 first derivative of m**4/4 + 4*m**3/3 - 5*m**2/2 + 454. Suppose p(o) = 0. Calculate o.
-5, 0, 1
Let y = 416 + -9983/24. Let u(h) be the first derivative of 2 + 0*h + y*h**6 + 3/16*h**4 - 3/20*h**5 + 0*h**2 - 1/12*h**3. Factor u(g).
g**2*(g - 1)**3/4
Let c(g) be the first derivative of -2/35*g**5 + 1/105*g**6 + 0*g**3 + 0*g**2 - 7 + 2/21*g**4 + g. Let h(l) be the first derivative of c(l). Factor h(m).
2*m**2*(m - 2)**2/7
Suppose 1/6*q**3 + 14/3 + 13/3*q**2 - 55/6*q = 0. Calculate q.
-28, 1
Let x(j) be the first derivative of 3*j**5/40 + 23*j**4/48 + 5*j**3/6 - j**2/2 + 33*j - 17. Let a(l) be the first derivative of x(l). Solve a(b) = 0 for b.
-2, 1/6
Let f(a) be the first derivative of a**5/25 - a**4/10 - a**3/5 - 131. Factor f(j).
j**2*(j - 3)*(j + 1)/5
Let p(t) = t**2 - t - 2. Let l be p(2). Suppose -4*x = -l*x - 12. Factor 2*v - 3*v**3 - x*v**3 - 2*v**4 + 0*v**4 - 2*v**4.
-2*v*(v + 1)**2*(2*v - 1)
Let j(x) be the third derivative of -x**5/4 - 35*x**4/6 - 125*x**3/6 - 74*x**2. Factor j(g).
-5*(g + 1)*(3*g + 25)
Let w(p) be the third derivative of p**9/30240 + p**8/1440 + p**7/168 + p**6/40 + p**5/15 + 2*p**2. Let j(v) be the third derivative of w(v). Factor j(n).
2*(n + 1)*(n + 3)**2
Let z(j) be the first derivative of j**4/4 - 14*j**3/3 - j**2/2 + 16*j - 17. Let d be z(14). Let 2 + 10*w**4 - 27/2*w**2 + 14*w**3 - d*w = 0. Calculate w.
-2, -2/5, 1/2
Let p be (3 - (-49)/(-15))*(-10)/6. Let t(y) be the first derivative of -8 + 4/3*y - p*y**3 + 1/3*y**4 - 2/3*y**2. Factor t(x).
4*(x - 1)**2*(x + 1)/3
Let i(s) = -4*s**3 + 5*s**2 + 4*s - 14. Let r(l) = -3*l**3 + 5*l**2 + 3*l - 11. Let x(w) = -2*i(w) + 3*r(w). Factor x(t).
-(t - 5)*(t - 1)*(t + 1)
Let z be 184/(-16) + 11 - 35/(-10). Find l such that 0*l + 0 - 15/4*l**2 - 5*l**z = 0.
-3/4, 0
Let y(v) be the third derivative of -v**5/60 - 4*v**4/3 - 128*v**3/3 - 100*v**2 - 1. Find d, given that y(d) = 0.
-16
Let z(f) = 17*f - 2*f + f + 4. Let g be z(6). Factor 3 - 75*i**3 + 96*i**2 + g*i**4 - 16*i - 3 - 105*i**3.
4*i*(i - 1)*(5*i - 2)**2
Find g, given that 63/5 - 27/5*g**2 + 33/5*g + 3/5*g**3 = 0.
-1, 3, 7
Let w(l) = -9*l**3 + 0*l - 8*l - 9*l**2 - l - 9*l**4. Let y(z) = -8*z - 38*z**4 - 10*z**3 + 30*z**4 - 9*z**2 + z**3. Let j(c) = -5*w(c) + 6*y(c). Factor j(g).
-3*g*(g + 1)**3
Let c be -29 + 12 + (-19)/(-1). Let -2/13*v**2 - 24/13 - c*v = 0. Calculate v.
-12, -1
Let q be (-2)/51*3 - 216/(-102). Factor -242/13 + 44/13*c - 2/13*c**q.
-2*(c - 11)**2/13
Suppose 2*f = 3*h + 19, -2*f + 42*h + 14 = 40*h. Factor 12/23*q**f + 0 - 18/23*q - 2/23*q**3.
-2*q*(q - 3)**2/23
Let h(j) = 12*j**3 - 48*j**2 - 477*j. Let x(p) = -3*p**3 + 9*p**2 + 119*p. Let a(i) = 5*h(i) + 21*x(i). Factor a(y).
-3*y*(y - 2)*(y + 19)
Let u(a) be the second derivative of -a**5/70 - a**4/14 + 8*a**3/7 + 80*a**2/7 - 5*a + 2. Factor u(d).
