- p**2 + 1/2*p**4 + 2/3*p**3. Factor d(i).
-4*(i - 1)*(i + 1)**4
Let b(v) be the third derivative of v**10/75600 - v**9/10080 + v**7/630 - 3*v**5/4 + 5*v**2 + 4. Let p(g) be the third derivative of b(g). Factor p(s).
2*s*(s - 2)**2*(s + 1)
Let j(k) = -k**3 - 249*k**2 - 5996*k - 442. Let r be j(-222). What is y in 4 - 2/9*y**r - 34/9*y = 0?
-18, 1
Let t(k) be the second derivative of -k**6/45 + 25*k**5/3 - 83*k**4/6 - 7529*k. Find c, given that t(c) = 0.
0, 1, 249
Factor 1/5*b**3 + 16*b + 17/5*b**2 + 64/5.
(b + 1)*(b + 8)**2/5
Find t such that 0 - t**4 + 333*t**3 + 0 - 128*t**2 - 311*t**3 + 224*t = 0.
0, 4, 14
Let r(t) = t**2 - 3*t - 7. Let z(j) = -2*j**3 - 4*j**2 - 5*j - 5. Let p be z(-2). Let g be r(p). Factor -23*f**3 + 26*f**3 - g*f + 5*f**2 + f.
f*(f + 2)*(3*f - 1)
Suppose 179*l + 52*l - 109299 - 8973 = 0. Factor -32*v**2 + 2/3*v**3 + l*v - 8192/3.
2*(v - 16)**3/3
Factor 501*n**2 + 17*n**3 - 366*n**2 + 264 + 24 - 14*n**3 - 426*n.
3*(n - 2)*(n - 1)*(n + 48)
Let r(j) = -12*j**2 - 1672*j + 84. Let d(t) = 14*t**2 + 1673*t - 105. Let l(b) = -4*d(b) - 5*r(b). Determine p, given that l(p) = 0.
-417, 0
Let x(q) be the third derivative of -q**7/252 + 19*q**6/144 - 65*q**5/36 + 155*q**4/12 - 50*q**3 + 5*q**2 + 48. What is u in x(u) = 0?
2, 5, 6
Let z be ((-147)/(-63))/(70/60). Factor -11/2*p**3 - 25/2*p + 35/2*p**z + 0 + 1/2*p**4.
p*(p - 5)**2*(p - 1)/2
Factor u**3 - 141053 - 246*u**2 + 489*u - 141207 + 282016.
(u - 244)*(u - 1)**2
Let j = 185 + 107. Suppose 0 = 9*f - 5*f - j. Factor f*a**4 - 142*a**4 + 72*a**4 + 3*a**5.
3*a**4*(a + 1)
Let y(k) be the third derivative of -k**5/300 - 152*k**4/15 - 32*k**2 - k + 6. Solve y(j) = 0 for j.
-1216, 0
Let p(t) be the second derivative of -1477*t**4/3 - 272*t**3 + 8*t**2 - 2151*t. Factor p(c).
-4*(7*c + 2)*(211*c - 2)
Let l(s) be the first derivative of 2*s**5/15 + s**4/12 - 29*s**3/9 - 17*s**2/3 + 8*s - 988. What is v in l(v) = 0?
-3, -2, 1/2, 4
Let p(z) = 4*z + 151 + 78 - 268 + 131. Let g be p(-22). Solve -9/4*s**2 - 3/4*s - 9/4*s**3 + 0 - 3/4*s**g = 0 for s.
-1, 0
Solve -8/3*f**5 + 262/3*f**4 - 9352/3*f**2 + 864 - 1630/3*f**3 + 2712*f = 0 for f.
-4, -1/4, 1, 18
Let p(i) = -i**3 - 2*i**2 - 20. Let r(z) = -2*z**3 - 3*z**2 - 41. Let d(f) = 9*p(f) - 4*r(f). Let w(j) be the first derivative of d(j). Factor w(h).
-3*h*(h + 4)
Let n(w) be the third derivative of w**5/360 - 37*w**4/48 + 182*w**3/9 - 1727*w**2. Factor n(y).
(y - 104)*(y - 7)/6
Let l(d) be the second derivative of d**4/15 + 76*d**3/15 - 528*d**2/5 - 31*d - 6. Factor l(a).
4*(a - 6)*(a + 44)/5
What is f in 10*f**2 - f**4 - 2*f**2 + 38930*f - 38918*f - f**3 = 0?
-2, 0, 3
Let y(l) = -649*l + 651. Let w be y(1). Determine g so that -6*g - 1/3*g**w - 27 = 0.
