0.
-1, 0
Let v(k) = 23*k**4 + 52*k**3 + 8*k**2 - 8*k. Let x = 53 - 56. Let y(b) = 8*b**4 + 17*b**3 + 3*b**2 - 3*b. Let a(f) = x*v(f) + 8*y(f). Solve a(w) = 0.
-4, 0
Let n(p) be the third derivative of 0 + 1/10*p**5 + 1/105*p**7 + 0*p**3 + 3/4*p**4 - 6*p**2 + 0*p - 1/12*p**6. Solve n(f) = 0.
-1, 0, 3
Factor -1744/3*p + 190096/3 + 4/3*p**2.
4*(p - 218)**2/3
Let d(s) = -231*s - 1386. Let r be d(-6). Let 0*g + r - 1/3*g**3 + 5/3*g**2 = 0. What is g?
0, 5
Let j(t) = -2*t - 16. Let d be j(-10). Let -100 - d*g**2 + 30*g + 32*g - 22*g = 0. Calculate g.
5
Let u(b) be the third derivative of 0*b + 0 - 1/240*b**5 - 1/32*b**4 + 4*b**2 + 0*b**3. Factor u(v).
-v*(v + 3)/4
Let g(z) be the first derivative of 2/5*z - 1/20*z**4 + 4 - 1/25*z**5 + 1/5*z**3 + 1/2*z**2. Factor g(u).
-(u - 2)*(u + 1)**3/5
Let d(r) = 6*r**2 + 263*r. Let a(g) = -3*g**2 - 126*g. Let l(b) = 13*a(b) + 6*d(b). Factor l(o).
-3*o*(o + 20)
Factor 40*s - 252 - 5*s**2 + 10*s**2 + 0*s**2 - 162*s - 3*s**2.
2*(s - 63)*(s + 2)
Let j(b) be the second derivative of -b**7/63 - b**6/15 - b**5/15 + b**4/9 + b**3/3 + b**2/3 - 14*b - 2. Find i, given that j(i) = 0.
-1, 1
Let q(z) be the third derivative of 0 - 5/2352*z**8 + 0*z**4 + 4/735*z**7 + 7*z**2 - 2*z + 0*z**3 - 1/280*z**6 + 0*z**5. Factor q(b).
-b**3*(b - 1)*(5*b - 3)/7
Let x(q) be the third derivative of q**5/210 + 41*q**4/84 - 2*q**2 - 7. Find m, given that x(m) = 0.
-41, 0
Let d be (-10)/6*-50*(-15)/(-520). Let x = d - 9/4. Factor -x*i + 2/13*i**2 - 4/13.
2*(i - 2)*(i + 1)/13
Suppose 16 = 4*m + v, 5*m + 5*v + 10 = 45. Let h be 39/(-13) + 0 + 0 + m. Let 0*b - 2/9*b**2 + h*b**3 + 2/9*b**4 + 0 = 0. What is b?
-1, 0, 1
Suppose -31*q = -30*q + 6, 4*n + 5*q = -30. Determine w so that 0 + n*w**2 - 2/9*w**5 - 4/9*w**3 + 0*w + 2/3*w**4 = 0.
0, 1, 2
Suppose 15 = 6*x - x. Let b = -19982/3 - -6661. Let 2*i**2 + 1/3*i**4 - 4/3*i - 4/3*i**x + b = 0. What is i?
1
Suppose 8*y + 60 = 276. Suppose -5*o - y = -37. Factor 0*x - 2/7*x**5 + 0 - 2/7*x**o + 2/7*x**4 + 2/7*x**3.
-2*x**2*(x - 1)**2*(x + 1)/7
Let l(t) be the second derivative of -2*t**6/15 - 2*t**5 - 13*t**4/3 + 40*t**3 - 72*t**2 - 178*t. Suppose l(k) = 0. Calculate k.
-6, 1
Let -3/5*k**3 + 81/5*k + 162/5 + 0*k**2 = 0. Calculate k.
-3, 6
Let c(r) = 7*r**2 + 86*r + 1600. Let x(k) = -k**2 - k. Let n(w) = c(w) + 6*x(w). Determine t so that n(t) = 0.
-40
Let k(q) be the second derivative of q**5/90 + 2*q**4/27 + q**3/9 - 568*q. Factor k(m).
2*m*(m + 1)*(m + 3)/9
Let b(f) be the third derivative of f**5/20 + 13*f**4/8 + 6*f**3 + 2*f**2 + 75. Factor b(j).
3*(j + 1)*(j + 12)
Let j(m) be the first derivative of m**7/525 + 11*m**2/2 + 7. Let o(d) be the second derivative of j(d). Factor o(n).
2*n**4/5
Let a(i) be the third derivative of -2/15*i**5 + 0*i**4 - 1/12*i**6 + 0 + 0*i**3 - 20*i**2 + 0*i. Factor a(z).
