l**2 + 27 - 15*l**3 - 4*l**5 + 5*l - 55/4*l**4. Factor z(y).
-5*(y + 1)**3*(4*y - 1)
Let f(u) be the second derivative of u**4/3 - 6*u**3 - 20*u**2 + 245*u. Factor f(a).
4*(a - 10)*(a + 1)
Let h(n) be the third derivative of 1/30*n**5 + 170*n**2 + 0*n + n**3 - 1/3*n**4 + 0. Factor h(i).
2*(i - 3)*(i - 1)
Let g(l) = l**5 + l**4 - 7*l**3 - 69*l**2 + 38*l + 102. Let s(o) = -2*o**5 + o**4 + 15*o**3 + 137*o**2 - 75*o - 205. Let b(t) = 5*g(t) + 2*s(t). Factor b(z).
(z - 2)**2*(z + 1)*(z + 5)**2
Let n(g) be the third derivative of -1/12*g**3 + 0*g**6 + 1/1260*g**7 - 1/18*g**4 + 0*g - 2*g**2 - 1/60*g**5 - 9. Find d, given that n(d) = 0.
-1, 3
Let z(w) be the first derivative of -1/12*w**4 - w**3 + 3*w + 101 + 1/6*w**2. Factor z(k).
-(k - 1)*(k + 1)*(k + 9)/3
Let f = -141164 - -988151/7. Factor -15/7*v - f*v**2 + 6.
-3*(v - 2)*(v + 7)/7
Let t(s) be the second derivative of s**6/20 - 219*s**5/20 - 149*s**4/2 - 150*s**3 - 2233*s. Solve t(z) = 0 for z.
-2, 0, 150
Let o(n) be the third derivative of n**6/420 - n**5/14 - n**4/2 + 136*n**3/21 + 104*n**2 - 2. Factor o(l).
2*(l - 17)*(l - 2)*(l + 4)/7
Let z(p) = -3*p - 64. Let c be z(21). Let w = c - -131. What is o in -3*o**3 + 0*o**4 + 3*o**5 - 9*o**4 - 3*o**w + 12*o**2 = 0?
-1, 0, 1, 4
Solve 54 + 39/2*l**2 + 60*l + 3/2*l**3 = 0.
-9, -2
Let a(v) be the third derivative of -v**8/336 - 13*v**7/315 - 59*v**6/360 + v**5/15 + 14*v**4/9 + 32*v**3/9 - v**2 + 2634. Suppose a(g) = 0. What is g?
-4, -1, 4/3
Let g(t) be the first derivative of t**6/3 - 2*t**5/5 - 9*t**4/2 - 22*t**3/3 - 4*t**2 + 7437. Suppose g(z) = 0. Calculate z.
-1, 0, 4
Suppose 556/3*p - 77284/3 - 1/3*p**2 = 0. What is p?
278
Let u(v) = -2*v**4 + 2*v**3 + 1. Let x(q) = -35*q**4 + q**3 - 58*q**2 - 16*q + 16. Let a(y) = 80*u(y) - 5*x(y). Factor a(j).
5*j*(j + 2)*(j + 8)*(3*j + 1)
Suppose -3*y = -33 - 21. Let t be 2/((28/y)/7). Solve -2 - 16 - 27*h + t*h**3 + 9*h + 33*h**2 - 6 = 0.
-4, -2/3, 1
Suppose -4*d - 4 = -3*n - 0, 24 = 5*n + 2*d. Let j be n + 72/(-20) + 23/5. Factor -121*r + 3 + 7 + 20*r**2 - j*r**3 + 96*r.
-5*(r - 2)*(r - 1)**2
Solve -219*n - 60 + 61*n - 5*n**4 + 45*n**2 + 62*n + 76*n = 0.
-3, -1, 2
Suppose -5*s = -3*x + 37, -7*s - 26 = -4*x - 5*s. Let v(o) = 2*o**2 - 8*o + 2. Let f be v(x). Factor 12 + 1/3*d**f - 4*d.
(d - 6)**2/3
Let j(p) be the first derivative of 0*p + 1/30*p**5 + 13/9*p**3 + 188 - 2*p**2 - 3/8*p**4. Factor j(t).
t*(t - 4)*(t - 3)*(t - 2)/6
Let t be (-118)/(-104) + 624/(-64) + 10. Let x = t - 41/39. Solve -1/3 - x*s**2 + 2/3*s = 0 for s.
1
Let f be ((-72)/1008)/((-2)/7). Let q(n) be the second derivative of -3/20*n**5 + 7*n - f*n**4 - 1/6*n**3 - 1/30*n**6 + 0*n**2 + 0. Find c, given that q(c) = 0.
