*f**2 = 0.
10, 13
Factor 0 + 0*w - 1/4*w**3 + 0*w**2.
-w**3/4
Let i(l) = -23*l**2 + 412*l - 365. Let o(g) = 3*g + 1. Let r(n) = -8*n**2 + 128*n - 123. Let t(c) = 3*o(c) + r(c). Let y(a) = 3*i(a) - 8*t(a). Factor y(f).
-5*(f - 27)*(f - 1)
Let v(y) be the second derivative of -y**6/30 + 13*y**5/10 - 17*y**4 + 84*y**3 + 142*y. Factor v(w).
-w*(w - 14)*(w - 6)**2
Let p(r) be the second derivative of -1372/27*r**4 - 14/45*r**6 - 1/189*r**7 + 0*r**2 + 0*r**3 - 2 - 98/15*r**5 + 6*r. Let p(c) = 0. Calculate c.
-14, 0
Let i(f) = 15*f**4 + 915*f**3 + 1720*f**2 + 5. Let s(k) = 23*k**4 + 1376*k**3 + 2580*k**2 + 8. Let q(l) = -8*i(l) + 5*s(l). Determine w, given that q(w) = 0.
-86, -2, 0
Factor -61952/5 + 312/5*o**2 + 9856/5*o - 2/5*o**4 - 56/5*o**3.
-2*(o - 8)**2*(o + 22)**2/5
Suppose -269*u = -270*u + 5. Let p(j) be the third derivative of 1/10*j**u - 2*j**2 - 4/3*j**3 + 0*j + 1/60*j**6 + 0 + 0*j**4. What is s in p(s) = 0?
-2, 1
Let 1302/5*k + 32/15*k**3 - 2608/5*k**2 - 488/15 = 0. What is k?
1/4, 244
Let k(w) be the first derivative of 29 + 14*w + 49/18*w**2 - 7/27*w**3 + 1/108*w**4. Let h(a) be the first derivative of k(a). Suppose h(v) = 0. What is v?
7
Let d(a) = 2*a**2 + a + 2. Let i(y) = -3*y**2 - 15*y - 18. Let o = -248 + 249. Let l(q) = o*i(q) + 2*d(q). Factor l(z).
(z - 14)*(z + 1)
Let r(q) be the second derivative of -q**5/20 - 13*q**4/2 - 266*q**3 - 1444*q**2 + 463*q + 2. Factor r(u).
-(u + 2)*(u + 38)**2
Let h be ((-1303)/(-5))/(54/135). Let y = 653 - h. Factor -y*d**5 - 7/2*d**3 - 4*d**4 + 0 + 0*d - d**2.
-d**2*(d + 1)**2*(3*d + 2)/2
Suppose -3*q = 3*i + i - 5, 0 = 2*i + 4*q. Let w(n) = 565*n + 12995. Let g be w(-23). Let 0*o + g + 0*o**i - 1/4*o**5 - o**3 - o**4 = 0. What is o?
-2, 0
Let h(b) = 4*b**3 + 8*b**2 + 10*b - 18. Let u(n) = -n**3 - n**2 + n - 1. Suppose 0 = -16*z + 3 - 19. Let m(l) = z*h(l) - 6*u(l). What is q in m(q) = 0?
-3, 2
Factor 1/4*f**4 - 5/4*f**2 + 9/4*f**3 - 225/4*f - 125.
(f - 5)*(f + 4)*(f + 5)**2/4
Let c = -560 + -142. Let b = -700 - c. Find m, given that -320/3*m**3 + 44/3*m + 32/3*m**b - 8/3 = 0.
-2/5, 1/4
Let i be ((-60)/1050)/((-10)/14 + -1). Let c(l) be the second derivative of 0 + 0*l**2 + 6*l - 4/15*l**3 + i*l**4. Factor c(j).
2*j*(j - 4)/5
What is w in -475*w**3 - 1330*w - 377*w**4 - 355*w**4 + 2*w**5 + 1275*w**2 + 3*w**5 + 777*w**4 + 480 = 0?
-16, 1, 2, 3
Let x(f) = -2*f**3 - 20*f**2 + 234*f - 172. Let p(u) = -3*u**3 - 13*u**2 + 236*u - 171. Let r(k) = 8*p(k) - 9*x(k). Factor r(s).
-2*(s - 9)*(s - 2)*(3*s - 5)
Let c(n) be the first derivative of -n**6/960 + n**5/480 + n**4/48 - n**3/12 + 46*n**2 - 58. Let w(r) be the second derivative of c(r). What is u in w(u) = 0?
-2, 1, 2
Find l, given that -115*l**3 - 19*l + 119*l**3 - 8*l + 292*l**2 + 3*l + 96*l**3 = 0.
