2*w**2 + 668*w + 20. Let g(o) = 11*f(o) - 8*p(o). Factor g(k).
-4*(k - 1)*(56*k + 1)
Let w(a) be the first derivative of -a**5 + 60*a**3 + 1730. Determine f, given that w(f) = 0.
-6, 0, 6
Determine n, given that -1/2*n**2 + 55*n + 111/2 = 0.
-1, 111
Let x = -23 + 27. Suppose 3*n = -3*a + 9, -x*a + 5 = a - 5*n. Factor -24*p - 2*p**2 + 40*p + 3*p**a - 8 + 72.
(p + 8)**2
Let m(c) be the second derivative of -8*c**4 - 230*c**3/3 + 50*c**2 + 6*c - 296. Factor m(n).
-4*(n + 5)*(24*n - 5)
Factor 20*u**4 + 8*u + 24*u**2 + 26*u**2 + 65*u**3 + 2*u + 5*u**2.
5*u*(u + 1)*(u + 2)*(4*u + 1)
Let r(n) = -41*n**3 + 646*n**2 - 4066*n + 3475. Let c(h) = 54*h**3 - 861*h**2 + 5422*h - 4633. Let k(b) = -7*c(b) - 9*r(b). Factor k(g).
-(g - 1)*(3*g - 34)**2
Suppose -58/17 - 2/17*i**2 - 60/17*i = 0. Calculate i.
-29, -1
Let q be ((-1)/3)/(15/(-135)). Let i be -5 + q/(((-24)/(-20))/2). Factor 0*j + 2/7*j**2 + 2/7*j**3 + i.
2*j**2*(j + 1)/7
Let g(r) be the second derivative of 5*r**4/12 - 475*r**3/6 + 12245*r. Factor g(d).
5*d*(d - 95)
Let t(f) = 10*f**3 + 17*f**2 - 11*f - 7. Let i be (-1 - 5/5) + 2 + 3. Let o(v) = -4*v**3 - 8*v**2 + 5*v + 3. Let z(y) = i*t(y) + 7*o(y). Solve z(k) = 0 for k.
0, 1/2, 2
Let z(w) = w**2 - 2*w + 3. Let s be z(0). Suppose -33 - 15 = -2*q. Factor -4*y**s + 21*y**2 + 22*y**3 + q - 42*y - 10*y**3 - 11*y**3.
-3*(y - 4)*(y - 2)*(y - 1)
Let l = -65/116 + 587/116. Let i = 503/28 - 110/7. Let -1 - 3*w - i*w**4 + l*w**3 + 7/4*w**2 = 0. What is w?
-2/3, -1/3, 1, 2
Let u(o) be the second derivative of -o**7/210 + o**6/25 + 6*o**5/25 - 4*o**4/3 - 56*o**3/5 - 144*o**2/5 + 2063*o. Factor u(n).
-(n - 6)**2*(n + 2)**3/5
Suppose 1 = -i + f, 6*f = -3*i + 31 + 11. Let v(t) be the second derivative of -5/12*t**i + 0*t**2 + 7*t + 5/6*t**3 + 0. Solve v(b) = 0.
0, 1
Let f = -404534/5 - -80912. Suppose 0*m**4 + 2/5*m**5 - 24/5*m**2 + 0*m + 0 - f*m**3 = 0. Calculate m.
-3, -1, 0, 4
Let g(v) = 96*v - 132. Let j be g(2). Suppose -10*a = -60 + j. Solve 0*k - 5/4*k**3 + 5/4*k**2 + a = 0 for k.
0, 1
Let u be (-1 - 3) + (36 - 32). Let m be (2/9 - 0)*(3 + u). Factor -4/3 - m*v**2 - 10/3*v + 4/3*v**3.
2*(v - 2)*(v + 1)*(2*v + 1)/3
Let r(q) be the third derivative of q**7/105 + 11*q**6/5 + 981*q**5/5 + 8415*q**4 + 195075*q**3 + 210*q**2. What is c in r(c) = 0?
-51, -15
Find l such that 1030*l**2 - 340*l**2 - 336*l**2 - l**3 - 135*l - 339*l**2 + 11*l**3 = 0.
-9/2, 0, 3
Factor -836/13 + 422/13*c - 2/13*c**2.
-2*(c - 209)*(c - 2)/13
Factor 0 - 32/9*f - 140/3*f**3 + 49/9*f**4 + 76/3*f**2.
f*(f - 8)*(7*f - 2)**2/9
Let j be 0 - (40/(-15))/((-2)/(-3)). Factor -2*h**4 - 3*h**j + 45 + 215*h**2 - 95*h**2 + 30*h**3 + 130*h.
-5*(h - 9)*(h + 1)**3
Suppose 64 = -2829*f + 2861*f. Solve 128000/19 - 9600/19*d + 240/19*d**f - 2/19*d**3 = 0.
