1
Determine a so that 0*a - 115/2*a**3 + 0 + 58*a**2 - 1/2*a**4 = 0.
-116, 0, 1
Let z = 6485 + -19415/3. Let y(x) be the first derivative of -15/2*x**4 + 0*x**5 + 0*x - 15/2*x**2 + 5/6*x**6 + z*x**3 - 5. Factor y(r).
5*r*(r - 1)**3*(r + 3)
What is j in -183*j**2 - 2649*j + 0*j**4 + 23*j**3 - 171*j**3 - 41*j**2 + 2841*j - 20*j**4 = 0?
-4, 0, 3/5
Let h = 317 - 189. What is c in 239*c + h*c**3 + 128 + 26*c**4 + 296*c**2 + 103*c + 2*c**5 - 22*c = 0?
-4, -2, -1
Let p(m) = 7*m**2 - 47*m. Let b(h) = -8*h**2 + 48*h. Let k = -428 - -431. Let s(u) = k*p(u) + 2*b(u). Factor s(i).
5*i*(i - 9)
Find f, given that 285*f + 991*f + 20*f**3 - 1452 + 303*f**2 - 131*f**2 - 16*f**3 = 0.
-33, -11, 1
Determine s so that 4/7*s**5 + 2/7*s**4 + 0 - 4/7*s**3 - 2/7*s**2 + 0*s = 0.
-1, -1/2, 0, 1
Let l(q) be the first derivative of -1/24*q**4 + 0*q + 1/9*q**3 - 1/30*q**5 + 70 + 0*q**2. Solve l(n) = 0.
-2, 0, 1
Let y(x) = 21*x**2 + 53*x + 11. Let u(a) = -2*a**2 - 4*a + 1. Let r(i) = 22*u(i) + 2*y(i). Find l, given that r(l) = 0.
-2, 11
Let h = -748802 + 2246444/3. Let 2/9*w**3 - 128/9*w + 34/9*w**4 + 2/3*w**5 - 40/9 - h*w**2 = 0. What is w?
-5, -1, -2/3, 2
Let a(n) = 7*n**2 + 12*n**2 + 133*n - 31 - 23*n**2. Let w be a(33). Solve -10/9*r + 4/9*r**w - 2/3 = 0.
-1/2, 3
Let p(c) = 21*c**3 + 16*c**2 + 37*c - 178. Let y(q) = -13*q**3 - 11*q**2 - 25*q + 118. Let i(z) = -5*p(z) - 8*y(z). Factor i(j).
-(j - 9)*(j - 2)*(j + 3)
Suppose 249 = 4*l - 231. Suppose -5 = o, -5*g - o + l = 3*o. What is h in -43*h**3 + 0*h + g*h**3 + 5*h**4 - 5*h + 19*h**2 - 4*h**2 = 0?
0, 1
Let v(f) = -8*f**3 + 28*f**2 - 5. Let q(s) = -3*s**3 - 39*s**2 - s - 12. Let d be q(-13). Let j(a) = -a**3 - a**2 - 1. Let c(m) = d*v(m) - 5*j(m). Factor c(z).
-3*z**2*(z - 11)
Let p = -651 - -659. Let q(d) = 11*d - 86. Let f be q(p). Factor -9/4*i - 3/4*i**f + 3.
-3*(i - 1)*(i + 4)/4
Let c(j) be the second derivative of -2*j**2 + 0 + 3/80*j**5 + 1/6*j**4 - 5/6*j**3 - 49*j. Find v, given that c(v) = 0.
-4, -2/3, 2
Let p = 482511 - 482509. Suppose 40/11*o + 6/11*o**p - 8/11 - 32/11*o**3 + 10/11*o**4 = 0. Calculate o.
-1, 1/5, 2
Find c, given that -50/7*c - 2/7*c**2 - 44 = 0.
-14, -11
Factor -52 + 20/3*f + 1/3*f**2.
(f - 6)*(f + 26)/3
Factor -2/11*a**4 - 2/11*a**3 + 0*a + 24/11*a**2 + 0.
-2*a**2*(a - 3)*(a + 4)/11
Suppose -320/13*a - 6/13*a**4 + 168/13*a**2 + 160/13*a**3 + 0 - 2/13*a**5 = 0. Calculate a.
-10, -2, 0, 1, 8
Factor 0*y + 0 + 0*y**2 - 81/4*y**5 - 33/4*y**4 + 0*y**3.
-3*y**4*(27*y + 11)/4
Let z(x) be the first derivative of 18*x**6/5 + 432*x**5/25 + 339*x**4/20 - 129*x**3/5 - 216*x**2/5 - 12*x + 1539. Suppose z(t) = 0. Calculate t.
