m/3 + 318. Factor r(c).
2*(c + 2)*(c + 4)**2/3
Let w(b) = b**3 - b + 3. Let a be w(0). Let z be a + 1 + (4 - 2). Factor 30 + z*p - 17 + 3*p**2 - 22.
3*(p - 1)*(p + 3)
Let h(a) = -2*a - 7. Let s be h(-3). Let f be (2 - 2)/(2 + s + -3). Factor f + 2/7*q**2 - 4/7*q**3 + 2/7*q**4 + 0*q.
2*q**2*(q - 1)**2/7
Let w(x) be the third derivative of x**7/210 + x**6/4 - x**5/60 - 5*x**4/4 + 78*x**2. Suppose w(z) = 0. What is z?
-30, -1, 0, 1
Suppose -4*l + 7*l = 3*o + 24, 4*o + 29 = 3*l. Let r(f) be the third derivative of -16/3*f**l + 6*f**2 + 0*f + 2/3*f**4 - 1/30*f**5 + 0. Factor r(s).
-2*(s - 4)**2
Let p be (-4)/22 + 4/22. Suppose -5*s + 5*a - 10 = 0, 0 = 2*s + a - p*a - 8. Factor -i**2 + i + 30*i**4 + 2*i**s - 31*i**4 - i**3.
-i*(i - 1)*(i + 1)**2
Let u(p) be the third derivative of 1/40*p**6 + 7/8*p**4 + 0 + 3/2*p**3 + 0*p + 1/4*p**5 + 7*p**2. Factor u(i).
3*(i + 1)**2*(i + 3)
Let n(j) be the second derivative of j**6/780 - j**5/390 + 33*j**2/2 - 48*j. Let f(w) be the first derivative of n(w). What is z in f(z) = 0?
0, 1
Let v(f) be the second derivative of 0 - 89/25*f**5 + 139/30*f**4 - 41*f + 12*f**3 - 2/105*f**7 - 20*f**2 - 13/25*f**6. Solve v(o) = 0 for o.
-10, -1, 1/2, 1
Suppose c = 3*c + v - 15, 5*c = v + 20. What is h in 6*h - 5*h - c*h**2 - 15 - 21*h = 0?
-3, -1
Let h(w) be the second derivative of -w**4/48 + w**3/4 + 27*w**2/8 + 2*w + 80. Solve h(f) = 0 for f.
-3, 9
Let l(d) be the second derivative of d**4/90 - d**3/15 - 109*d. Suppose l(k) = 0. Calculate k.
0, 3
Let h(r) be the second derivative of r**10/166320 - r**9/27720 + r**8/12320 - r**7/13860 - r**4 - r. Let j(t) be the third derivative of h(t). Factor j(n).
2*n**2*(n - 1)**3/11
Let a(v) be the second derivative of v**7/2520 - v**6/240 - v**5/30 + 3*v**4/2 + 3*v. Let t(s) be the third derivative of a(s). Factor t(l).
(l - 4)*(l + 1)
Let g(z) be the first derivative of 2*z**6/3 - 28*z**5/5 - 2*z**4 + 56*z**3/3 + 2*z**2 - 28*z - 5. Suppose g(q) = 0. Calculate q.
-1, 1, 7
Let h be ((-2)/(-5))/((-56)/35)*-1124. Factor 20*m + 22*m**3 - h*m**2 + 5*m**4 + 3*m**3 + 321*m**2.
5*m*(m + 1)*(m + 2)**2
Let -43 + 85*b + 43 - 5*b**2 = 0. What is b?
0, 17
Let t(a) be the first derivative of -a**4/21 - 32*a**3/21 - 128*a**2/7 - a - 7. Let v(c) be the first derivative of t(c). Determine m, given that v(m) = 0.
-8
Let r(l) be the first derivative of -l**5/2 + 75*l**4/8 - 45*l**3/2 + 65*l**2/4 - 31. Determine m so that r(m) = 0.
0, 1, 13
Let z(r) = -3*r**5 - 12*r**4 + 3*r**3 + 3*r**2 - 9. Let b(m) = -m**5 - 6*m**4 + m**3 + 2*m**2 - 4. Let p = 43 - 47. Let g(w) = p*z(w) + 9*b(w). Factor g(d).
3*d**2*(d - 2)*(d - 1)*(d + 1)
Let p(s) be the first derivative of -4*s**3 - 27*s**2/2 - 6*s + 169. Suppose p(q) = 0. What is q?
-2, -1/4
Let v(r) be the first derivative of 1/33*r**3 + 4/11*r + 9 + 5/22*r**2. What is x in v(x) = 0?
