h**5/10 + 15*h**4/4 - h**3/2 - 5*h - 53. Let a(u) be the first derivative of p(u). Factor a(f).
-3*f*(f - 1)*(14*f - 1)
Suppose -16*t + 49*t - 91 = 8. Determine d, given that -22/9*d**4 - 8/9*d**t + 0 + 0*d + 0*d**2 + 2/3*d**5 = 0.
-1/3, 0, 4
Factor 179 - 5*k**2 + 31 + 90 - 55*k.
-5*(k - 4)*(k + 15)
Factor 47 - 202*m + 30*m**2 + 28 - 28*m - 225*m.
5*(m - 15)*(6*m - 1)
Factor -16*d + 0*d**2 + 3*d**3 + 0 + 1/2*d**4.
d*(d - 2)*(d + 4)**2/2
Let p(l) be the second derivative of -50 + 0*l**2 - 1/60*l**5 + 17/9*l**3 + l + 5/12*l**4. Factor p(w).
-w*(w - 17)*(w + 2)/3
Let x = -25 + 33. Suppose 0*k - x = -4*k. Factor -53*u**3 - 192*u + 49*u**3 + 144 + 53*u**2 - u**k.
-4*(u - 6)**2*(u - 1)
Let n(w) be the second derivative of 5*w**4/18 + 367*w**3/9 + 146*w**2/3 + 2*w - 330. Find k such that n(k) = 0.
-73, -2/5
Let d be ((-7)/(-2))/((-43923)/(-484) + -89). Suppose 0 - d*p**4 - 2/3*p**3 + 4/3*p - 2/3*p**5 + 2*p**2 = 0. What is p?
-2, -1, 0, 1
Let 100/9*p + 2/3 + 280/9*p**3 - 386/9*p**2 = 0. What is p?
-1/20, 3/7, 1
Let f(x) be the first derivative of 4/35*x**5 + 12/7*x**3 + 0*x + 73 + 10/7*x**4 + 0*x**2. Find j such that f(j) = 0.
-9, -1, 0
Let r(f) be the third derivative of -f**6/900 - f**5/100 + 22*f**3 + 80*f**2. Let n(y) be the first derivative of r(y). Factor n(j).
-2*j*(j + 3)/5
Let f(a) be the third derivative of 2/25*a**5 + 0 + 1/150*a**7 + 37/600*a**6 - 8/15*a**3 + 0*a - 13/30*a**4 + 91*a**2. Let f(y) = 0. What is y?
-4, -2, -2/7, 1
Suppose 6*z = c + 8*z, 2 = -2*z. Factor -v**c + 2*v**3 - 3*v**2 - 19*v**2 - 36*v + 9*v**2.
2*v*(v - 9)*(v + 2)
Let x(t) = t - 8. Let w be x(10). Let f be 2 + -1 + (-24)/(-32) - (-41)/(-28). Suppose 40/7*h + f*h**w + 200/7 = 0. Calculate h.
-10
Let t = -3/87586 + 306557/175172. Find b such that -9/2*b - t*b**2 + 0 + 1/4*b**3 = 0.
-2, 0, 9
Suppose -468*r = -1341*r + 1746. Factor 2/5*z**r + 4/5 + 6/5*z.
2*(z + 1)*(z + 2)/5
Let -5424/7*y**2 - 640/7 + 1720/7*y**3 + 3488/7*y + 100/7*y**4 = 0. Calculate y.
-20, 2/5, 2
Suppose 3*k - 27 = -4*f, -5 = f - k - 3. Factor 0*p + 7/4*p**2 - 1/4*p**f + 0.
-p**2*(p - 7)/4
Let -3168*k - 2973*k + 1425*k**2 - 2121*k - 5*k**3 + 8400 + 1232*k = 0. Calculate k.
2, 3, 280
Let f(c) be the first derivative of 7/6*c**3 - 7/4*c**2 + 31 + c - 1/4*c**4. Factor f(k).
-(k - 2)*(k - 1)*(2*k - 1)/2
Let x = -1122630 + 1122714. Factor -1 - x*v - 7221/4*v**2 - 6889/4*v**3.
-(v + 1)*(83*v + 2)**2/4
What is s in 67059*s**3 - 67056*s**3 + 290*s**2 - 14*s + 2*s - 2184 + 256*s**2 = 0?
-182, -2, 2
Let g(c) be the second derivative of -c**5/45 + 7*c**4/27 + 2*c**3/3 - 14*c**2 - 2*c - 143. Factor g(y).
-4*(y - 7)*(y - 3)*(y + 3)/9
Let -5/2*r**5 - 515/2*r**4 + 0 + 6760*r**2 + 0*r - 6500*r**3 = 0. Calculate r.
