i**2 + 2*i. Let w(k) = 6*k**3 - 20*k**2 + 178*k - 144. Suppose 3*t + 15 = 4*t. Let r(p) = t*a(p) - 3*w(p). Let r(u) = 0. What is u?
1, 12
Let c(p) be the third derivative of -p**5/270 - p**4/54 + 8*p**3/27 + p**2 + 206*p. Factor c(f).
-2*(f - 2)*(f + 4)/9
Let l be 315/234 + (-6)/(-39). Let n be (-1)/2 + (-4 + 8 - 2). Factor l*c**3 - n*c + 3/2*c**2 - 3/2.
3*(c - 1)*(c + 1)**2/2
What is r in -43 - 10379*r**2 - 10381*r**2 + 20759*r**2 + 44*r = 0?
1, 43
Let v(q) be the first derivative of -4/3*q**3 + 0*q**2 + 23*q - 1/3*q**4 + 38. Let f(l) be the first derivative of v(l). Let f(w) = 0. Calculate w.
-2, 0
Let j = -117734 + 117739. Solve 16/3*n**4 - 8/3 + 16/3*n**3 - 8/3*n**2 + 4/3*n**j - 20/3*n = 0 for n.
-2, -1, 1
Let n(k) be the third derivative of k**5/80 + 2713*k**4/16 + 7360369*k**3/8 - 476*k**2 - 2*k + 1. Factor n(r).
3*(r + 2713)**2/4
Let x = 41 + -65. Let q = x - -44. Factor -21*i - q + 24 - 4*i + 5*i**2 - 34.
5*(i - 6)*(i + 1)
Factor 8473 + 144*l - 8410 + 3*l**2 - 78*l.
3*(l + 1)*(l + 21)
Find x, given that 17*x**4 + 4*x**5 + 0*x**5 + 14880*x - 14880*x + 7*x**4 - 28*x**3 = 0.
-7, 0, 1
Let y be (-1398)/7020 - 14/(-63). Let r(j) be the third derivative of 0*j**3 + 12*j**2 + 0*j + 0 + y*j**5 - 1/78*j**4. Factor r(m).
2*m*(9*m - 2)/13
Let a(d) be the second derivative of d**4/12 + 5*d**3/2 + 8*d**2 + 6*d. Let p be a(-14). Find o such that 0*o**2 - 5*o - o**3 + 5*o - p*o + 3*o**2 = 0.
0, 1, 2
Factor -395*o**3 - 385*o**2 + 390 + 186*o - 93*o + 303*o - 5*o**4 - o.
-5*(o - 1)*(o + 1)**2*(o + 78)
Let l = -4643 + 148577/32. Let j(s) be the third derivative of 0*s - 28*s**2 + 1/12*s**3 + l*s**4 + 0 + 1/240*s**5. Let j(v) = 0. Calculate v.
-2, -1
Let p(t) be the first derivative of -t**3/2 + 22563*t**2/16 - 705*t - 399. Suppose p(c) = 0. What is c?
1/4, 1880
Let j = -35/2838 + 1997/8514. What is s in -2/3*s**2 - 10/9 - j*s**3 + 2*s = 0?
-5, 1
Suppose 4*k = -5*v + 15, 4*k = v - 5*v + 12. Factor 0 + 23*u - 18 - 16*u - 22*u - v*u**2.
-3*(u + 2)*(u + 3)
Find w such that 12/11*w**4 + 48/11*w - 12/11*w**2 + 6/11*w**5 - 54/11*w**3 + 0 = 0.
-4, -1, 0, 1, 2
Let m be -16 + (-29)/145 + 637/35. Let -2 + 6*j**3 - 5/2*j**m - 6*j + 9/2*j**4 = 0. Calculate j.
-1, -2/3, 1
Let y = 24584 + -24578. Let g(c) be the third derivative of -1/20*c**5 + 0*c + 0 + 9/2*c**3 + 1/120*c**y - 3/8*c**4 - 34*c**2. Factor g(i).
(i - 3)**2*(i + 3)
Let y(o) = -24 + 5 - 11*o**2 + 5 - 23*o + 6. Let g(k) = 57*k**2 + 114*k + 42. Let h(b) = 4*g(b) + 21*y(b). Let h(n) = 0. What is n?
-9, 0
Let w = 33946 - 33946. Let x be ((-10)/(-15))/((-1)/(-6)). Suppose w - 1/3*d + 2/3*d**x + 4/3*d**3 - 2/3*d**2 - d**5 = 0. What is d?
-1, -1/3, 0, 1
Let m = 3127 + -3124. Let z(g) be the second derivative of -1/35*g**5 + 0*g**2 + 2/21*g**m - 1/42*g**4 + 0 + 1/105*g**6 + 13*g. Determine u so that z(u) = 0.