-4, -1
Let v(y) be the third derivative of 13/70*y**7 + 1/4*y**4 + 0*y**3 + 29*y**2 + 0 - 5/112*y**8 - 9/40*y**6 + 0*y - 1/20*y**5. Factor v(d).
-3*d*(d - 1)**3*(5*d + 2)
Let w(c) be the second derivative of c**8/84 - 2*c**7/105 - c**6/10 + c**5/15 + c**4/3 - 11*c**2/2 - c. Let p(a) be the first derivative of w(a). Factor p(s).
4*s*(s - 2)*(s - 1)*(s + 1)**2
Factor -4*z**2 - 18 - 21*z + 0*z**3 - 11*z**2 - z**3 + 7*z**2.
-(z + 2)*(z + 3)**2
Factor 3*v**2 + 100*v**3 - 46*v**3 + 10*v + 10 + 7*v - v**4 - 59*v**3.
-(v - 2)*(v + 1)**2*(v + 5)
Suppose 5*u = -0*u + 20. Let c(f) = 10*f + 8. Let v be c(0). Factor 2*l**2 + 17*l**3 + l - 13*l - v*l**2 - 5*l**3 - 3 + 9*l**u.
3*(l - 1)*(l + 1)**2*(3*l + 1)
Let l(h) = 2*h**4 + 17*h**3 + 17*h**2 + 2*h. Let b(o) = -o**4 - 9*o**3 - 9*o**2 - o. Let s(q) = 11*b(q) + 6*l(q). Factor s(a).
a*(a + 1)**3
Let k(g) be the third derivative of g**6/180 - g**5/30 - 66*g**2. Find r such that k(r) = 0.
0, 3
Let t(z) be the third derivative of -24*z**3 + 27*z**2 + 0*z + 5/168*z**8 - 187/15*z**5 + 25*z**4 - 52/105*z**7 + 41/12*z**6 + 0. Find m such that t(m) = 0.
2/5, 2, 3
Let m(r) = -3*r**3 - 8*r + 19*r - 10*r - r**2 + 2*r**3 + 1. Let z be m(1). Factor 2/3*p**5 + 0*p**4 + 0*p + z - 4/3*p**2 - 2*p**3.
2*p**2*(p - 2)*(p + 1)**2/3
Suppose 61*q**2 + 23*q**2 - 4*q**4 - 15*q**2 + 148*q**3 - 143*q + 91*q**2 - 161*q = 0. Calculate q.
-2, 0, 1, 38
Suppose 41 = 18*o - 13. Factor -105*v**o - 3*v**4 + 52*v**3 + 53*v**3.
-3*v**4
Let j(l) = 36*l**4 + 22*l + 22. Suppose -5*q = -0*q - 220. Let h(m) = -5*m**4 - 3*m - 3. Let n(a) = q*h(a) + 6*j(a). Solve n(u) = 0 for u.
0
Let t(z) be the third derivative of -z**5/40 + z**4/8 + 15*z**3/4 - 924*z**2. Solve t(s) = 0.
-3, 5
Let m(k) be the third derivative of -k**7/140 - 9*k**6/80 + 11*k**5/20 + 393*k**2. Factor m(s).
-3*s**2*(s - 2)*(s + 11)/2
Let c(q) be the second derivative of 1/75*q**6 + 1/105*q**7 + 11*q - 11/15*q**3 + 0 - 3/25*q**5 - 7/15*q**4 - 3/5*q**2. Let c(w) = 0. Calculate w.
-1, 3
Let h be 1911/3332 - 1/(-4). Solve h*k**3 + 4/17*k**4 + 12/17*k**2 - 2/17*k - 4/17 = 0 for k.
-2, -1, 1/2
Let d(o) be the third derivative of o**6/80 + 9*o**5/40 + 3*o**4/2 + 5*o**3 - 148*o**2. Let d(u) = 0. What is u?
-5, -2
Let c(d) = -4*d**3 + 59*d**2 - 896*d + 847. Let f(p) = 15*p**3 - 236*p**2 + 3585*p - 3386. Let q(k) = 22*c(k) + 6*f(k). What is j in q(j) = 0?
1, 29
Let u(m) = -31*m**5 - 5*m**4 - 5*m**3 + 5*m**2. Let v(g) = 36*g**5 + 6*g**4 + 6*g**3 - 6*g**2. Let t(i) = 7*u(i) + 6*v(i). Find a such that t(a) = 0.
-1, 0, 1
Suppose -416 = -18*l - 8*l. Suppose 7*o - 5 = l. Solve -1/2 + 1/4*k**o - 3/4*k + 0*k**2 = 0.
-1, 2
Factor 15/8*o**2 + 3/8*o**3 + 0*o + 0.