40
Let d(j) be the first derivative of 5*j**7/42 - 5*j**6/6 + 9*j**5/4 - 35*j**4/12 + 5*j**3/3 + 19*j + 166. Let w(o) be the first derivative of d(o). Factor w(k).
5*k*(k - 2)*(k - 1)**3
Let r(m) = -1345*m - 1 - 2*m**2 + 125 + 1359*m. Let p be r(12). Factor -2/3*g**5 + 2/3*g**p + 0*g + 0 - 2/3*g**2 + 2/3*g**3.
-2*g**2*(g - 1)**2*(g + 1)/3
Let s(t) = -26403*t + 343241. Let c be s(13). Find r such that -1/11*r + 4/11*r**3 + 0 - 3/11*r**c = 0.
-1/4, 0, 1
Factor 5 + 111*p**2 + 21 + 2938*p**4 - 47*p**3 - 5871*p**4 + 2936*p**4 - 93*p.
(p - 13)*(p - 1)**2*(3*p - 2)
Let k = -376 + 378. Suppose 12*c**3 + 67*c**k - 5*c**4 + 5*c**4 - 59*c**2 - 4*c**5 = 0. What is c?
-1, 0, 2
Let a be (-5)/2*(108/(-99) - (-32)/110). Factor 0 - 4/3*g - 4/3*g**3 + 8/3*g**a.
-4*g*(g - 1)**2/3
Let x(v) = 322*v + 3546. Let d be x(-11). Let q(z) be the first derivative of 20/3*z + 4/9*z**3 - 23 + d*z**2. Determine k so that q(k) = 0.
-5, -1
Suppose 0 = -24*j + 25*j - 3. What is k in -4*k + 485*k**2 - 2*k - 3*k**j - 494*k**2 = 0?
-2, -1, 0
Suppose 22 = 3*t + 8*t. Factor t*h - 17*h + h**2 + 19*h.
h*(h + 4)
Let c(s) be the third derivative of 0*s**4 + 1/10*s**6 + 0*s**3 + 0 + 1/70*s**7 + 0*s**5 + 3*s + 7*s**2. Find t such that c(t) = 0.
-4, 0
Let q = 7299/32 - 51029/224. Factor 52/7 - 58/7*a**3 + q*a**4 + 162/7*a**2 - 158/7*a.
2*(a - 26)*(a - 1)**3/7
Let h(r) = 17*r**3 - 617*r**2 - 32*r - 32. Let u(n) = 14*n**3 - 494*n**2 - 26*n - 26. Let g(f) = -13*h(f) + 16*u(f). Solve g(a) = 0 for a.
-39, 0
Factor 870*w - 44*w**2 + 2/3*w**3 - 13456/3.
2*(w - 29)**2*(w - 8)/3
Let j = -24493/24 + 8175/8. Let n(u) be the second derivative of 0 + 27*u + u**4 - 2*u**2 - j*u**3. Find l such that n(l) = 0.
-1/3, 1
Let x(s) be the third derivative of s**6/180 + 119*s**5/60 + 445*s**4/2 + 7921*s**3/18 - 152*s**2. Factor x(z).
(z + 89)**2*(2*z + 1)/3
Factor -5526*f**2 + 387036*f - 3*f**3 - 1812732*f - 694426632 - 1967268*f.
-3*(f + 614)**3
Determine f, given that -5 + 5 + 4038*f**2 - 4033*f**2 - 64*f - 11*f = 0.
0, 15
Let p(d) be the first derivative of d**7/14 - 3*d**5/10 + d**3/2 + 4*d - 36. Let q(t) be the first derivative of p(t). Factor q(u).
3*u*(u - 1)**2*(u + 1)**2
Let r be 0 - (-171)/9 - -5. Let h be (2/(-28))/((-1)/r). Factor -4/7*w**3 - 20/7*w**2 + 36/7 - h*w.
-4*(w - 1)*(w + 3)**2/7
Let v be (8/10)/((-6)/(-30)). Suppose -3*d - 5*q = 20, -9 + 25 = 5*d - v*q. Factor d - 1/4*s**4 - 3/4*s + 3/4*s**3 + 1/4*s**2.
-s*(s - 3)*(s - 1)*(s + 1)/4
Let k = 77 - -159. Suppose k*w - 32 = 220*w. Determine u so that -216/5*u**w - 12/5 - 48/5*u**3 - 99/5*u = 0.
-4, -1/4
Let j(o) be the first derivative of 60*o + 88 + 20*o**2 + 5/3*o**3. Factor j(s).