-2*(d - 5)*(d + 4)**2/7
Factor -32/5 + 0*v + 2/5*v**2.
2*(v - 4)*(v + 4)/5
Let o = -279 + 281. Let x(z) be the third derivative of 7*z**o - 1/30*z**5 + 1/18*z**4 + 0*z + 0*z**3 - 1/36*z**6 + 0. Factor x(n).
-2*n*(n + 1)*(5*n - 2)/3
Let x be 1/7 + (-260)/(-91). Determine u so that 4/9*u**2 + 14/9*u**x - 4/9 - 14/9*u = 0.
-1, -2/7, 1
Let z(k) be the second derivative of k**7/5040 - k**6/480 + k**5/120 + k**4 - 3*k. Let d(s) be the third derivative of z(s). Suppose d(o) = 0. What is o?
1, 2
Let c = -319 + 962/3. Factor 1/3 + 5/3*b**4 + c*b + 10/3*b**2 + 1/3*b**5 + 10/3*b**3.
(b + 1)**5/3
Let g(a) be the second derivative of -a**5 - 115*a**4/12 - 35*a**3/3 + 25*a**2/2 + 149*a. Factor g(n).
-5*(n + 1)*(n + 5)*(4*n - 1)
Let c(s) be the second derivative of -s**7/2520 - s**6/60 - 3*s**5/10 + s**4 - 13*s. Let q(u) be the third derivative of c(u). Find v, given that q(v) = 0.
-6
Let p(x) = 5*x**2 - 10*x + 30. Let t(c) = 2*c**2 - 4*c + 15. Let g(d) = -3*p(d) + 7*t(d). Factor g(f).
-(f - 5)*(f + 3)
Let o = -78 - -71. Let y(m) = 3*m**2 + 21*m. Let l be y(o). Factor -2/3*b - 4*b**3 + 8/3*b**4 + 8/3*b**2 + l - 2/3*b**5.
-2*b*(b - 1)**4/3
Let g(t) be the first derivative of -t**6/27 + 62*t**5/9 - 4055*t**4/9 + 32980*t**3/3 - 30345*t**2 + 29478*t + 436. Find p such that g(p) = 0.
1, 51
Let y(w) be the third derivative of w**9/105840 - w**8/47040 - 3*w**4/8 - 13*w**2. Let b(f) be the second derivative of y(f). Find k, given that b(k) = 0.
0, 1
Let s(b) be the first derivative of b**3/5 - 177*b**2/10 - 36*b - 49. Factor s(d).
3*(d - 60)*(d + 1)/5
Let y be (2 + -2)/(1 + 1). Let k(j) be the first derivative of 1 - 2/9*j - 2/45*j**5 + 0*j**2 + 4/27*j**3 + y*j**4. Factor k(d).
-2*(d - 1)**2*(d + 1)**2/9
Let p(q) be the first derivative of -q**3/7 + 6*q**2/7 + 36*q/7 - 207. Suppose p(u) = 0. What is u?
-2, 6
Let y be 5/90*(17/2 + -7). Let n(a) be the second derivative of 0 + 0*a**2 - 1/3*a**3 + y*a**4 - 6*a. Determine k, given that n(k) = 0.
0, 2
Let r(j) be the second derivative of -j**6/120 - j**5/80 + j**4/48 + j**3/24 - 3*j - 3. Factor r(m).
-m*(m - 1)*(m + 1)**2/4
Let t = -57274/365 - -242/73. Let y = -153 - t. What is q in y*q + 0 + 3/5*q**2 = 0?
-1, 0
Let d(v) be the third derivative of v**5/240 + 5*v**4/48 + v**3 + 3*v**2 + 22*v. Factor d(r).
(r + 4)*(r + 6)/4
Let l(a) be the second derivative of -a**7/12 + 163*a**6/60 + 129*a**5/40 - 211*a**4/24 - 61*a**3/6 + 12*a**2 - 10*a + 14. Find n, given that l(n) = 0.
-1, 2/7, 1, 24
Let q(o) be the third derivative of o**6/1380 - 13*o**4/276 - 4*o**3/23 + 22*o**2 + o. Solve q(c) = 0 for c.
-3, -1, 4
Let j be (5 + (-70)/20)/((-12)/(-8) - 1). Determine b so that 1/4*b**j - 1/2 - b + 1/8*b**2 = 0.
-2, -1/2, 2
Let j(y) = -y**2 - 7*y + 11. Let o be j(1). Let i(z) be the first derivative of -14 + 0*z + 1/9*z**o + 1/6*z**2. Let i(r) = 0. What is r?
