 1)**2
Let y(m) be the second derivative of m**4/78 - m**3/39 - 151*m. Factor y(v).
2*v*(v - 1)/13
Let f(a) = -7*a**3 + 13 + 34*a**2 - a**3 + 27*a**2 - 83*a + 32. Let c(z) = 52*z**3 - 396*z**2 + 540*z - 292. Let m(u) = 5*c(u) + 32*f(u). Solve m(x) = 0.
1, 5
Let x = 256 - 171. Let n = -85 + x. Solve -8/9*a**4 + 0*a + n - 2/9*a**3 + 0*a**2 = 0 for a.
-1/4, 0
Let r be (((-7)/(-3))/7)/1*9. Suppose -7*p = r*p - 3*p. Factor p*q - 3/4*q**2 - 3/4*q**3 + 0.
-3*q**2*(q + 1)/4
Let v be 6/(-2) + 50/(-2 - -7). Let x(f) be the first derivative of 3/8*f**2 + 1/4*f**3 + 1/4*f - v + 1/16*f**4. Factor x(p).
(p + 1)**3/4
Let h(p) be the second derivative of p**4/32 + 7*p**3/8 + 9*p**2 + 60*p. Factor h(d).
3*(d + 6)*(d + 8)/8
Suppose 4*d = -3*k + 8*k - 6, -5*k = -d - 9. Let f(w) be the first derivative of 2/15*w**3 + 18/5*w - 5 - 6/5*w**k. Solve f(b) = 0.
3
Suppose 0 = -17*z - 2*z - 2736. Let p = z + 434/3. Factor 2/3 - 4/3*j**2 - p*j.
-2*(j + 1)*(2*j - 1)/3
Let j(n) = -13*n**3 - 7*n**2 - 16*n + 42. Let a(z) = 28*z**3 + 12*z**2 + 32*z - 85. Let v(s) = -6*a(s) - 13*j(s). Factor v(f).
(f - 1)*(f + 2)*(f + 18)
Suppose 3*q - 8 = 4*r, -3*r + 9 = q + 2*r. Solve -2*h**q - h**4 + 58*h**3 - 50*h**3 - 4*h**2 - h**4 = 0 for h.
0, 1
Let w = -125 + 128. Suppose w*k = -3*h + 15, 3*h + 2*k = 10 + 2. Factor 0*q**3 + 2*q**h + 0 - 4/3*q - 2/3*q**4.
-2*q*(q - 1)**2*(q + 2)/3
Let n(y) be the first derivative of y**4/3 - 8*y**3/9 - 8*y**2/3 + 32*y/3 + 34. Let n(w) = 0. Calculate w.
-2, 2
Let i(x) be the first derivative of -x**4/72 + x**3/9 + 26*x - 26. Let a(f) be the first derivative of i(f). Determine k, given that a(k) = 0.
0, 4
Let r(n) be the first derivative of -n**3/24 - 9*n**2/16 - 9*n/4 - 65. Factor r(k).
-(k + 3)*(k + 6)/8
Let z(t) be the third derivative of t**6/160 - 61*t**5/240 + 10*t**4/3 - 25*t**3/6 - 87*t**2 - 2. Factor z(f).
(f - 10)**2*(3*f - 1)/4
Suppose -6 = m - 3*i, 2*m - 17 - 1 = -4*i. Let g(f) be the third derivative of 0 + 10*f**2 - f**m - 1/8*f**4 + 0*f + 3/20*f**5. Factor g(l).
3*(l - 1)*(3*l + 2)
Suppose -48*p + 38*p = -27*p. Let i(j) be the first derivative of p*j - 12 - 1/2*j**2 - 1/2*j**3 - 1/8*j**4. Find l, given that i(l) = 0.
-2, -1, 0
Let n = -261059/6 + 43510. Let -1/6 + n*o**2 - 1/6*o + 1/6*o**3 = 0. Calculate o.
-1, 1
Let h = -4584 - -4586. Factor 18/11 - 6/11*d**h - 12/11*d.
-6*(d - 1)*(d + 3)/11
Let b(c) be the third derivative of -c**7/5670 + c**6/810 + c**5/90 + c**4/6 + 10*c**2. Let g(w) be the second derivative of b(w). Factor g(a).
-4*(a - 3)*(a + 1)/9
Let k be (-3 - -2) + 6 + -2. Let y be 2 - (k/(-1) + 3). What is j in -2 + 2*j**y + 0 + 0 = 0?
-1, 1
Let x(r) = r**5 - 2*r**4 + 4*r**3 + 14*r**2 - r + 8. Let i(g) = -g**3 - g**2 - g - 1. Let c(h) = 6*i(h) + x(h). Factor c(n).