5*(s + 2)*(s + 6)
Let n = -29132/33 - -29143/33. Factor -8*u**3 + 0 + n*u**4 - 80/3*u + 28*u**2.
u*(u - 20)*(u - 2)**2/3
Let w(c) be the first derivative of 2*c**3/51 + 18*c**2/17 + 112*c/17 + 85. Suppose w(l) = 0. What is l?
-14, -4
Suppose 36*n - 47/2*n**4 + 47/2*n**2 + 0 + 7/2*n**5 - 79/2*n**3 = 0. What is n?
-9/7, -1, 0, 1, 8
Find i, given that 2/3*i**2 + 4*i + 10/3 = 0.
-5, -1
Suppose x - 4*u = 22, 3*x - 12*u = -10*u + 46. Let t be 40/(-170)*(-49)/x. Factor -t*h + 2/17*h**2 + 0.
2*h*(h - 7)/17
Determine k so that 82*k**2 + 3*k**3 + 2*k**2 + 2558*k - 2399*k + 78 = 0.
-26, -1
Solve -61/7*j**3 + 0 + 680/7*j**2 + 1/7*j**4 + 1156*j = 0 for j.
-7, 0, 34
Let j = -139634/5 - -27937. Determine m so that 3/5*m**2 + j - 54/5*m = 0.
1, 17
Let o be (-447)/1192*(-3264)/324. Factor o + 1/9*x**2 - 19/9*x.
(x - 17)*(x - 2)/9
Let p(t) be the first derivative of -14*t**6 + 316*t**5/5 - 105*t**4 + 76*t**3 - 20*t**2 + 764. Suppose p(b) = 0. What is b?
0, 1/3, 1, 10/7
Factor 1616/3*k - 4/3*k**2 - 163216/3.
-4*(k - 202)**2/3
Let b(s) = s - 1. Let l be b(5). Suppose -10*z + 2*w - 68 = -120, -4*w - 47 = -z. Factor 7/5*h**l + 0 - 5*h**2 + 12/5*h**z + 6/5*h.
h*(h - 1)*(h + 3)*(7*h - 2)/5
Let p(g) be the first derivative of g**4/4 + 16*g**3/3 - 19*g**2/2 - 31*g + 15. Let j be p(-17). What is s in -s**4 - 2*s**4 - s + 3*s**j - 2*s + 3*s**2 = 0?
-1, 0, 1
Let i be (-1)/((-28)/(-21)) - (-10686)/1096. Solve 30*p**2 + 0 - i*p**3 - 28*p + 1/2*p**4 = 0.
0, 2, 14
Let m be ((9 - 6) + 10 - (23 + -2)) + -3 + 13. Let r be (4/2 - -2)*1. Factor -1/3*i**m + 0 + 5/3*i**r + 0*i - 4/3*i**3.
i**2*(i - 1)*(5*i + 1)/3
Let r = 347791 - 2434521/7. Find i such that -r*i**2 + 2/7*i**5 + 4/7*i**4 + 32/7 - 22/7*i**3 + 40/7*i = 0.
-4, -1, 2
Let j = -58 + 349/6. Suppose 3129 = -3*z - n + 3136, -3*z + 8 = 2*n. Factor -j*x**3 - 35/6*x - 25/6 - 11/6*x**z.
-(x + 1)*(x + 5)**2/6
Let l be 6723/1485 + 9/33. Let u = -43/10 + l. Factor 0 + 0*y - 1/2*y**5 + u*y**4 + y**3 + 0*y**2.
-y**3*(y - 2)*(y + 1)/2
Let o(w) be the first derivative of -w**5/30 + 5*w**4/6 - 3*w**3 + 13*w**2/3 - 91*w + 97. Let n(y) be the first derivative of o(y). Factor n(u).
-2*(u - 13)*(u - 1)**2/3
Let n(o) be the first derivative of o**4 - 64*o**3/3 + 170*o**2 - 600*o - 1003. Suppose n(r) = 0. What is r?
5, 6
Let i be (2 - 3) + (-2 - -5). Let p = -967129/4 + 241783. Factor 0 + 1/4*x**3 - 1/2*x + 3/4*x**4 - p*x**i + 1/4*x**5.
x*(x - 1)*(x + 1)**2*(x + 2)/4
Let p(v) = 3*v**5 - 17*v**4 - 3*v**3 + 58*v**2 - 37*v. Let z(s) = 2*s**5 + 2*s**4 - s**2 + s. Let l(u) = -p(u) + z(u). Factor l(b).
-b*(b - 19)*(b - 1)**2*(b + 2)
Let y(m) be the second derivative of m**6/180 + m**5/12 + m**4/2 - 32*m**3/3 + 4*m. Let i(s) be the second derivative of y(s). Find r such that i(r) = 0.
-3, -2
Let g = 9258 - 9255. Let m(y) be the first derivative of 20/3*y**g + 10*y - 25/2*y**2 - 1