-3, 0, 2/25
Let c(d) be the third derivative of 31/48*d**4 + 7/18*d**5 + 49/720*d**6 - 32*d**2 + 1/2*d**3 + 0*d + 0. Factor c(h).
(h + 2)*(7*h + 3)**2/6
Suppose -200*l - 70 = -205*l. Let m be 21/l + 3/(-4)*2. Factor m - 1/4*j**3 + 1/2*j - 1/4*j**2.
-j*(j - 1)*(j + 2)/4
Factor -212*n**2 - 8672 + 125*n**2 + 91*n**2 + 4328*n.
4*(n - 2)*(n + 1084)
Suppose -3*j = 4*f + 4011, 17*j + 3*f = 13*j - 5355. Let s = j - -4024/3. Factor -1/6*i**5 + 2/3*i**3 + 0*i**4 - s + 1/3*i**2 - 1/2*i.
-(i - 2)*(i - 1)*(i + 1)**3/6
Let u(w) = -24*w**2 + 192*w + 8. Let t be u(8). Let g(a) be the first derivative of -t*a - 27 - 7/2*a**2 + 1/3*a**3. Determine j so that g(j) = 0.
-1, 8
Factor a**4 - 2*a**3 + 0 - 28/3*a**2 + 1/3*a**5 - 8*a.
a*(a - 3)*(a + 2)**3/3
Suppose 0 = -2*v - 49 + 59. Let z(h) be the first derivative of -5/9*h**3 - 1/4*h**4 - 15 + 3/5*h**v + 0*h - 1/6*h**2. Determine s so that z(s) = 0.
-1/3, 0, 1
Factor 20819*m + 5*m**2 + 28 + 668 - m**2 - 20959*m.
4*(m - 29)*(m - 6)
Let g(d) be the first derivative of -5*d**4/8 - 626*d**3/3 + 755*d**2/4 + 251*d - 1890. Solve g(h) = 0.
-251, -2/5, 1
Let -2*s**3 + 2/13*s**4 - 296/13*s**2 - 672/13 - 808/13*s = 0. Calculate s.
-4, -2, 21
Let v be (-10)/(-2*57/(-48)). Let a = v + 415/76. Find i, given that -7/2*i - 3/4*i**2 + a = 0.
-5, 1/3
Factor 4/7*t**3 + 145780/7*t - 1552/7*t**2 + 931416/7.
4*(t - 197)**2*(t + 6)/7
Solve 548*i**3 - 108*i**4 + 4*i**5 + 1800*i + 533555 + 2460*i**2 - 533555 = 0.
-2, -1, 0, 15
Let d be ((7 - 9) + 0)/(4 - (-69)/(-15)). Suppose -1/6*i**2 - d + 3/2*i = 0. Calculate i.
4, 5
Let v be ((-3)/13 - (-28593)/4589) + (-62)/12. Let i(t) be the second derivative of -1/12*t**4 - v*t**3 + 3*t**2 + 0 + 4*t. Factor i(h).
-(h - 1)*(h + 6)
Factor 4586444 - 4932*z**2 - 1410974 - 6*z**3 + 3*z**3 - 2022111*z + 888504.
-3*(z - 2)*(z + 823)**2
Let y(t) be the second derivative of t**5/30 - 52*t**4/9 - 767*t**3/9 - 370*t**2 - 2711*t. Factor y(s).
2*(s - 111)*(s + 2)*(s + 5)/3
Factor 6*u**3 - 52/3*u - u**2 + 1/3*u**4 + 12.
(u - 1)**2*(u + 2)*(u + 18)/3
Let l(r) = 14*r**2 + 20280*r - 17136560. Let h(j) = 4*j**2 + 6760*j - 5712188. Let a(m) = 20*h(m) - 6*l(m). Factor a(p).
-4*(p - 1690)**2
Suppose 0 = 3*t + 358 - 952. Let v be t/21 - 3/7. Suppose 5*m - 8 - v*m - 6*m**2 - 6*m - 4*m = 0. What is m?
-4/3, -1
Suppose -20 = -96*f + 86*f. Find p, given that -3*p**3 + 3*p**4 - 68*p**2 - 59*p**f + 5*p**3 + 95*p**2 + 63 - 2*p**4 + 30*p = 0.
-7, -1, 3
Let b(w) be the third derivative of w**8/2688 + w**7/840 - w**6/40 + w**5/30 + 5*w**4/12 - 2*w**3 + 3436*w**2. Factor b(u).
(u - 2)**3*(u + 2)*(u + 6)/8
Let m(s) be the second derivative of -s**5/10 - 91*s**4/6 + 62*s**3 - 938*s. Let m(n) = 0. Calculate n.