-52, 0, 1
Suppose -50*a + 37*a + 39 = 0. Determine h so that 12 - 8*h**4 - 114*h**2 - 47*h**3 - 22*h**a + 6 - 11*h - 28*h - 4*h**4 = 0.
-3, -2, -1, 1/4
Let b(m) be the third derivative of m**5/540 - 7*m**4/54 + 65*m**3/18 - 547*m**2. Find i such that b(i) = 0.
13, 15
Suppose -320 = 18*o - 34*o. Let q(w) be the first derivative of -o*w - 184/15*w**3 - 12/5*w**4 - 24*w**2 - 4/25*w**5 + 21. Factor q(h).
-4*(h + 1)**2*(h + 5)**2/5
Let t be -17 + 20/(140/177) - 6/1. Factor 0*a - t*a**2 - 2/7*a**3 + 0.
-2*a**2*(a + 8)/7
Let k = 4/69049 - -158674574/483343. Factor k*r**3 - 14310/7*r**2 + 22275/7*r - 141/7*r**4 - 10125/7 + 3/7*r**5.
3*(r - 15)**3*(r - 1)**2/7
Let z(p) be the second derivative of p**4/3 - 14*p**3/3 - 4*p + 130. Factor z(h).
4*h*(h - 7)
Let d(z) = -z**3 - 8*z**2 + 35*z - 386. Let s be d(-13). Let g(p) be the first derivative of -12 + 3*p**2 - 2/3*p**3 - s*p. Determine c so that g(c) = 0.
1, 2
Let r(x) be the first derivative of -3*x**4/16 + 4*x**3 - 51*x**2/2 + 60*x + 1457. Determine c, given that r(c) = 0.
2, 4, 10
Let c be (-7)/28 + (-1518)/264 - -6. Factor c*h - 216/11 + 18/11*h**2 + 2/11*h**3.
2*(h - 3)*(h + 6)**2/11
Factor -6224272/9 - 292/3*b**2 + 2/9*b**3 + 42632/3*b.
2*(b - 146)**3/9
Let m(f) be the second derivative of f**4/36 - 238*f**3/9 + 28322*f**2/3 - 35*f - 11. Suppose m(g) = 0. What is g?
238
Factor 206/9*j - 344/9*j**2 + 20/9 + 118/9*j**3.
2*(j - 2)*(j - 1)*(59*j + 5)/9
Suppose 651*r - 3028 = 2180. Let h(a) be the second derivative of 1/3*a**4 + 1 + 6*a + 8/3*a**3 + r*a**2. Factor h(x).
4*(x + 2)**2
Let b = -66529 + 332646/5. Factor 11/5*c + b*c**2 + 18/5.
(c + 2)*(c + 9)/5
Let v(g) be the second derivative of -3*g**5/8 - 107*g**4/24 - 7*g**3/6 - 259*g + 11. Factor v(h).
-h*(h + 7)*(15*h + 2)/2
What is d in 12/5*d - 4 + 8/5*d**2 = 0?
-5/2, 1
Suppose -15411*w**2 - 120*w + 51*w**4 + 3*w**5 + 12*w**5 + 8082*w**2 - 462*w**3 + 8037*w**2 - 192 = 0. Calculate w.
-8, -2/5, 1, 2
Factor -3/2*b**3 + 154*b - 14*b**2 - 96.
-(b - 6)*(b + 16)*(3*b - 2)/2
Solve -6/13*v**5 + 18/13*v + 32/13*v**4 + 0 - 28/13*v**3 - 48/13*v**2 = 0.
-1, 0, 1/3, 3
Suppose 4*a - 2334 = -690. Let g = 413 - a. Factor -1/3*z**3 - z - 1/3 - z**g.
-(z + 1)**3/3
Factor -4/3*c**2 - 260/3*c + 1400/3.
-4*(c - 5)*(c + 70)/3
Let f(b) be the first derivative of b**3/6 + 23*b**2/4 - 165*b - 367. Factor f(j).
(j - 10)*(j + 33)/2
Let -7*x + 20/3 + 1/3*x**2 = 0. Calculate x.
1, 20
Let d = 297 - -37. Factor -150 - 174 - 5*m**2 + 5*m + d.
-5*(m - 2)*(m + 1)
Suppose -1 = -a - 0*a. Let c be (-1 - 6/(-21))*-7. Factor 8*l**2 - a - 2*l - 4*l**2 - c*l**2 + 0*l**2.
-(l + 1)**2
Let p be 287/((-67445)/(-282))*((-6)/(-21) + (-128)/(-42)). Solve 0*u + 28/5*u**3 + 2*u**2 - 6/5*u**p + 0 = 0.
-1/3, 0, 5
Let k(d) be the third derivative of d**5/90 + 13*d**4/12 + 40*d**3 + 583*d**2 + 3. Factor k(q).
