 + 23*p**2 - 32*p. Let v(r) be the first derivative of k(r). Factor v(n).
(n - 1)*(n + 2)*(3*n + 1)/3
Let o(m) be the first derivative of -m**5/5 + 27*m**4/4 + 124*m**3/3 + 6862. Factor o(l).
-l**2*(l - 31)*(l + 4)
Let t(m) = m**3 + 203*m**2 + 3330*m + 3. Let w be t(-18). Suppose 4/3*p - 3*p**4 + 7*p**w + 0 - 16/3*p**2 = 0. What is p?
0, 2/3, 1
Factor -1978/9*f + 529/3 + 14/3*f**3 + 1/9*f**4 + 116/3*f**2.
(f - 3)*(f - 1)*(f + 23)**2/9
Let q(s) be the second derivative of -s**6/5 + 17*s**5/30 + 35*s**4/18 - 17*s**3/9 - 26*s**2/3 - 109*s + 43. Determine m, given that q(m) = 0.
-1, 1, 26/9
Let l(w) be the third derivative of w**8/42 + 74*w**7/105 - 14*w**6/15 - 167*w**5/15 + 40*w**4/3 + 152*w**3/3 - 172*w**2 - 3*w. Let l(t) = 0. What is t?
-19, -2, -1/2, 1, 2
Let n(b) be the first derivative of b**4 - 16*b**3 + 1024*b - 642. Factor n(z).
4*(z - 8)**2*(z + 4)
Factor -26*l - 148/3 - 2/3*l**2.
-2*(l + 2)*(l + 37)/3
Let -16/5*t**3 + 372/5*t**2 - 192 - 992/5*t = 0. Calculate t.
-3/4, 4, 20
Let s(w) = -5*w**3 - 159*w**2 - 110*w - 4542. Let l be s(-32). Factor 13/2*v + 7/2*v**l + 3 - 1/2*v**3 - 1/2*v**4.
-(v - 3)*(v + 1)**2*(v + 2)/2
Let n(h) = -h**3 - h**2. Let g = -33 + 36. Let j(m) = 679*m**3 + 409*m**2 + 72*m + 4. Let l(c) = g*j(c) + 12*n(c). What is r in l(r) = 0?
-1/3, -2/15
Let j = 36102 + -36058. Let b(c) be the third derivative of -j*c**2 + 0 + 0*c - 7/6*c**4 + 8/3*c**3 + 1/10*c**5. Factor b(i).
2*(i - 4)*(3*i - 2)
Let x(u) be the first derivative of -9/2*u**4 + 32*u**2 + 24*u + 10*u**3 + 12. Factor x(k).
-2*(k - 3)*(3*k + 2)**2
Let 950*d**3 + 80*d + 15*d**2 + 89 - 29 - 955*d**3 = 0. What is d?
-2, -1, 6
Let w(s) be the third derivative of -s**5/20 + 15*s**4/4 - 225*s**3/2 + 358*s**2. Factor w(m).
-3*(m - 15)**2
Let s(p) be the first derivative of -10/3*p + 2 + 4/3*p**2 - 2/3*p**4 - 2/15*p**5 + 4/3*p**3. Determine l, given that s(l) = 0.
-5, -1, 1
Let h(z) be the second derivative of z**5/40 + 4*z**4/3 + 28*z**3 + 288*z**2 + 165*z. Factor h(r).
(r + 8)*(r + 12)**2/2
Let n(a) = 2*a**2 + 9563*a + 9555. Let p(s) = 45*s**2 + 210385*s + 210210. Let f(l) = 65*n(l) - 3*p(l). Factor f(c).
-5*(c + 1)*(c + 1911)
Let b = 800769 - 800767. Solve 3/7*c**b + 30/7 - 33/7*c = 0 for c.
1, 10
Let m(x) = -3*x**2 - 22*x - 7. Let n = -341 + 335. Let a(f) = -f**2 - 10*f - 3. Let g(c) = n*m(c) + 14*a(c). Factor g(q).
4*q*(q - 2)
Let p = -94 + 96. Factor t + 2 - 21*t + 2*t - 3*t**p - 17.
-3*(t + 1)*(t + 5)
Suppose -2*c + 13*c + 27 = 4*p + 6*c, 3*p = -3*c. Factor 2/3*r + 0*r**4 + 4/9*r**2 - 8/9*r**p - 4/9 + 2/9*r**5.
2*(r - 1)**3*(r + 1)*(r + 2)/9
Let h = -1538723/5 + 307745. Let -h*z**3 - 18 + 2/5*z**2 + 42/5*z = 0. What is z?
-5, 3
Let i = 198300/143 + -17980/13. Factor 9/11*n**3 - 4/11 - 37/11*n**2 + i*n.