-1, 0
Let l be (-378)/(-35) + (-2)/15 - (4 - 0). Let f(w) be the first derivative of -5/9*w**3 - l*w - 20 - 25/6*w**2. Factor f(c).
-5*(c + 1)*(c + 4)/3
Let k = 4568059/5 + -913553. Find j, given that 0 - 6/5*j**5 - k*j - 468/5*j**3 - 96/5*j**4 - 672/5*j**2 = 0.
-7, -1, 0
Let k(a) be the first derivative of 2*a**5/15 + 7*a**4/6 + 2*a**3 - 7*a**2/3 - 20*a/3 - 791. Solve k(y) = 0.
-5, -2, -1, 1
Let n = 4230/307 - 25073/1842. Suppose 1/6*o + 0 + 0*o**2 - n*o**3 = 0. Calculate o.
-1, 0, 1
Let r(k) be the second derivative of 0*k**4 + 8*k + 0*k**2 + 1/165*k**6 - 7 + 0*k**3 - 1/22*k**5. Factor r(y).
2*y**3*(y - 5)/11
Let x be 270/(-30)*2/(-6). Suppose 6*d + 5*o = d + 10, x*o + 18 = 5*d. Factor 2/13*l**2 - 4/13*l + 2/13*l**d + 0.
2*l*(l - 1)*(l + 2)/13
Let k(g) be the third derivative of -2*g**2 - 1/12*g**6 + 5/24*g**4 + 1/4*g**3 + 5/336*g**8 - 1/4*g**5 + 0 + 9/140*g**7 + 75*g. Solve k(b) = 0.
-3, -1, -1/5, 1/2, 1
Let b(d) = 2*d**2 - 158*d - 321. Let s be b(-2). Let 80/3*y + 64/3 + 32/3*y**2 + 4/3*y**s = 0. What is y?
-4, -2
Let m(o) = -10*o**5 + 307*o**4 + 875*o**3 + 276*o**2 - 872*o - 555. Let c(n) = 2*n**5 - n**4 - n**3 - 3. Let g(p) = 7*c(p) + m(p). Determine w so that g(w) = 0.
-72, -2, -1, 1
Let u(y) be the second derivative of -y**4/54 + 586*y**3/27 + 392*y**2/3 + y - 25. Factor u(w).
-2*(w - 588)*(w + 2)/9
Factor -8*s**2 + 0*s**3 + 2/3*s**4 + 0 + 32/3*s.
2*s*(s - 2)**2*(s + 4)/3
Let i(r) = 9*r**2 + 39*r + 3. Let h be i(-6). Suppose 90*m + 12*m - h*m**3 + 3*m**2 - 15*m**4 - 13 + 37 - 21*m**4 = 0. Calculate m.
-2, -4/3, -1/4, 1
Suppose -32 = -x - 2*b, 18 + 22 = 2*x - 2*b. Let l be ((-85)/30 + 2)/((-15)/x). Factor 0 + 0*r + 1/3*r**5 - 2/3*r**2 + 5/3*r**3 - l*r**4.
r**2*(r - 2)*(r - 1)**2/3
Let r(x) be the third derivative of x**6/40 + 19*x**5/10 + 99*x**4/2 + 324*x**3 - 31*x**2. What is l in r(l) = 0?
-18, -2
Determine q so that 0 + 2/17*q**5 + 16/17*q - 16/17*q**4 + 42/17*q**3 - 44/17*q**2 = 0.
0, 1, 2, 4
Suppose -5*i - 56 = -226. Let v = 38 - i. Solve v*x**3 - 4*x**2 + x**2 + x**2 - 2*x**4 = 0 for x.
0, 1
Let d(c) = c**2 + 157*c + 0*c**2 - 159*c. Let p(l) = -3*l**2 + 180*l + 2352. Let f(r) = 6*d(r) + p(r). Factor f(x).
3*(x + 28)**2
Let r = 306 - 306. Suppose 5*i - 14 - 1 = r. Factor 0*y**2 - 1/3*y**5 + 0*y**4 + 2/3*y**i + 0 - 1/3*y.
-y*(y - 1)**2*(y + 1)**2/3
Let q(b) be the third derivative of 1/96*b**4 - 1/240*b**6 + 1/1344*b**8 + 0*b - 1/840*b**7 - 1/24*b**3 + 15*b**2 + 1/120*b**5 + 0. Find u, given that q(u) = 0.
-1, 1
Let v(z) be the first derivative of 0*z - 5*z**2 - 30 - 5/4*z**4 - 5*z**3. Suppose v(r) = 0. What is r?
-2, -1, 0
Let d(b) be the third derivative of 0*b + 3/385*b**7 + 0 + 14/165*b**5 + 17/330*b**6 - 2/33*b**4 + 58*b**2 + 0*b**3. Factor d(p).