-2*z**2*(5*z + 4)
Let b(d) be the second derivative of 3/5*d**5 + 1/15*d**6 + 2*d**4 + 0 + 10/3*d**3 + 3*d**2 - 17*d. Find n, given that b(n) = 0.
-3, -1
Let a(s) be the second derivative of -s**4/36 - 2*s**3/9 + 2*s - 12. Solve a(f) = 0.
-4, 0
Let v = -65 - -68. Find k such that 75 + k**2 - 73 - v*k + 0*k**2 = 0.
1, 2
Let r(w) = -w**3 + 2*w - 1. Let m(x) = 16*x**2 + 28*x - 2. Let a(b) = 2*m(b) - 4*r(b). Solve a(z) = 0.
-6, -2, 0
Let r(d) = d**5 - 7*d**4 - 3*d**3 + d**2 - 4*d. Let j(m) = -6*m**4 - 2*m**3 + 2*m**2 - 2*m. Let i(w) = 6*j(w) - 4*r(w). Solve i(u) = 0.
-1, 0, 1
Let z = -12 - -16. Let k(q) be the first derivative of 2/3*q**3 - q**5 + 5 - 3/4*q**z + 0*q**2 + 0*q. Factor k(l).
-l**2*(l + 1)*(5*l - 2)
Let b be (-1027)/(-364) - (3 + (-85)/35). Let -b*t**5 + 0*t + 0*t**2 - 3/2*t**4 + 3/4*t**3 + 0 = 0. What is t?
-1, 0, 1/3
Let i = -279 + 283. Let t(q) be the first derivative of -1/3*q**2 + 1/12*q**i + 4 - 1/9*q**3 + 0*q. Determine b, given that t(b) = 0.
-1, 0, 2
Let q(h) be the third derivative of h**8/112 + 13*h**7/70 + 7*h**6/8 - 49*h**5/20 - 199*h**2. Factor q(c).
3*c**2*(c - 1)*(c + 7)**2
Determine o so that -1008*o + 16*o**3 + 38 + 124 + 8*o**3 - 24 + 46 + 1082*o**2 = 0.
-46, 1/4, 2/3
Let h(p) = -12*p**3 + 32*p**2 - 4. Let a(v) = -v**2 - 2*v + 1. Let m(t) = -4*a(t) - h(t). Suppose m(k) = 0. Calculate k.
0, 1/3, 2
Factor 994*n + 8*n**4 - 2*n**3 - 8*n**2 - 1002*n + 2*n**5 + 8*n**3.
2*n*(n - 1)*(n + 1)*(n + 2)**2
Let a(w) = -w**3 - 10*w**2 - w - 8. Suppose 60 = 14*i - 20*i. Let m be a(i). Factor -2/13*b - 6/13*b**3 + 6/13*b**m + 2/13*b**4 + 0.
2*b*(b - 1)**3/13
Factor -50 + 269*j**2 - 284*j**2 + 76*j + 9*j.
-5*(j - 5)*(3*j - 2)
Let q(p) be the first derivative of p**5/15 - 2*p**4 + 24*p**3 - 19*p**2 - 4. Let a(o) be the second derivative of q(o). Factor a(k).
4*(k - 6)**2
Suppose -6*m + 2 = -10. Find u such that -5*u**3 + 8*u + u**4 - u**2 - m*u**5 - 2*u**5 + 7*u**5 - 6*u = 0.
-1, 0, 2/3, 1
Let f(v) = -5*v**2 - 5*v - 45. Let i be (1/4)/(11/(-44)). Let z(l) = l. Let d(k) = i*f(k) + 25*z(k). Suppose d(a) = 0. What is a?
-3
What is j in -25/2*j**4 - j - 29/2*j**2 - 26*j**3 + 0 = 0?
-1, -2/25, 0
Let t = 428 + -425. Let k be 0/1 - 0 - -2. What is a in 3*a**3 + 3*a**k - 2*a**2 - a**3 + a**t - 4*a**4 = 0?
-1/4, 0, 1
Suppose 0 = -r + 4*r. Suppose -2 = -b - r. Factor h**3 + 9*h - 2*h**4 - h - 12*h**b - 4*h**2 + 9*h**3.
-2*h*(h - 2)**2*(h - 1)
Let l = 503 - 497. Let x(w) be the third derivative of 1/35*w**7 + 0 + 0*w**3 + 3/20*w**5 - 1/16*w**4 + 4*w**2 + 0*w - 9/80*w**l. Let x(k) = 0. What is k?
0, 1/4, 1
Let b(k) be the first derivative of -2*k**3/9 - 71. Factor b(a).
-2*a**2/3
Let c(w) = -3*w**3 - 33*w**2 + 45*w - 29. Let v(u) = -2*u**3 - 17*u**2 + 22*u - 15. Let o(r) = -3*c(r) + 5*v(r). Determine m so that o(m) = 0.
1, 12
Suppose 0 = -4*h + 29 + 3. Let z be (2/h)/((-7)/(-8)). Factor 4/7 + 2/7*w + z*w**4 - 6/7*w**2 - 2/7*w**3.
2