(n - 1)**4*(n + 2)
Let z(v) be the first derivative of v**5/30 - v**4/6 + v**3/6 + v**2/3 - 2*v/3 + 204. Determine t so that z(t) = 0.
-1, 1, 2
Let r(p) be the third derivative of p**6/480 - p**5/40 - p**4/6 - 29*p**2. Factor r(s).
s*(s - 8)*(s + 2)/4
Factor -8 - 1/4*l**2 - 9/2*l.
-(l + 2)*(l + 16)/4
Factor -28*m - 9 - 15*m**2 + 11*m**2 - 15.
-4*(m + 1)*(m + 6)
Suppose 9*n - n = 0. Factor 54*s - 1 - 51*s + n - 3*s**2 + s**3.
(s - 1)**3
Suppose -2*b + 1017 = 61. Let a be 479 + (2 - 4) + 1. Factor b*g - a*g + 4*g**4.
4*g**4
Let c be (2 - 376/160) + 12/20. Find u such that 1/4*u**3 - c*u + 1/4*u**2 - 1/4 = 0.
-1, 1
Factor 2192/5*s - 300304/5 - 4/5*s**2.
-4*(s - 274)**2/5
Suppose -3*c + 25 - 10 = 0. Suppose -6 = 2*j - c*j. Let -14*x**3 + 1 + 12*x**5 + j*x - 7 - 6*x**2 - 6*x**2 + 7 + 11*x**4 = 0. What is x?
-1, -1/4, 1/3, 1
Let g be (2/(-10))/((-13 - (-1670)/100) + -4). Factor -2*m + 4/3 + g*m**2.
2*(m - 2)*(m - 1)/3
Let k(o) = -13*o**5 + o**4 + 18*o**3 + 6*o**2 - 12*o. Let g(l) = 4*l**5 - 6*l**3 - 2*l**2 + 4*l. Let q(b) = -14*g(b) - 4*k(b). Suppose q(n) = 0. What is n?
-2, -1, 0, 1
Let a = 67 - 61. Factor -a*u + 5*u**2 + 7 + 6 - 2*u**2 - 22.
3*(u - 3)*(u + 1)
Factor 4*v**4 + 2*v + v**4 + 15*v**2 + 15*v**3 + 3*v.
5*v*(v + 1)**3
Let r(t) be the third derivative of -1/30*t**6 + 15*t**2 + 0*t**5 + 0*t + 0*t**4 + 0 + 1/21*t**7 + 0*t**3 + 1/24*t**8. Suppose r(j) = 0. Calculate j.
-1, 0, 2/7
Factor 29/11 - 1/11*u**2 - 28/11*u.
-(u - 1)*(u + 29)/11
Let t(r) be the second derivative of 3*r**5/4 + 55*r**4/12 - 5*r**3 - 20*r**2 - 25*r + 3. Factor t(w).
5*(w - 1)*(w + 4)*(3*w + 2)
Let h = 58 + -56. Let m(f) be the first derivative of -2/39*f**3 - h - 4/13*f**2 - 8/13*f. Suppose m(o) = 0. What is o?
-2
Let m(l) = 2*l**2 - 6*l - 11. Let b(g) = -4*g**2 + 14*g + 23. Let z(n) = -3*b(n) - 5*m(n). Let z(a) = 0. Calculate a.
-1, 7
Let g(u) be the first derivative of u**7/21 - u**6/5 + u**5/5 + 18*u + 7. Let v(f) be the first derivative of g(f). What is k in v(k) = 0?
0, 1, 2
Let y(j) be the second derivative of 0 - 6/13*j**2 - 2/3*j**4 + 2/195*j**6 - 31/39*j**3 - 3/13*j**5 + 5/273*j**7 + 24*j. Let y(v) = 0. What is v?
-1, -2/5, 3
What is g in -6*g**3 - 5*g**4 - 42 - 5*g**3 + 30*g**2 + 42 + 6*g**3 = 0?
-3, 0, 2
Let o(m) be the third derivative of 1/3*m**4 + 0*m - 2*m**2 - 1/12*m**5 - 2/3*m**3 + 1/120*m**6 + 0. Factor o(k).
(k - 2)**2*(k - 1)
Let b be (-50)/(-4)*(-6)/10 - -8. Factor b*i**2 + 0 + 1/2*i**4 - i**3 + 0*i.
i**2*(i - 1)**2/2
Let n = -86 - -86. Suppose 28*i = 11*i. Suppose i - 2/5*q**3 - 1/5*q**4 + 0*q**2 + n*q = 0. What is q?
-2, 0
Let q(d) be the second derivative of 2/7*d**2 + 0 - 1/140*d**5 - 3/14*d**3 + 1/14*d**4 - 20*d. Factor q(m).