-9
Let y(s) be the third derivative of -s**8/2352 - 557*s**7/294 - 80852*s**6/35 - 161472*s**5/35 + s**2 + 498*s. Find z, given that y(z) = 0.
-1392, -1, 0
Let z(k) be the third derivative of -4/15*k**3 - 2/75*k**6 + 7/60*k**4 + 0 + 1/75*k**5 + 0*k - 71*k**2 + 1/840*k**8 + 2/525*k**7. Let z(w) = 0. Calculate w.
-4, -1, 1
Let y(k) = 37*k**2 + 3937*k - 772245. Let a(w) = -31*w**2 - 3936*w + 772245. Let j(m) = 7*a(m) + 6*y(m). Suppose j(r) = 0. Calculate r.
393
Let x(f) = f - 18. Let u(g) = 17. Let h(b) = -5*u(b) - 4*x(b). Let v be h(-8). Find r such that -1 + 3*r**3 + 4 + 9*r**2 - 10*r + v*r = 0.
-1
Solve -16/9 + 2/3*w**4 - 5/9*w**3 + 4*w - 1/9*w**5 - 20/9*w**2 = 0 for w.
-2, 1, 2, 4
Let j(c) = -3*c**3 - 42*c**2 + 42*c. Let p = 546 - 542. Let d(m) = 5*m**3 + 42*m**2 - 43*m. Let o(i) = p*j(i) + 3*d(i). Factor o(g).
3*g*(g - 13)*(g - 1)
Let y be (-11 - -1) + 9/(-45) + 1045/100. Determine o so that -y*o**3 - 1/2*o**2 + 0 + 0*o = 0.
-2, 0
Let d(r) = 8*r**2 - 39*r + 32. Let v be d(4). Find t, given that 0 - 1/2*t**2 + t**3 + 1/2*t**v - t = 0.
-2, -1, 0, 1
Let u be (21/(-140))/(9/(-8)). What is k in -56/15*k + 392/15 + u*k**2 = 0?
14
Let o = -53 - -589/11. Let u be 300/(-55) - 0 - 43/(688/64) - -10. Let 0 + 2/11*z + o*z**3 - u*z**2 - 2/11*z**4 = 0. Calculate z.
0, 1
Let r(b) be the third derivative of b**6/216 + b**5/18 + 5*b**4/18 + 4*b**3 + 110*b**2. Let f(l) be the first derivative of r(l). Determine s so that f(s) = 0.
-2
Let -182*m - 5*m**2 - 43 + 24 - 64 + 11 = 0. Calculate m.
-36, -2/5
Let k(i) be the third derivative of -i**5/20 - 655*i**4/2 - 858050*i**3 + 11571*i**2. Determine c, given that k(c) = 0.
-1310
Let a = 375 - 372. Solve -32*n - 64*n**2 - 2*n**5 + 434*n**3 - 136*n**3 - 184*n**a - 16*n**4 - 162*n**3 = 0.
-2, 0
Let f(c) = 20*c**2 + 414*c - 522. Let d(r) = r**2 + r - 6. Let a(q) = -22*d(q) + f(q). Factor a(b).
-2*(b - 195)*(b - 1)
Let v = 133 - 1461/11. Let u = 2/248181 + 1489064/2729991. Determine s, given that -8/11*s + u + v*s**2 = 0.
1, 3
Factor -999/2*j**3 - 63423/4*j - 8019/2*j**2 - 123/4*j**4 - 3/4*j**5 - 98415/4.
-3*(j + 5)*(j + 9)**4/4
Let b = -474773275/6942258 - 2/385681. Let h = b - -620/9. Factor -2*f + h*f**2 + 3/2.
(f - 3)*(f - 1)/2
Let f be 9/4*4/3. Find z such that 203*z**4 - 24*z + 15*z**3 - f*z**2 - 200*z**4 + 9*z**3 = 0.
-8, -1, 0, 1
Factor -51*h**2 + 42 + 128 - 15*h**3 + 205*h - 62 + 47*h.
-3*(h - 3)*(h + 6)*(5*h + 2)
Let o(a) = a**4 - 3*a**3 - 4*a**2. Suppose -75 = -80*d + 65*d. Let q = -7 - -11. Let n(s) = -s**4 + 4*s**3 + 5*s**2. Let h(f) = d*o(f) + q*n(f). Factor h(m).
m**3*(m + 1)
Suppose -4*o + 20 = 2*r, 3*r = o - 5*o + 24. Suppose -3*b - 24 = -162. Find q such that -168*q**2 + 40*q**r - 2 - b*q - 40*q - 54*q**3 - 10 = 0.
-1, -2/5, -1/4, 3
Let u(j) be the second derivative of j**5/10 - 5*j**4/2 + 23*j**3/3 + 39*j**2 - 953*j. What is r in u(r) = 0?