-1, 0, 1, 2
Let b(u) = 15*u**5 + 4*u**4 + u**3 - 7*u**2 - 27*u - 15. Let n(s) = -2*s**5 - s**2 + s + 1. Let w(i) = -2*b(i) - 14*n(i). Solve w(z) = 0.
-2, -1, 2
Let t = 45/2651 + 214506/13255. What is c in -t*c**4 - 87/5*c**3 + 0 + 81/5*c**2 + 84/5*c + 3/5*c**5 = 0?
-1, 0, 1, 28
Let k(r) be the first derivative of 11*r**4/7 - 212*r**3/21 - 328*r**2/7 - 16*r - 146. Solve k(w) = 0 for w.
-2, -2/11, 7
Let f(j) be the first derivative of -2*j**5/35 - 9*j**4/7 - 54*j**3/7 - 16*j**2 - 96*j/7 + 3139. Let f(r) = 0. What is r?
-12, -4, -1
Let a(c) = 3*c**2 - 25*c + 42. Let s be ((-16)/(-4) + 2)*(13 + -12). Let w be a(s). Let -1/4*i**5 + 0*i + i**4 + w + 1/2*i**2 - 5/4*i**3 = 0. Calculate i.
0, 1, 2
Let i = -67 + 135/2. Factor -i*x**3 + 0 + 5/2*x**2 + 0*x.
-x**2*(x - 5)/2
Let f(b) = -16*b**3 - 9*b**2 - 15*b + 32. Let m(l) = 7*l**3 + 4*l**2 + 8*l - 16. Let c(a) = -4*f(a) - 9*m(a). Factor c(q).
(q - 2)**2*(q + 4)
Let u = 133 - 35. Suppose 0 = 115*s - u*s - 34. What is i in s*i**3 + 0*i**4 + 1 - 3/2*i - i**2 - 1/2*i**5 = 0?
-2, -1, 1
Let r(l) = l**2 - 477*l + 17088. Let g be r(39). Let -4*h**3 - 9/4 + 7/2*h**2 + 3/4*h**4 + g*h = 0. Calculate h.
-1, 1/3, 3
Let i(t) = 21*t - 39. Let b = 72 + -63. Let p be i(b). Determine l so that -78*l**3 - 18*l**2 + p*l**3 + 27*l - 69*l**3 = 0.
0, 3
Suppose 1802 - 11691 = 31*u. Let c be (-342)/(-87) + (-22)/u. Suppose -8*s - 10/3*s**c - 16*s**3 - 70/3*s**2 + 8/3 = 0. What is s?
-2, -1, 1/5
Let o be 6/(-63) - (-768)/126. Solve -o*q**3 - 3*q**4 + 16*q**2 + 22*q**3 - q**4 - 4*q**5 = 0.
-2, -1, 0, 2
Let j = -434/5 - -1322/15. Let x(f) be the first derivative of 6*f**2 + 8*f + j*f**3 - 16. Factor x(p).
4*(p + 1)*(p + 2)
Let u = 1/63137 + 694505/126274. Factor u*n**2 + 0 + n.
n*(11*n + 2)/2
Let w be (-9)/((-3465)/1705) - ((-8)/(-4) - 10)/(-2). What is t in 24/7*t + 45/7 + w*t**2 = 0?
-5, -3
Suppose -2*j + 11 = -m, 41*j = 36*j - 4*m + 21. Factor -j*h - 23*h + 3*h**2 - 36 + 40*h.
3*(h - 2)*(h + 6)
Suppose -35 + 7 = -4*j. Let r be 31/j + (-8)/((-40)/(-15)). Factor 22/7*a + 2/7*a**3 + 2*a**2 + r.
2*(a + 1)**2*(a + 5)/7
Suppose s - 10 = 3*v, 2*v - 30 = -3*s - 2*v. Let f(i) = s - 33*i - 6*i - 22 + 156. Let l(w) = -w**2 + 79*w - 289. Let x(m) = 5*f(m) + 3*l(m). Factor x(g).
-3*(g - 7)**2
Suppose -3*k + 6*k = 4*r - 193, 146 = 3*r - 2*k. Suppose 5*q - q - 20 = 0. Factor 56*g - q*g**3 - 24*g - r*g + 25*g**2.
-5*g*(g - 4)*(g - 1)
Let x(m) be the second derivative of 0*m**2 + 0 + 1/90*m**5 + 26/27*m**3 + 165*m + 5/18*m**4. Factor x(t).
2*t*(t + 2)*(t + 13)/9
Factor -3*n**2 + 15331*n + 0*n**2 - 2*n**2 - 12161*n - 502445.
-5*(n - 317)**2
Suppose 838 = -11*y - 4277. Let n be (-2)/3 + (-403)/y. Factor 0 + n*j**2 - 1/5*j**4 - 3/5*j**3 + 3/5*j.