3*o**2*(o + 5)/8
Let u be 7/(-35) - (-84)/20. Let m be u - 3 - (-9)/15. Find t, given that m*t + 2/5*t**2 + 8/5 = 0.
-2
Factor -2 - 17*q + q + 12 - 32 - 4*q**2 + 6.
-4*(q + 2)**2
Factor 12/7*q**2 + 0 + 2/7*q**3 + 18/7*q.
2*q*(q + 3)**2/7
Let u = 12 - 18. Let t be 4/u - 352/(-24). Let 19*j**2 - 25*j**3 + t*j**2 - 3*j**2 - 9*j = 0. What is j?
0, 3/5
Let w be 180/35 + -8 + 3. Let k(d) be the second derivative of 0 + 5/42*d**4 + w*d**3 - 2*d - 2/7*d**2. Solve k(j) = 0.
-1, 2/5
Factor -14/3*q - 8/15*q**2 - 16/5.
-2*(q + 8)*(4*q + 3)/15
Suppose -240 = -8*z + 152. Suppose z*s - 12 = 45*s. Determine x so that -4/7*x**5 - 4/7*x**2 - 12/7*x**s + 0*x + 0 - 12/7*x**4 = 0.
-1, 0
Let t = -26 + 40. Factor -5*u**2 - u**2 + 10 - 15*u**3 + t - 41*u + 101*u.
-3*(u - 2)*(u + 2)*(5*u + 2)
Suppose 7/2*j**5 - 1/2*j**3 + 0 + 23/2*j**2 - 3*j - 23/2*j**4 = 0. Calculate j.
-1, 0, 2/7, 1, 3
Let l(c) be the third derivative of c**8/1344 + c**7/560 - c**6/120 - c**5/30 + 9*c**2. Let z(w) be the third derivative of l(w). What is i in z(i) = 0?
-1, 2/5
Let l(y) be the first derivative of y**4/2 + 10*y**3/3 - 36*y**2 + 519. Solve l(h) = 0 for h.
-9, 0, 4
Let j(n) be the second derivative of -n**6/240 - 11*n**5/160 - 43*n**4/96 - 23*n**3/16 - 9*n**2/4 - 28*n + 3. Determine y so that j(y) = 0.
-4, -3, -1
Let r(g) be the third derivative of g**5/330 - 5*g**4/132 - g**2 + 248*g. Suppose r(d) = 0. What is d?
0, 5
Let v(g) be the first derivative of g**7/1260 + g**6/180 + g**5/90 + 3*g**3 - 9. Let t(n) be the third derivative of v(n). Determine l so that t(l) = 0.
-2, -1, 0
Let x = 25333/4 + -6331. Let -3*s + 3/2*s**3 + x*s**2 - 3 - 3/4*s**4 = 0. Calculate s.
-1, 2
Let t(c) = -3210*c**2 - 88990*c - 588115. Let z(w) = -119*w**2 - 3296*w - 21782. Let x(i) = 2*t(i) - 55*z(i). Factor x(v).
5*(5*v + 66)**2
Let a(b) = -8*b**2 - 24*b + 37. Let k(s) = s**2 - 2. Let l(y) = a(y) + 5*k(y). Factor l(d).
-3*(d - 1)*(d + 9)
Let i be (((-50)/35)/5)/(1/(-7)). Factor -8*m + 28*m**2 + 20*m**3 - 30*m**3 - 12*m**2 + i*m**4 + 0*m.
2*m*(m - 2)**2*(m - 1)
Let f = -83/63 - -10/7. Let k(b) be the second derivative of 0*b**2 + f*b**3 - 6*b + 0 - 1/36*b**4. Solve k(n) = 0.
0, 2
Let f(s) be the first derivative of 0*s - 4/3*s**3 + 14*s**2 - 21. Factor f(o).
-4*o*(o - 7)
Let h be (102/63 - 2)*126/(-108). Factor -8/9*y**2 + 2/9*y**3 - h + 10/9*y.
2*(y - 2)*(y - 1)**2/9
Let s(r) be the first derivative of -r**6/255 - 3*r**5/170 - r**4/34 - r**3/51 - 26*r + 22. Let g(w) be the first derivative of s(w). Factor g(j).
-2*j*(j + 1)**3/17
Determine i so that -2/9*i**3 - 74/9*i + 4 + 40/9*i**2 = 0.
1, 18
Let n(s) = -4*s**2 - 5*s - 1. Let y(f) = 3*f**2 + 4*f + 1. Let r(q) = 5*q - 31. Let u be r(7). Let i(v) = u*n(v) + 5*y(v). Factor i(t).
-(t - 1)*(t + 1)
Let p(d