. Factor 5 + f + 2*p**4 - 8*p**3 - 15*p**2 + t*p**4 - 21*p**2.
4*(p - 2)*(p + 1)**2*(3*p - 2)
Suppose 67*a - 39*a = -196. Let o be (a + 7)/(8/20*-5). Factor -2*w**4 + 8/11*w**2 + o + 6/11*w**5 + 16/11*w**3 + 0*w.
2*w**2*(w - 2)**2*(3*w + 1)/11
Suppose -4*q = -0*q - 8. Find x such that -13*x**4 + 55*x**3 - 541 - 595*x + 8*x**4 + 51 - 45*x**q = 0.
-2, -1, 7
Let u = -616/225 - -69/25. Let g(h) be the third derivative of 12*h**2 - u*h**5 + 0 - 2/9*h**3 + 1/60*h**6 - 7/36*h**4 + 0*h. Factor g(d).
2*(d - 2)*(d + 1)*(3*d + 1)/3
Suppose -184*g**3 - 768*g - 54*g**3 + 627*g**2 + 213*g**2 + 43967*g**5 - 50*g**3 + 144 - 43955*g**5 - 3*g**4 = 0. What is g?
-6, 1/4, 2
Let g(n) = -34 - 64*n - 3 + 1534*n**2 + 20*n - 1538*n**2. Let s(i) = -4*i**2 - 44*i - 36. Let k(t) = 4*g(t) - 3*s(t). Factor k(c).
-4*(c + 1)*(c + 10)
Find m, given that -132 + 754*m**2 - 3*m - 104*m**2 - 440 + m + 2*m**3 - 78*m**2 = 0.
-286, -1, 1
Let u(a) be the third derivative of a**8/2240 + a**7/120 + a**6/15 + 3*a**5/10 + 79*a**4/24 + 82*a**2. Let s(q) be the second derivative of u(q). Factor s(n).
3*(n + 2)**2*(n + 3)
Suppose v = 3*l + 21 - 30, 2*v + 6 = 0. Let k be (-2)/4 + -1 - (-7)/l. Factor 0*u + 2/9*u**k - 2/9.
2*(u - 1)*(u + 1)/9
Let a(r) = r**3 + 20*r**2. Let p be a(-20). Find t such that 4*t + 2*t**2 + 0*t - 59*t**4 - 4*t**3 + p*t**3 + 57*t**4 = 0.
-2, -1, 0, 1
Suppose -4*g = -c + 6*c + 7, 4*c + 12 = 0. What is f in 6*f**4 - f**2 - 7*f**5 + 8*f**5 + 0*f**g - f**4 - f**3 - 4*f**4 = 0?
-1, 0, 1
Let v(s) = s**4 - s**2 + 1. Suppose -9*y = 235 - 271. Let x(p) = p**5 + 4*p**4 + 10*p**3 + p**2 - 11*p - 8. Let t(i) = y*x(i) + 12*v(i). Factor t(o).
4*(o - 1)*(o + 1)**3*(o + 5)
Factor 33/5*s**2 + 9/5 + 42/5*s.
3*(s + 1)*(11*s + 3)/5
Let r(k) be the second derivative of k**5/40 - 5*k**4/2 - 187*k**3/12 - 63*k**2/2 + 65*k + 3. Let r(w) = 0. Calculate w.
-2, -1, 63
Let m(d) be the second derivative of -9/20*d**5 + 3/2*d**3 + 1/4*d**4 + 0*d**2 - 1/10*d**6 + 11*d + 0. Factor m(x).
-3*x*(x - 1)*(x + 1)*(x + 3)
Let p(v) be the second derivative of -v**5/60 - 7*v**4/36 - 535*v. Determine n so that p(n) = 0.
-7, 0
Let i(q) = 2*q**2 - 29*q + 79. Let m be i(11). Let p be ((-1269)/(-987))/(-6*m/(-16)). Factor -2/7*h**2 + 9/7 + p*h - 4/7*h**3 + 1/7*h**4.
(h - 3)**2*(h + 1)**2/7
Suppose 28*t**3 - 82/3*t - 64/3*t**2 + 24 - 2/3*t**5 - 8/3*t**4 = 0. Calculate t.
-9, -1, 1, 4
Let l(i) be the first derivative of -i**5/20 + i**4/2 - 2*i**3 + i**2/2 + 14*i + 18. Let r(g) be the second derivative of l(g). Factor r(y).
-3*(y - 2)**2
Suppose -2*v = -3*u - 23, -2*u - v + 0*v - 13 = 0. Let y be u/(-2) - (5 + -4). Determine l, given that y*l**3 - 9/2*l**2 + 7/2*l - 1/2*l**4 - 1 = 0.
1, 2
Solve 32*m - 79 + 42*m - 48*m**2 + 49*m**2 - 54 - 98 = 0 for m.