-j*(j - 1)*(j + 1)*(j + 3)/5
Solve -8/5*o**2 + 12/5*o**3 - 8/5 - 28/5*o = 0.
-1, -1/3, 2
Let d(k) be the third derivative of -1/630*k**5 + 0*k**3 + 0*k - 82*k**2 + 0 + 1/84*k**4. Solve d(c) = 0.
0, 3
Suppose -p = -4*v - 52, -35*v + 32 = 2*p - 37*v. Determine t so that 0 + 18/5*t**3 + 12/5*t**p + 3/5*t**5 + 12/5*t**2 + 3/5*t = 0.
-1, 0
Let q = -407193/28 - -14541. Let p = -6/7 - q. Factor 3/2*h + 0*h**2 - p*h**4 + 3/4 - 3/2*h**3.
-3*(h - 1)*(h + 1)**3/4
Let r = 25774 + -25770. Suppose 2*m - 4*m = 0. Factor m*t**2 - 1/2*t - 1/4*t**r + 1/2*t**3 + 1/4.
-(t - 1)**3*(t + 1)/4
Let q(v) = 3*v**2 + 12*v + 10. Let u = -7 - -11. Suppose 13 = u*t - 15. Let j(l) = 9*l**2 + 36*l + 29. Let m(x) = t*q(x) - 2*j(x). Let m(z) = 0. Calculate z.
-2
Let t(f) be the first derivative of 3*f**5/5 + 15*f**4/4 - 47*f**3 + 117*f**2/2 + 270*f - 1982. Let t(n) = 0. Calculate n.
-10, -1, 3
Suppose x = -3*y + 2*x + 2, 2*y - 2*x + 4 = 0. Let u = 4420 - 4417. Solve 0 + 1/12*p**u - 1/12*p**y - 1/6*p = 0.
-1, 0, 2
Let c(p) be the third derivative of -p**5/140 + 25*p**4/14 + 981*p**3/14 + 2397*p**2. Let c(h) = 0. Calculate h.
-9, 109
Let w(b) be the first derivative of 16/3*b**3 - 1/3*b**4 - 5*b - 32*b**2 + 18. Let j(l) be the first derivative of w(l). Factor j(n).
-4*(n - 4)**2
Let i(m) be the second derivative of 0 - 3/20*m**5 - 4*m**3 - 7/4*m**4 - 91*m + 24*m**2. Factor i(j).
-3*(j - 1)*(j + 4)**2
Find y such that 280/3 + 22/3*y**4 + 104*y**3 + 592*y + 1354/3*y**2 = 0.
-7, -5, -2, -2/11
Let r(t) be the second derivative of t**7/105 - 26*t**6/75 + 38*t**5/25 + 116*t**4/3 + 2816*t**3/15 + 2048*t**2/5 + 832*t - 2. Suppose r(b) = 0. Calculate b.
-2, 16
Let x(c) = c**3 - 33*c**2 - 5. Let y(f) = -f**3 + 41*f**2 + 2*f + 6. Let b(o) = 6*x(o) + 5*y(o). Factor b(t).
t*(t + 2)*(t + 5)
Suppose -299*q - 72 = -317*q. Let d(l) be the second derivative of 5/6*l**3 + 3*l + 1/20*l**5 - 1/3*l**q + 0 - l**2. What is u in d(u) = 0?
1, 2
Let j(c) be the first derivative of c**5 + 5*c**4/2 - 200*c**3/3 + 160*c**2 + 7514. Factor j(l).
5*l*(l - 4)*(l - 2)*(l + 8)
Factor 21/4*v - 39/2*v**2 + 0.
-3*v*(26*v - 7)/4
Let j(c) be the third derivative of c**8/392 + 4*c**7/245 - 19*c**6/70 + 6*c**5/7 - 27*c**4/28 - 2*c**2 - 1406. Solve j(v) = 0 for v.
-9, 0, 1, 3
Let z(q) = 225*q**2 + 420*q + 478. Let i(b) = -43*b**2 - 84*b - 96. Let m(a) = 31*i(a) + 6*z(a). Suppose m(r) = 0. What is r?
-18/17, 6
Factor 21*s**2 + 41/2*s + 1/6*s**3 - 125/3.
(s - 1)*(s + 2)*(s + 125)/6
Factor -128*p + 125*p**2 - 25*p**2 - 4*p**3 + 69 - 59*p.
-(p - 23)*(2*p - 3)*(2*p - 1)
Determine j so that -375769/3 - 1226/3*j - 1/3*j**2 = 0.
-613
Suppose -r + 9*q - 10*q = -1, 0 = -2*r - 4*q - 6. Solve 41*a**2 + 18*a**3 - 181*a**2 + 11*a + 42*a**3 - 7*a + 76*a - r*a**5