-1, 3, 13
Let v(r) be the second derivative of -3*r**5/40 + 32*r**4 + 129*r**3 - 3520*r. Factor v(y).
-3*y*(y - 258)*(y + 2)/2
Suppose -5*o = -10*o - 4*m + 179, 3*o = -3*m + 108. Let q be (-7)/(o/(-2))*(-105)/(-28). Determine p so that 3/2*p**2 - q + 0*p = 0.
-1, 1
Let b be (-96)/(-132) - 198/3267. Factor -2/3*a**4 + 0 + 1/3*a**3 + b*a + 5/3*a**2.
-a*(a - 2)*(a + 1)*(2*a + 1)/3
Let g = -3814 + 3829. Let i(c) be the first derivative of 10/3*c**3 - 5/2*c**2 + 5/4*c**4 + g - 10*c. Factor i(j).
5*(j - 1)*(j + 1)*(j + 2)
Let o(b) be the second derivative of -b**7/189 - 7*b**6/27 - 143*b**5/30 - 2057*b**4/54 - 2662*b**3/27 + 4*b - 158. Find m such that o(m) = 0.
-11, -2, 0
Let c be (3088/(-1930))/(((-8)/15)/2). Let g(v) be the second derivative of -4/3*v**3 + c*v**2 + 0 - 1/3*v**4 + 19*v. Factor g(y).
-4*(y - 1)*(y + 3)
Suppose -22*h - 18 = -31*h. Let 5*k**2 - 11*k**h + 37 + 2*k**4 - 33 - 2*k**3 + 2*k = 0. Calculate k.
-1, 1, 2
Let p(g) be the second derivative of -25*g**2 + 51/4*g**4 + 1/6*g**6 + 0 - 53/20*g**5 - 110*g - 55/6*g**3. Suppose p(r) = 0. What is r?
-2/5, 1, 5
Let -2/7*o**2 - 570/7*o - 568/7 = 0. What is o?
-284, -1
Factor 112/3 - 116/3*y + 4/3*y**2.
4*(y - 28)*(y - 1)/3
Let t(p) be the second derivative of 0 + 11/24*p**4 + 3/8*p**2 - 9/40*p**5 - 1/168*p**7 + 7/120*p**6 - 13/24*p**3 - 113*p. Factor t(f).
-(f - 3)*(f - 1)**4/4
Let k(t) = t**3 + 40*t**2 - 2*t - 76. Let s be k(-40). Let g(u) be the third derivative of 0*u**3 + 0*u**s - 9*u**2 + 0*u + 0 - 1/12*u**5. Factor g(q).
-5*q**2
Let p = -378 - -381. Factor -4*h**p - 74*h**2 - 108 - 92*h**2 - 220*h + 50*h**2.
-4*(h + 1)**2*(h + 27)
Suppose 3*a**2 + 0 - 7/2*a + 1/2*a**3 = 0. What is a?
-7, 0, 1
Let l(x) be the second derivative of -x**5/20 - 7*x**4/3 - 55*x**3/2 + 225*x**2 - 1730*x. Factor l(d).
-(d - 2)*(d + 15)**2
Let f = 15599/22 + -709. Let r = f - -81/154. Factor -4/7*j**3 + r*j - 2/7*j**2 + 2/7.
-2*(j - 1)*(j + 1)*(2*j + 1)/7
Let f = 386 - 440. Let z be (-1 - -1)/(57 + f). Factor -5*w**2 + z + 0*w**3 + 5/3*w**4 + 10/3*w.
5*w*(w - 1)**2*(w + 2)/3
Suppose 0 = 689*a - 128*a. Let v(l) = l**3 + 4*l**2 + 2*l - 3. Let d be v(-3). Determine r, given that d*r - 1/4*r**4 + 7/8*r**3 + a - 3/8*r**5 - 1/4*r**2 = 0.
-2, 0, 1/3, 1
Let k = -67899/20 - -3395. Let z(l) be the first derivative of 0*l + k*l**2 + 14 - 1/30*l**3. Factor z(u).
-u*(u - 1)/10
Let x(a) = a**4 - a**3 - a**2 - 2*a - 2. Let u(c) = -2*c**4 - 19*c**3 - 108*c**2 - 88*c + 2. Let h(k) = -2*u(k) - 2*x(k). Determine w, given that h(w) = 0.
-10, -9, -1, 0
Let y(q) be the second derivative of q**6/480 + q**5/80 + q**4/32 + q**3/24 - 12*q**2 + 6*q. Let c(t) be the first derivative of y(t). Solve c(n) = 0 fo