2*p*(p + 2)**2*(9*p - 2)/11
Suppose -2*z - 4 = -3*z. Let h(r) = -9*r**2 + 17*r. Let c be h(0). Find x such that -4/3*x**5 + 0 + 4/3*x**z + 0*x + 0*x**3 + c*x**2 = 0.
0, 1
Suppose -d = 3, 2*d + 49 = 2*h + 37. Let i(w) be the second derivative of 7/24*w**4 + 3/40*w**5 + 21*w + 0 - 7/12*w**h - 3/4*w**2. Factor i(p).
(p - 1)*(p + 3)*(3*p + 1)/2
Let s(n) be the second derivative of n**7/168 + 47*n**6/20 + 26507*n**5/80 + 415151*n**4/24 - 2209*n**3/2 - 103823*n**2 - 34*n. Suppose s(y) = 0. Calculate y.
-94, -1, 1
Let z(o) be the third derivative of o**2 - 5*o + 1/28*o**5 - 8/7*o**3 + 0 - 19/28*o**4. Factor z(t).
3*(t - 8)*(5*t + 2)/7
Let t(w) be the third derivative of w**6/360 - 7*w**5/60 + w**4 + 24*w**3 - 3*w**2 + 44*w. Solve t(u) = 0.
-3, 12
Let t(w) be the first derivative of -3*w**3 - 11*w + 21/2*w**2 - 1/4*w**4 - 24. Find d, given that t(d) = 0.
-11, 1
Let i = -2/937 - 1856/8433. Let p = 62/45 - i. Find k, given that 22/5*k**3 - 2*k**2 - p*k**4 + 0 - 4/5*k = 0.
-1/4, 0, 1, 2
Let l = 73209 + -73206. Factor -14/3*u + 2/3*u**2 - 2/3*u**4 + 0 + 14/3*u**l.
-2*u*(u - 7)*(u - 1)*(u + 1)/3
Let u(v) be the first derivative of 1/15*v**3 + 2/5*v**2 - 1/8*v**4 + 1/50*v**5 + 0*v - 21. Determine k so that u(k) = 0.
-1, 0, 2, 4
Let y(k) be the third derivative of 0*k + 4*k**2 - 1/1050*k**7 - 2/25*k**5 - 11 + 0*k**3 + 3/10*k**4 - 11/600*k**6. Factor y(u).
-u*(u - 1)*(u + 6)**2/5
Let w be ((-4)/(-14))/(((-16)/(-70))/2). Determine z, given that 0*z - 5*z**2 - 15/2*z**3 - w*z**4 + 0 = 0.
-2, -1, 0
Let m(b) be the first derivative of 225/4*b + 1/16*b**4 + 255/8*b**2 - 152 + 31/12*b**3. Suppose m(d) = 0. Calculate d.
-15, -1
Let z(o) = 3*o**2 + 100*o - 50. Let j be z(-34). Let c be 20/15*(-7)/((-280)/j). Solve -c*n**2 - 3 - 18/5*n = 0 for n.
-5, -1
Let m(l) be the third derivative of -37*l**2 - 1/18*l**6 + 1 - 8/315*l**7 + 1/9*l**4 + 0*l**3 + 7/45*l**5 + 0*l. Find o such that m(o) = 0.
-2, -1/4, 0, 1
Factor -7*q**2 + 2*q**2 + 362*q + 6*q**2 - 1026*q.
q*(q - 664)
Let i = -1/114204 + 380681/114204. What is r in 2/3*r - i*r**2 + 4 = 0?
-1, 6/5
Let v(d) be the third derivative of -d**7/70 + 3*d**6/5 - 103*d**5/20 + 39*d**4/2 - 38*d**3 + 1481*d**2. Determine a so that v(a) = 0.
1, 2, 19
Suppose -69 = y - 2*d - 72, -3*y - 3*d + 9 = 0. Let v(p) be the third derivative of 0 + 20/3*p**y + 14*p**2 - 1/12*p**5 - 5/12*p**4 + 0*p. Factor v(x).
-5*(x - 2)*(x + 4)
Let o(t) be the third derivative of 0*t**3 - 2 + 0*t**4 + 8*t**2 + 1/24*t**5 + 0*t. Factor o(d).
5*d**2/2
Suppose 1140*s = 1156*s - 48. Let g be (-3 + -1)/2 + 2. Let -6/5*u + 7/5*u**s + g + 19/5*u**2 = 0. What is u?
-3, 0, 2/7
Let r(n) be the second derivative of -3 - 9*n**2 + 0*n**4 - 15*n - 3/20*n**5 + 7/2*n**3. Factor r(m).
-3*(m - 2)*(m - 1)*(m + 3)
Let q(w) be the third derivative of -1/40*w**5 + 18*w**2 + 0*w + 1/16*w**4 + 3 + 0*w**3.