-1, 0
Suppose 0 = -0*i - 2*i + 4*b + 2, -5*i = 5*b - 65. Suppose -3*y + 0 + i = 0. Factor 3*w - w**3 - 3*w**3 - 3*w**y + 4*w**3.
-3*w*(w - 1)*(w + 1)
Suppose -2*s - 2*i + 16 = 0, 3*s - i = 8 + 4. Factor 71 + 2*k**2 - 20*k**3 + 20*k**4 - s*k**5 - 12*k**2 + 25*k - 81.
-5*(k - 2)*(k - 1)**3*(k + 1)
Let r(w) = -w**3 + 10*w**2 - 11*w. Let t be r(8). Determine c, given that 96*c**4 + 22*c**3 - 4*c - 4 + t*c - 64*c**5 + 6*c**3 - 92*c**2 = 0.
-1, 1/4, 1
Suppose -3*v = -5*g - 10, 2*v - g = -0*g + 2. Suppose 10*x - x + 6*x + v*x**2 + 3*x**2 = 0. What is x?
-5, 0
Let y = 2968/10683 + -66/1187. Factor 2/9*g - 4/9 + y*g**2.
2*(g - 1)*(g + 2)/9
Suppose -2*v + 2*d = 24, -4*v + 9*v = -d - 30. Let w be (v/(-84))/((-6)/(-16)) + 0. Factor 2/9*n**2 - w*n - 4/9.
2*(n - 2)*(n + 1)/9
Let z = 78 - 1010/13. Let k be 2/13*(-1 + 2). Factor -4/13*s**2 - k*s**5 + 2/13 + z*s**3 + 2/13*s**4 - 2/13*s.
-2*(s - 1)**3*(s + 1)**2/13
What is r in -r**3 + 27 - 9*r + 162*r**2 + 0*r**3 - 6*r - 173*r**2 = 0?
-9, -3, 1
Solve 27*i - 315*i - 178 - 302 - 54*i**2 - 3*i**3 = 0 for i.
-10, -4
Factor 0 - 2/5*s**4 + 16/5*s - 4/5*s**2 - 2*s**3.
-2*s*(s - 1)*(s + 2)*(s + 4)/5
Let d(y) be the third derivative of -y**7/105 - y**6/60 + y**5/5 + y**4/3 - 8*y**3/3 - 31*y**2 + 5*y. Let d(w) = 0. Calculate w.
-2, 1, 2
Let k(n) be the first derivative of 2*n**3/21 - 16*n**2/7 + 78*n/7 - 370. Factor k(f).
2*(f - 13)*(f - 3)/7
Let k(x) be the second derivative of x**4/12 - 5*x**3/6 + 2*x**2 - 16*x - 2. Suppose k(o) = 0. Calculate o.
1, 4
Let b(k) = -5*k**2 - 2*k + 10. Let d be b(-6). Let m = d - -488/3. Solve 2/3*f**5 - 10/3*f**4 + 4/3*f + 0 + 6*f**3 - m*f**2 = 0 for f.
0, 1, 2
Suppose -42*h - 285 = -99*h. Suppose -6/11*p**3 + 0 + 6/11*p**h + 0*p - 2/11*p**2 + 2/11*p**4 = 0. What is p?
-1, -1/3, 0, 1
Let r(y) be the first derivative of -14 - 4/45*y**5 + 0*y + 0*y**2 - 1/18*y**4 - 1/27*y**6 + 0*y**3. Factor r(k).
-2*k**3*(k + 1)**2/9
Let p be ((-2)/(-3))/((-4)/(-18)). Let t(i) = -i**3 + 5*i**2 - 5*i - 3. Let c be t(3). Factor 0*n + 1/3*n**p + c - 1/3*n**2.
n**2*(n - 1)/3
Let q(p) be the third derivative of 0 - 22*p**2 + 1/8*p**4 - 1/60*p**5 + 0*p - 1/3*p**3. Solve q(z) = 0.
1, 2
Let g(u) = -u**3 + 52*u**2 + 52*u + 56. Let c be g(53). Factor 12/5*s**c - 8/5 - 26/5*s**2 - 2/5*s**4 + 24/5*s.
-2*(s - 2)**2*(s - 1)**2/5
Let h be 18/81 - ((-2)/(-19) - 14500/22230). Let h*g**2 + 2/13*g + 0 = 0. Calculate g.
-1/5, 0
Suppose 0 + 2/21*s**2 - 2/7*s + 8/21*s**3 = 0. Calculate s.
-1, 0, 3/4
Let d = 541/7 + -514/7. Factor 0*h + 0 - d*h**2 + 18/7*h**3 - 3/7*h**4.
-3*h**2*(h - 3)**2/7
Suppose 9 = 3*l - 3*t, 2*t = 