-77, 3
Let 30*w**2 - 57*w**3 - 35 + 17*w**3 + 4781*w + 5*w**4 - 4741*w = 0. What is w?
-1, 1, 7
Let k(n) be the third derivative of n**7/1365 + n**6/780 - 8*n**5/195 - 4*n**4/39 + 18*n**2. Determine s so that k(s) = 0.
-4, -1, 0, 4
Let p(x) be the third derivative of x**5/270 + 59*x**4/36 + 176*x**3/27 + x**2 - 372*x + 3. Factor p(s).
2*(s + 1)*(s + 176)/9
Let n(h) be the second derivative of 7/6*h**3 - 115*h - 1/8*h**4 + 1/60*h**6 - 2*h**2 - 1/10*h**5 + 0. Solve n(v) = 0 for v.
-2, 1, 4
Factor -2/17*p**5 + 1720/17 + 10328/17*p**2 - 6882/17*p - 6892/17*p**3 + 1728/17*p**4.
-2*(p - 860)*(p - 1)**4/17
Let h(a) = -60*a + 2040. Let k be h(34). Let p(d) be the third derivative of -10*d**2 + 0*d**3 - 1/180*d**5 + 1/108*d**4 + 1/1080*d**6 + 0 + k*d. Factor p(q).
q*(q - 2)*(q - 1)/9
Find z such that -233*z**4 - 223*z**3 - 538*z**2 + 7*z**4 + 279*z**2 + 275*z**2 - 15*z**5 + 28*z = 0.
-14, -1, -2/5, 0, 1/3
Suppose 129*l + 372 - 251 = 508. Find h such that 3/7*h**4 - 1458/7*h - 10935/7 + 66/7*h**l + 324/7*h**2 = 0.
-9, 5
Factor 20*b - 264/5 - 4/5*b**2.
-4*(b - 22)*(b - 3)/5
Suppose 5*o = -4 + 84. Suppose -o*d = -13*d - 12. Factor 50*z**3 - 21*z**4 - 48*z - 12 - 75*z**2 - 3*z**5 + 0*z**d - 107*z**3.
-3*(z + 1)**3*(z + 2)**2
Let t(l) be the first derivative of l**3/5 + 87*l**2/5 + 171*l/5 + 380. Factor t(s).
3*(s + 1)*(s + 57)/5
Let a(s) be the first derivative of -1/7*s**3 - 97 - 9/14*s**2 - 6/7*s. Factor a(d).
-3*(d + 1)*(d + 2)/7
Let q(n) = -n - 6*n**2 + 5 + 17*n**2 - 7*n**2 - 8*n**2. Let p(s) = -7*s**2 - s + 8. Let f(d) = -3*p(d) + 5*q(d). Find a such that f(a) = 0.
1
Suppose 4*t - 713 = -i, -7*i + 3*i = 5*t - 905. Let h = t - 177. Find w such that 0 + h*w - 2/7*w**2 + 2/7*w**3 = 0.
0, 1
What is a in 0 + 2*a**4 - 11/2*a**3 - 5*a - 43/2*a**2 = 0?
-2, -1/4, 0, 5
Let c = -428645 - -1285951/3. Let 0*x - c*x**3 - x**2 - 4/3*x**5 + 0 - 17/3*x**4 = 0. What is x?
-3, -1, -1/4, 0
Suppose 5*o + 27 = 2*t, -2*o - 16*t + 18*t = 36. Factor 0 - 3/7*j - 1/7*j**o - 4/7*j**2.
-j*(j + 1)*(j + 3)/7
Let f(t) be the first derivative of -8/95*t**5 + 4/19*t**2 - 24 + 0*t - 3/38*t**4 - 1/57*t**6 + 8/57*t**3. Suppose f(v) = 0. Calculate v.
-2, -1, 0, 1
Let n = -29 + -39. Let i be (-140)/112*32/n. Suppose 2/17*u**3 + 6/17 + 2/17*u**2 - i*u = 0. Calculate u.
-3, 1
Solve -408*d**4 + 201*d**4 + 351*d**2 + 208*d**4 - 177*d**3 - 175*d = 0 for d.
0, 1, 175
Let p(m) = -m**2 + 22*m + 51. Let q be p(24). Suppose 2*w + 2*w = -5*g + 17, q*w = -2*g + 11. Factor 0 + 3/2*t**w - 3*t**2 + 0*t.
3*t**2*(t - 2)/2
Let y(i) = -26*i**3 + 3*i**2 + 22*i + 53. Let k be y(-3). Let z = -712 + k. What is f in -8/9*f - 2/3*f**3 + 0 + 2/9*f**5 + 16/9*f**2 - 4/9*f**z = 0?
-2, 0, 1, 2
Let j(h) be the second derivative of 1/36*h**4 - 1/90*h**6 + 45*h - 1/60*h**5 + 0*h**2 + 1/18*h**3 + 0. Solve j(n) = 0 for n.