-(m - 4)*(m - 1)**2/7
Let l be 5/(-2 + 27/6). Let z(k) be the third derivative of 0*k**4 - 3*k**l + 0*k + 0*k**3 + 0 + 1/20*k**6 - 1/168*k**8 + 0*k**7 - 1/15*k**5. Factor z(p).
-2*p**2*(p - 1)**2*(p + 2)
Suppose -3*a - 4*q + 5 = -4*a, -2*a + 34 = 3*q. Let w(g) be the second derivative of -3/4*g**4 + 0 + 0*g**2 + g**3 + 0*g**5 + 1/10*g**6 - a*g. Factor w(v).
3*v*(v - 1)**2*(v + 2)
Solve -50*s**2 + 70*s**2 - 16*s - 6*s**2 - 2*s**5 - 14*s**4 + 18*s**3 = 0 for s.
-8, -1, 0, 1
Let u(k) be the second derivative of k**5/10 - 55*k**4/6 - 172*k**3/3 - 116*k**2 + k + 16. Factor u(h).
2*(h - 58)*(h + 1)*(h + 2)
Suppose 4*s + 5*y + 13 = 0, 3*s = -0*s + 2*y + 19. Let 6 + 13 - 20 + s*n**2 + 16 - 18*n = 0. What is n?
1, 5
Suppose -41*n + 7 = 7. Solve 3/4*f**5 + 3*f**4 + n + 3*f**3 + 0*f + 0*f**2 = 0.
-2, 0
Let p(v) = -3 - 4*v**3 - 11 + 22 + 3*v**2. Let n(r) = r**3 - r**2 - 3. Let o(m) = -8*n(m) - 3*p(m). Find c, given that o(c) = 0.
0, 1/4
Let i(p) be the first derivative of 2/51*p**3 + 11 + 8/17*p - 5/17*p**2. Determine c so that i(c) = 0.
1, 4
Let x = -19498/91455 + 43/201. Let u(a) be the third derivative of 1/39*a**3 + 0*a**5 + 0*a - 1/78*a**4 + 0 - x*a**7 - a**2 + 1/390*a**6. Solve u(l) = 0.
-1, 1
Let w(o) = -o - 3 + 2 + o**2 - 2 + 0*o**2. Let d be w(3). Suppose -6/13*r**4 - 2/13*r**2 + 6/13*r**d + 0*r + 2/13*r**5 + 0 = 0. What is r?
0, 1
Suppose -49*v - 54*v = -96*v. Factor 4/7*m - 4/7*m**2 + v.
-4*m*(m - 1)/7
Let b(w) = -w**3 - 52*w**2 + 104*w - 214. Let i be b(-54). Factor 2/3*x**3 + 2/3 + 2*x + i*x**2.
2*(x + 1)**3/3
Let x(u) = 18*u + 57. Let m be x(8). Suppose -m + 204 = w. What is j in 0*j - 2/3*j**2 - 2*j**4 - 2*j**w - 2/3*j**5 + 0 = 0?
-1, 0
Let j(i) be the third derivative of i**4/6 + 6*i**3 + 42*i**2. Let o be j(-9). Let 4/5*k**2 + 12/5*k + o = 0. Calculate k.
-3, 0
Let h(d) be the first derivative of 2*d**6/3 - 3*d**4 + 8*d**3/3 + 112. Find c such that h(c) = 0.
-2, 0, 1
Let b = 46396/3 + -15465. Factor -4/3 - b*m**2 - 5/3*m.
-(m + 1)*(m + 4)/3
Let a(x) = 2*x**2 - 11*x - 87. Let c be a(10). Let l(f) be the first derivative of 3/8*f + 1/24*f**c - 8 - 1/4*f**2. Suppose l(s) = 0. What is s?
1, 3
Let d(t) be the first derivative of -2*t**5/11 + 9*t**4/11 - 8*t**3/11 - 8*t**2/11 + 67. Factor d(z).
-2*z*(z - 2)**2*(5*z + 2)/11
Let -5/3*i**2 + 0 - 2/3*i - 1/3*i**4 - 4/3*i**3 = 0. Calculate i.
-2, -1, 0
Let z(h) = 4*h**4 - 16*h**3 - 46*h**2 - 56*h + 10. Let t(g) = -3*g**2 - 1. Let x(l) = -10*t(l) - z(l). Factor x(j).
-4*j*(j - 7)*(j + 1)*(j + 2)
Let w(x) be the first derivative of 0*x**3 + 0*x**2 - 1/12*x**4 + 6*x - 2. Let h(b) be the first derivative of w(b). Factor h(u).
-u**2
Let a(m) be the first derivative of m**8/672 - m**7/60 + m**6/16 - 3*m**5/40 + 10*m**2 + 3. Let u(w) be the second derivative of a(w). Solve u(f) = 0.
0, 1, 3
Suppose 10 = 4*w - 