(n - 2)**2*(9*n - 1)/11
Suppose -12 = -9*w + 6. Factor 416*l**w + 2899*l - 839 - 61 - 64*l**3 - 3319*l.
-4*(l + 1)*(4*l - 15)**2
Let z(v) be the first derivative of -2*v**7/105 - v**6/5 + 3*v**5/5 + 7*v**4/3 + 185*v**2/2 + 50. Let w(i) be the second derivative of z(i). Factor w(a).
-4*a*(a - 2)*(a + 1)*(a + 7)
Factor 1356*z**3 + 4*z**2 + 1346*z**3 - 31*z**2 + 9*z**4 - 2693*z**3 + 6*z**4 + 3*z**5.
3*z**2*(z - 1)*(z + 3)**2
Let a = 17/624 + 3/208. Let w(d) be the third derivative of -1/3*d**3 + a*d**4 + 13*d**2 + 0 + 0*d + 1/60*d**5. Factor w(s).
(s - 1)*(s + 2)
Factor 3/4*c**3 - 33/2*c - 63/4*c**2 + 0.
3*c*(c - 22)*(c + 1)/4
Let i be ((-50)/(-4) - (-19)/(133/(-42))) + 343/(-98). Determine f so that -2199/5*f**i - 120 - 21/5*f**5 + 174/5*f**2 + 444*f + 426/5*f**4 = 0.
-1, 2/7, 1, 10
Let d(s) be the first derivative of -3*s**4/4 + 219*s**3 + 1332*s**2 + 2676*s - 1426. Determine o so that d(o) = 0.
-2, 223
Let n be -16*(-24)/(-704)*(-88)/30. Determine w, given that -n*w - 6/5 - 2/5*w**2 = 0.
-3, -1
Let h be 100/(-10) - (-6 - -2). Let t(i) = 0*i - 1 - i**3 + 8*i - 2*i - 5*i. Let o(q) = q**3 - 10*q**2 - q + 13. Let x(b) = h*t(b) - 2*o(b). Factor x(u).
4*(u - 1)*(u + 1)*(u + 5)
Let f be 16/(-84)*(-49)/280. Let v(i) be the third derivative of 0 + 18*i**3 + 12*i**2 + 0*i + 3/5*i**5 + f*i**6 + 9/2*i**4. Factor v(q).
4*(q + 3)**3
Let r = -41063/70 + 3904/7. Let f = 152/5 + r. Factor g + 1/2*g**3 + f*g**2 + 0.
g*(g + 1)*(g + 2)/2
Let r(n) be the third derivative of -1/12*n**5 + 31*n - 5/4*n**4 - 3*n**2 + 40/3*n**3 + 0. Find v such that r(v) = 0.
-8, 2
Suppose 5*j = -3*a + 136, -2*j + 5*a + 67 = 2*a. Let u(y) be the first derivative of 5/3*y**3 + 0*y - 5/2*y**4 + j + 0*y**2. Find c such that u(c) = 0.
0, 1/2
Let j(p) be the third derivative of p**5/90 - 19*p**4/36 - 14*p**3/3 - 514*p**2. Factor j(b).
2*(b - 21)*(b + 2)/3
Let x = 22 + 3. Let d = x + -22. What is p in -20*p + 19*p + p**3 + 0*p**d = 0?
-1, 0, 1
Solve 68/9*c + 64*c**2 + 2/9*c**4 - 68/9*c**3 - 578/9 = 0 for c.
-1, 1, 17
Let r be -51 + (-13 - (20 + -84)). Solve 1/5*h**2 - 1/5*h**4 + r + 2/5*h**3 - 2/5*h = 0.
-1, 0, 1, 2
Let u(q) be the third derivative of -5*q**3 + 55/24*q**4 - 1/24*q**6 + 0*q - 1/3*q**5 + 0 + 281*q**2. Factor u(s).
-5*(s - 1)**2*(s + 6)
Let b be (-198)/(-44)*20/3. Suppose 2*j**2 - b*j - 1011*j**3 - 6*j**2 - 5*j**2 + 1014*j**3 = 0. Calculate j.
-2, 0, 5
Let s(z) be the second derivative of z**6/60 - 11*z**5/40 + 3*z**4/2 - 3*z**3 - 663*z. Factor s(d).
d*(d - 6)*(d - 3)*(d - 2)/2
Let s(j) be the third derivative of -j**5/300 + 11*j**4/60 - 7*j**3/2 - 1272*j**2. What is u in s(u) = 0?
7, 15
Determine c so that 316/5*c**3 + 2/5*c**5 + 42/5*c**4 + 90*c - 350 + 188*c**2 = 0.