-2, -5/6, -1/6, 1
Find j such that 0 + 165/8*j**4 - 117/8*j**3 - 57/8*j**2 + 9/8*j**5 + 0*j = 0.
-19, -1/3, 0, 1
Let m(o) be the third derivative of -11*o**6/80 + 17*o**5/40 - 3*o**4/8 - 771*o**2. Solve m(x) = 0.
0, 6/11, 1
What is b in -177*b - 3*b**3 + 147*b + 90*b + 57*b**2 = 0?
-1, 0, 20
Let u(y) be the second derivative of 0*y**3 + 0*y**2 + 23*y - 5/42*y**7 + 0 + 5/6*y**6 - 25/12*y**4 + 1/4*y**5. Let u(j) = 0. What is j?
-1, 0, 1, 5
Let c(i) be the first derivative of 1/6*i**4 - 2/3*i**2 + 1/15*i**5 - 1/3*i**3 + 4/3*i - 245. Find y such that c(y) = 0.
-2, 1
Let g(i) be the third derivative of i**8/336 - 13*i**7/735 - 47*i**6/280 + 71*i**5/105 - 19*i**4/42 - 8*i**3/7 - 6*i**2 + 63. Find w, given that g(w) = 0.
-4, -2/7, 1, 6
Let q be -1 + (-2 + 3 + -10)*-3. Find o such that -q*o**3 + 79*o - 14 - 7*o**4 - 123*o**2 + 28*o**3 + 63*o**3 = 0.
2/7, 1, 7
Let c(y) be the second derivative of 5*y**4/9 + 529*y**3/9 - 53*y**2/3 + 3798*y. Factor c(x).
2*(x + 53)*(10*x - 1)/3
Let p(h) be the first derivative of 2*h**3/3 + 374*h**2 - 452. Suppose p(o) = 0. What is o?
-374, 0
Let t(w) = 5*w**3 + 44*w**2 + 50*w - 75. Let c(h) = 22*h**3 + 178*h**2 + 203*h - 299. Let x(b) = -6*c(b) + 26*t(b). Factor x(p).
-2*(p - 39)*(p - 1)*(p + 2)
Let s be ((-2)/5 + (180/(-50) - -4))/(-2). Let j(h) be the first derivative of 0*h + 1/10*h**5 + 11 + 1/8*h**4 + 0*h**2 + s*h**3. Let j(p) = 0. Calculate p.
-1, 0
Suppose -4*t - 1340 = -m - 2*m, 5*t - 4*m = -1676. Let c be (-3)/(-5) - (t/5 + 3). Factor -v**4 + 64 - v - c - 3*v**2 - 3*v**3.
-v*(v + 1)**3
Suppose 8 = -2*j, 0 = 2*d - 4*j - 1184 + 4924. Let f be (d/(-270) - 7)*-5. Find v such that f*v**2 + 0 - 2/3*v = 0.
0, 3
Let d(j) be the second derivative of -j**4/6 - 4066*j**3/3 - 4133089*j**2 - 8244*j. Factor d(n).
-2*(n + 2033)**2
Factor 2/7*w**2 - 82/7*w + 0.
2*w*(w - 41)/7
Let j(s) = s**2 + s + 1. Let n = 4 - 14. Let g(b) = -6*b**2 + 14*b - 10. Suppose -5*h + 1 = 2*y, y = -8*h + 5*h. Let l(c) = h*g(c) + n*j(c). Factor l(t).
-4*t*(t + 6)
Let x(d) be the second derivative of -d**9/60480 + d**8/13440 - d**7/10080 + 67*d**4/6 + 58*d + 1. Let k(a) be the third derivative of x(a). Factor k(s).
-s**2*(s - 1)**2/4
Let u = -448419/5 + 89686. Solve 1/5*m**2 + 12/5*m + u = 0 for m.
-11, -1
Let u(p) be the first derivative of -p**4/8 - 169*p**3/6 - 6699*p**2/4 + 37845*p/2 + 1890. What is w in u(w) = 0?
-87, 5
Let f(o) be the second derivative of 5/42*o**4 + 136*o + 5/21*o**3 - 1/14*o**5 + 0 - 2/7*o**2 - 1/35*o**6. Suppose f(g) = 0. What is g?
-2, -1, 1/3, 1
Let u(a) be the second derivative of 1/210*a**6 - 11/84*a**4 - 9/140*a**5 + 3/14*a**3 + 5/7*a**2 + 287*a + 0. Find l such that u(l) = 0.
-1, 1, 10
Let x(p) = -p - 16. Let h be x(-11). Let i be (-75)/(-875)*2/((-2)/h). Factor i*s**3 - 9/7*s - 6/7*s**2 + 0.
3*s*(s - 3)*(s + 1)/7
Let z = 376 + -379. Let d be (-12)/8 - (-7 - z)*1. Factor 1/4*k**2 + 25/4 - d*k.