2*(q + 15)*(q + 24)/3
Let z be (0 - -1 - 91/65)*-5. Factor -1233*q - 3*q**3 + 5832 + 54*q**z + 0*q**3 + 2*q**3 + 261*q.
-(q - 18)**3
Suppose -31/3*s**2 + 2/3 - 7/3*s**4 + 3*s + 9*s**3 = 0. What is s?
-1/7, 1, 2
Suppose 22*d + 21*d - 802 + 587 = 0. Let f(v) be the third derivative of 1/120*v**d - 16*v**2 + 0 + 5/24*v**3 - 7/96*v**4 + 0*v. Factor f(r).
(r - 1)*(2*r - 5)/4
Suppose -u - q + 23 = 0, -5*u + 7*q = 9*q - 127. Suppose 26*y - 17*y = u. Factor -l**y - 4/3 + 0*l + 7/3*l**2.
-(l - 2)*(l - 1)*(3*l + 2)/3
Let f(l) be the first derivative of -75*l**4/16 + 1830*l**3 - 4383*l**2/2 + 876*l - 3137. Factor f(h).
-3*(h - 292)*(5*h - 2)**2/4
Factor -1071*a**2 + 73560*a + 27*a**2 + 4*a**3 - 67600 - 4920*a.
4*(a - 130)**2*(a - 1)
Determine n so that 1/5*n**4 + 0 + 0*n + 312/5*n**2 - 37/5*n**3 = 0.
0, 13, 24
Let w be (-336)/280 + (-3 - 198/(-40)). Factor 1/4*b**3 + 7/4*b - w - 5/4*b**2.
(b - 3)*(b - 1)**2/4
Find f, given that 0 + 2/9*f**4 - 16/9*f**2 + 0*f - 4/9*f**3 = 0.
-2, 0, 4
Let l(u) = u**2 - u. Let q(r) = 4*r + r**2 - 10*r + r**2 + 4*r**2. Let t be 0/(-4) + 0 + 4. Let z(o) = t*q(o) - 22*l(o). Let z(c) = 0. What is c?
0, 1
Let h(z) = z**3 - 24*z**2 - 196*z + 5442. Let q be h(21). Determine s, given that 6*s**4 + 276/7*s**2 - 48/7 + 198/7*s**q + 72/7*s = 0.
-2, -1, 2/7
Let k be (2*(-6)/36)/((-1)/6). Let b**5 + 3*b + 0*b - 4*b**3 + 7*b**k - 7*b**2 - 2 + 2*b**2 = 0. What is b?
-2, -1, 1
Factor 67/12*v**2 + 3 - 17/12*v**3 + 1/12*v**4 - 29/4*v.
(v - 12)*(v - 3)*(v - 1)**2/12
Let u = 6993 + -4806. Let t = -6557/3 + u. Suppose 0*l + 5/3*l**4 + 0 + t*l**2 - 7/3*l**5 + 16/3*l**3 = 0. Calculate l.
-1, -2/7, 0, 2
Let i(j) be the second derivative of 5*j**4/18 - 11*j**3/18 - 7*j**2/2 - 541*j + 3. Factor i(a).
(a + 1)*(10*a - 21)/3
Let p(a) = -38*a**4 + 4*a**3 + 4*a**2 - 20*a + 22. Let i(t) = -28*t**4 + 5*t**3 + 2*t**2 - 21*t + 21. Let o(d) = -4*i(d) + 3*p(d). Factor o(w).
-2*(w - 1)**2*(w + 3)**2
Let c(b) = -281*b + 63. Let l be c(-5). Let u = l + -1468. Factor 2/11*j**4 - 2/11*j**2 + 0*j**3 + 0*j + u.
2*j**2*(j - 1)*(j + 1)/11
Determine g so that -406125/2*g - 74100*g**2 - 5/2*g**5 + 260*g**4 + 0 - 5335*g**3 = 0.
-5, 0, 57
Let o(j) be the first derivative of -20*j**2 + 0*j - 294 - 5/3*j**3. Factor o(s).
-5*s*(s + 8)
Let d = -81596 - -244934/3. Determine p so that 2/3*p**2 - d + 48*p = 0.
-73, 1
Let z(y) = 82*y**2 + 5981*y + 5984. Let s(b) = 58*b**2 + 4272*b + 4274. Let r(u) = -17*s(u) + 12*z(u). Factor r(o).
-2*(o + 1)*(o + 425)
Let x(h) be the third derivative of h**6/40 - 3*h**4/8 - h**3 + 1282*h**2. Factor x(t).
3*(t - 2)*(t + 1)**2
Solve 18*f**2 - 16*f + 128 - 55*f + 8*f**3 + 25*f**2 - 89*f + 5*f**2 - 4*f**4 = 0.
-4, 2
Suppose -j = -5*x + 129, -5*x = -8*x + 2*j + 83