-7, -5, 1
Let w be (-2)/4*((-12)/18)/((-29)/(-174)). Determine d so that -10/9*d - 25/9 - 1/9*d**w = 0.
-5
Let k(b) be the first derivative of -b**2 + 18*b - 4. Let f be k(8). Factor -5*r - 113*r**2 + r + 115*r**f.
2*r*(r - 2)
Let j(i) be the second derivative of -2/3*i**4 - 32/9*i**2 + 2 + 56/27*i**3 - 67*i - 1/135*i**6 + 1/9*i**5. Factor j(q).
-2*(q - 4)*(q - 2)**3/9
Let x(p) be the third derivative of p**6/300 - 19*p**4/60 + 2*p**3 - 261*p**2. Determine u, given that x(u) = 0.
-5, 2, 3
Let y(x) be the second derivative of x**6/30 + 3*x**5/2 + 21*x**4 + 108*x**3 - 459*x. What is t in y(t) = 0?
-18, -6, 0
Let j = 69 - 61. Find m, given that j*m**3 - m + m - 65*m**2 - 3*m**3 = 0.
0, 13
Suppose 6 = 5*y - 4. Suppose m + 12 = 4*q, -m - m - 9 = -5*q. Determine z, given that 6*z + 10*z**2 - 10*z**4 - 2*z**5 + m + 10*z - 8*z**y - 14*z**3 = 0.
-2, -1, 1
Let c(j) be the third derivative of -j**6/15 + 119*j**5/6 + 149*j**4/12 - 3*j**2 + 1330. Factor c(i).
-2*i*(i - 149)*(4*i + 1)
Let z(x) be the first derivative of -x**7/35 - x**6/60 + 101*x**2/2 - 151. Let m(l) be the second derivative of z(l). Suppose m(y) = 0. What is y?
-1/3, 0
Let j = -40493 + 122723/3. Let l = j - 414. Factor 1/3*f - 1/3*f**3 + 2/3 - l*f**2.
-(f - 1)*(f + 1)*(f + 2)/3
Suppose -3*a - 96 = -0*a + 2*u, 5*u - 185 = 5*a. Let j be (448/a)/(-7) + (-8)/(-68). Solve 0 - 2/7*s**4 + 0*s + 12/7*s**3 - 18/7*s**j = 0 for s.
0, 3
Let x(b) be the second derivative of 0 + 9/7*b**2 + 1/42*b**4 + 118*b + 10/21*b**3. Factor x(c).
2*(c + 1)*(c + 9)/7
Let p(a) be the third derivative of -a**8/112 + 22*a**7/35 + 93*a**6/40 - 11*a**5/5 - 23*a**4/2 + 3400*a**2. Suppose p(o) = 0. What is o?
-2, -1, 0, 1, 46
Let c be (-8)/12*(7 + (14 - 130/6)). What is b in 0 - 2/9*b**2 - c*b = 0?
-2, 0
Factor -32*c**2 - 609*c + 360 - 1541*c**3 + 1561*c**3 + 21*c.
4*(c - 6)*(c + 5)*(5*c - 3)
Let -12/7 - 1/7*b**4 - 11/7*b**3 + 13/7*b**2 + 11/7*b = 0. Calculate b.
-12, -1, 1
Let b = -120487 + 120491. Factor -b*g**2 + 0 - 14/5*g**3 + 0*g - 2/5*g**4.
-2*g**2*(g + 2)*(g + 5)/5
Let b(k) be the first derivative of -k**5/450 - 11*k**4/180 + 4*k**3/15 - k**2/2 + 6*k + 102. Let w(q) be the second derivative of b(q). Factor w(l).
-2*(l - 1)*(l + 12)/15
Let t(x) be the third derivative of -x**5/160 - 13*x**4/32 + 27*x**3/16 + 8957*x**2 - 2*x. Let t(o) = 0. Calculate o.
-27, 1
Suppose -310*n - 14931 = -317*n. Factor n*x + 2*x**3 + 186*x + 65*x + 658*x + 55*x**2 - 211*x**2.
2*x*(x - 39)**2
Let x = 613 + -613. Let l be (8 + 125/(-15))*x. Let -1/4*u - 1/2*u**2 - 1/4*u**3 + l = 0. Calculate u.
-1, 0
Let q(z) = z**4 + 9*z - 1. Let t(w) = w**4 + 174*w**3 - 171*w**2 + 36*w - 4. Let a(n) = 4*q(n) - t(n). Suppose a(r) = 0. What is r?
0, 1, 57
Let u = -149652 - -149655. Solve -4/13*b - 6/13*b**4 + 8/13*b**2 - 2/13 + 4/13*b**u = 0 fo