-1, 0, 1
Find o, given that 286*o**3 + 9*o**2 - 94*o**3 + o - 171*o**3 - 13*o = 0.
-1, 0, 4/7
Suppose 53 = l - 9*i + 4*i, 3*l - 79 = -5*i. Let h(j) be the first derivative of 3*j**5 - 25/4*j**4 + 5/2*j**2 + 5/3*j**3 + 0*j - l. Factor h(s).
5*s*(s - 1)**2*(3*s + 1)
Suppose 664*s - 8139*s**3 - 3565*s**3 - 483*s**3 - 2255*s**3 + 7569*s**4 + 6193*s**2 + 16 = 0. Calculate s.
-4/87, 1
Let i(o) be the first derivative of -o**3 + 213*o**2/2 + 900*o - 3520. Factor i(l).
-3*(l - 75)*(l + 4)
Let h(x) be the third derivative of x**8/1176 + 2*x**7/147 + 8*x**6/105 + 13*x**5/105 - 11*x**4/28 - 12*x**3/7 + 2191*x**2. Let h(r) = 0. Calculate r.
-4, -3, -1, 1
Let d(n) be the third derivative of 1/15*n**4 + n**2 + 0*n**3 + 2/75*n**5 - 1/525*n**7 - 1/300*n**6 - 2 + 0*n. Factor d(u).
-2*u*(u - 2)*(u + 1)*(u + 2)/5
Let y = 8035 - 8035. Let n(p) be the second derivative of -1/3*p**4 - p**3 + 0 - 19*p + y*p**2 - 1/30*p**5. Factor n(s).
-2*s*(s + 3)**2/3
Factor -243/4 + 3/4*n**2 + 0*n.
3*(n - 9)*(n + 9)/4
Suppose 52 - 108 = -52*s + 48. Let f be -1 + (1 - -2) + 1. Solve 2*y**f - s*y**5 + 2*y**4 - 2*y**2 - 6*y**4 + 6*y**4 = 0.
-1, 0, 1
Factor 135/4*r**2 + 243/8*r + 3/8*r**5 + 33/8*r**4 + 81/8 + 69/4*r**3.
3*(r + 1)**2*(r + 3)**3/8
Factor -2/3*c**2 - 12093362/3 + 9836/3*c.
-2*(c - 2459)**2/3
Let x = -56 + 394/7. Let h(c) be the second derivative of -5/21*c**4 - 4*c + x*c**3 + 1/35*c**5 + 18/7*c**2 + 0. Factor h(m).
4*(m - 3)**2*(m + 1)/7
Let j(r) be the second derivative of 1/90*r**6 + 2/9*r**3 - 1/60*r**5 + 0*r**2 + 0 + 99*r - 1/9*r**4. Suppose j(p) = 0. What is p?
-2, 0, 1, 2
Let w(c) = c**3 + 47*c**2 - 960*c + 3012. Let a(p) = p**3 + 43*p**2 - 960*p + 3016. Let g(h) = -6*a(h) + 7*w(h). Suppose g(r) = 0. Calculate r.
-83, 6
Let k be 200032/15040*(4/14)/((-1)/(-6)). What is z in 204/5*z**2 - 3/5*z**5 + 54/5 + 6*z**4 - k*z**3 - 171/5*z = 0?
1, 2, 3
Let d = -12 + 12. Suppose 199*s + 110168 = 110566. Suppose 9/2*f**s + 0 + 3*f - 3/2*f**4 + d*f**3 = 0. Calculate f.
-1, 0, 2
Let i(w) be the second derivative of w**6/120 - 21*w**5/40 + 4*w**4 - 131*w**3/12 + 111*w**2/8 + 3*w + 189. Factor i(s).
(s - 37)*(s - 3)*(s - 1)**2/4
Find u such that 0 - 1/6*u**3 + 29/2*u**2 - 85/3*u = 0.
0, 2, 85
Suppose r = 5*f - 1534, -8 = -r - 7. Let h = -613/2 + f. Factor 0 + 0*m + 0*m**2 + 1/2*m**4 + m**5 - h*m**3.
m**3*(m + 1)*(2*m - 1)/2
Let x(b) be the second derivative of 4 + 190/3*b**3 + 90*b**2 + 1/6*b**6 + 9*b + 265/12*b**4 + 7/2*b**5. Factor x(g).
5*(g + 1)*(g + 2)**2*(g + 9)
Let i(s) = 7*s**2 - 22*s - 143. Let r(f) = 12*f**2 - 36*f - 286. Let m(t) = 5*i(t) - 3*r(t). What is z in m(z) = 0?
-13, 11
Let j(x) = -x**4 + x**3 + 2*x - 1. Let q(m) = 3*m**4 - 4*m**3 - 7*m**2 + 4