(k - 5)**2/4
Determine i, given that 13824/11*i + 2358/11*i**3 + 2/11*i**5 - 120/11*i**4 + 0 - 16064/11*i**2 = 0.
0, 1, 16, 27
Let c(s) be the first derivative of -s**3/4 - 819*s**2/2 - 223587*s + 1215. Suppose c(d) = 0. Calculate d.
-546
Let o(r) be the first derivative of -24*r**4 - 79 - 224*r**2 + 192*r + 352/3*r**3 - 4/5*r**5 + 2/3*r**6. Find l, given that o(l) = 0.
-6, 1, 2
Suppose 68*j - 67*j - k + 11 = 0, 4*j + 3*k - 54 = 0. Factor 63/5*z**j - 6*z**4 - 816/5*z + 204/5*z**2 + 576/5 + 3/5*z**5.
3*(z - 4)**3*(z - 1)*(z + 3)/5
Suppose 22*b - 1591*b - 2*b**2 - 705*b = 0. What is b?
-1137, 0
Determine a so that 3251*a + 60*a**4 - 597*a**3 + 98*a**2 - 3656*a + 3*a**5 + 63*a**3 + 778*a**2 = 0.
-27, 0, 1, 5
Suppose 0 = -3*c + 2*c. Let n be ((-94245)/9064 - ((-108)/33 + 3))/(-3). Factor -9/2*p**2 + 3/2*p + c + n*p**3.
3*p*(3*p - 2)**2/8
Determine s so that -189/5*s - 42/5*s**2 - 1/5*s**3 - 148/5 = 0.
-37, -4, -1
Let -4/5*w**3 - 187/5*w**2 - 137/5*w + 46/5 = 0. What is w?
-46, -1, 1/4
Let t(h) be the third derivative of -h**8/2016 + 41*h**7/1260 - 19*h**6/120 - h**5/90 + 19*h**4/18 + 18*h**2 + 55*h. Let t(b) = 0. Calculate b.
-1, 0, 2, 38
Let o = -4049 + 4054. Suppose 0 + 1/2*n**2 + 0*n - 1/2*n**3 - 1/2*n**4 + 1/2*n**o = 0. Calculate n.
-1, 0, 1
Suppose g + 2*c - 43 = 0, -2*g + 2*c + 263 = 3*g. Let q = -49 + g. Factor -2 + 4 + 8*k**3 - 56*k + 10 + 28*k**q + 8*k**3.
4*(k - 1)*(k + 3)*(4*k - 1)
Let d be (-2)/8 + 740/16. Let a = d - 44. Factor -2*q - 7*q**4 + 12*q**3 + 0*q**4 - 10*q**3 + 8*q**a - q**2.
-q*(q - 1)*(q + 1)*(7*q - 2)
Let g(j) be the first derivative of 23*j**5/5 + 33*j**4/2 + 20*j**3 + 7*j**2 - 3*j - 1503. Determine k so that g(k) = 0.
-1, 3/23
Let f(o) be the first derivative of 4*o**4 + 14 + o**2 - 10/3*o**3 - 8/5*o**5 + 0*o. Factor f(d).
-2*d*(d - 1)*(2*d - 1)**2
Let f(i) be the third derivative of -i**6/40 - 119*i**5/20 - 4687*i**4/8 - 61017*i**3/2 - 18*i**2 - 138. Factor f(c).
-3*(c + 33)*(c + 43)**2
Let i(g) be the second derivative of 1/8*g**4 + 0*g**2 + 1/40*g**5 - 1/20*g**6 + 0 - 1/6*g**3 + 1/84*g**7 + 22*g. Factor i(m).
m*(m - 2)*(m - 1)**2*(m + 1)/2
Let l(r) be the second derivative of -r**6/10 + 111*r**5/20 - 391*r**4/4 + 867*r**3/2 + 1207*r. Suppose l(i) = 0. Calculate i.
0, 3, 17
Let r(w) be the first derivative of -7*w**5/15 + 3*w**4 + 2*w**3/9 - 6*w**2 + 5*w/3 - 58. Find m, given that r(m) = 0.
-1, 1/7, 1, 5
Let v be 112/7 - 290/20 - 14/12. Let q = 42 - 125/3. Factor 2/3*g + q*g**2 + v.
(g + 1)**2/3
Let x = 324017 + -324009. Factor 4/5*j**2 + 0 + x*j.
4*j*(j + 10)/5
Suppose -60 + 6 = -18*t. Let v(s) be the third derivative of 0 + 1/600*s**5 + 30*s**2 - 1/240*s**4 + 0*s**t + 0*s. Factor v(h).
h*(h - 1)/10
Let y(p) be the first derivative of -p**