-93, 0, 2
Let h be ((-28)/8 - 1)*50/(-2975)*14. Factor -2/17*b**4 + 0 + 0*b - 16/17*b**3 + h*b**2.
-2*b**2*(b - 1)*(b + 9)/17
Let o(r) be the first derivative of 3*r**4 + 3320*r**3/9 + 368*r**2/3 - 528. Determine t, given that o(t) = 0.
-92, -2/9, 0
Let j(r) = -96*r + 1152. Let y(d) = -d**2. Let z be (40/16 - (-3)/6) + -7. Let g(m) = z*y(m) + 2*j(m). Factor g(k).
4*(k - 24)**2
Let s = -4864 + 4868. Let m(l) be the third derivative of 0 - 7/20*l**5 + 18*l**2 + 9/8*l**s + 0*l - l**3. Solve m(h) = 0.
2/7, 1
Let k(o) be the third derivative of -o**6/2700 - 4*o**5/225 - 16*o**4/45 + 53*o**3/3 + 95*o**2. Let d(q) be the first derivative of k(q). Solve d(h) = 0.
-8
Factor -358*v**2 - 693 - 2*v**3 - 263*v**2 - 4*v**3 + 124*v**2 + 56*v**2 + 1608*v.
-3*(v - 3)*(v + 77)*(2*v - 1)
Let c(d) be the second derivative of -d**10/10800 - d**9/18900 - d**4/4 - 39*d. Let j(m) be the third derivative of c(m). Factor j(h).
-2*h**4*(7*h + 2)/5
Let p = -21824866/18535 + -390/3707. Let d = p + 1178. Factor d*q**2 + 4*q + 10.
2*(q + 5)**2/5
Suppose 4*f - v = -0*v + 8, f - v - 2 = 0. Factor -13*q**3 - 7*q**2 + 15*q**f + 9*q**3.
-4*q**2*(q - 2)
Let h(n) = -4*n**3 - 143*n**2 - 1126*n - 982. Let m(q) = 12*q**3 + 430*q**2 + 3376*q + 2944. Let t(b) = 14*h(b) + 5*m(b). Solve t(a) = 0 for a.
-27, -9, -1
Let p = -428 + 12841/30. Let l(r) be the second derivative of -11*r + 1/12*r**4 - p*r**6 - 1/42*r**7 + 0*r**2 + 3/20*r**5 + 0 - 1/3*r**3. Factor l(n).
-n*(n - 1)**2*(n + 1)*(n + 2)
Let u(o) = o - 41. Let y be u(39). Let z(v) = v**3 + 7*v**2 + 10*v. Let r be z(y). Solve 27/2*j**2 - 3*j - 21/2*j**3 + r = 0.
0, 2/7, 1
Let s = 482 + -485. Let u(h) = -1. Suppose 0 = -3*d - b - 43, -5*d + 4*b + 16 - 99 = 0. Let k(x) = x**2 - 4*x + 8. Let q(m) = d*u(m) + s*k(m). Factor q(t).
-3*(t - 3)*(t - 1)
Let d = -1914 - -1931. Let l(u) be the third derivative of d*u**2 + 1/160*u**5 + 7/320*u**6 + 0*u + 0*u**3 + 0 + 0*u**4. Factor l(k).
3*k**2*(7*k + 1)/8
Let b be (2/42)/(820/574). Let q(g) be the third derivative of -16/3*g**3 + 0*g + b*g**6 + 0 + 2*g**4 - 2*g**2 - 2/5*g**5. Find c such that q(c) = 0.
2
Suppose -304*o**2 + 160*o**2 + 3*o**3 - 500*o**2 + o**3 = 0. Calculate o.
0, 161
Let i be (-3 - -16) + (-27)/(864/404). Factor 3/8*p**2 - 9/4 + i*p.
3*(p - 2)*(p + 3)/8
Let u(b) be the second derivative of b**5/100 + 89*b**4/20 - b**3/30 - 267*b**2/10 + 113*b. Let u(o) = 0. Calculate o.
-267, -1, 1
Factor 250*p**2 - 220*p - 252*p**2 - 4052*p - 2281248.
-2*(p + 1068)**2
Factor 182/5*k + 43 - 7*k**2 - 2/5*k**3.
-(k - 5)*(k + 1)*(2*k + 43)/5
Factor -438*j - 3/4*j**3 + 237/4*j**2 + 852.
-3*(j - 71)*(j - 4)**2/4
Let v = -158 - -161. Factor 8*z**2 - 131*z**5 + 95*z**4 + 156*z**5 + 4*z**2 + 42*z**3 + 22*z**v.
z**2*(z + 3)*(5*z + 2)**2
Let o(r) be the first derivative of 160*r**2 + r**4 + 4 - 2