0*y - 65. Let v(m) = -3*m**2 - 119*m + 124*m - 16 + 2*m**2. Let j(u) = -6*t(u) + 25*v(u). Factor j(d).
5*(d - 1)*(d + 2)
Let y(z) be the second derivative of 1/6*z**3 + 4 + 0*z**2 + 1/120*z**5 - z - 7/72*z**4. Solve y(d) = 0 for d.
0, 1, 6
Let h(q) be the second derivative of q**5/420 + q**4/56 + 3*q**2 + 28*q. Let f(n) be the first derivative of h(n). Let f(a) = 0. What is a?
-3, 0
Let r(g) be the third derivative of 0*g**4 - 1/105*g**7 + 0*g**3 + 1/120*g**6 + 0*g**5 + 1/336*g**8 + 0 + 0*g + 26*g**2. Factor r(b).
b**3*(b - 1)**2
Suppose 0 = t + t - 4. Let i = -20 - -24. Suppose 17 - 17 - 2*u**3 - i*u + 6*u**t = 0. Calculate u.
0, 1, 2
Let s(z) be the first derivative of z**3/6 - z**2/2 - 4*z + 302. Solve s(x) = 0.
-2, 4
Let t be ((-43)/45 - -1)*(-12)/(-8). Let i(n) be the second derivative of 3*n - n**2 + 2/5*n**5 - n**4 + 4/3*n**3 - t*n**6 + 0. Factor i(j).
-2*(j - 1)**4
Let m(f) = -37*f**2 + 382*f - 240. Let c(n) = 25*n**2 - 255*n + 160. Let d(t) = 8*c(t) + 5*m(t). Let d(a) = 0. Calculate a.
2/3, 8
Let o(z) be the first derivative of -17*z**4 + 40*z**3/3 - 42. Factor o(r).
-4*r**2*(17*r - 10)
Let t(s) be the third derivative of -1/30*s**5 - 13*s**2 + 1/12*s**4 + 0 + 0*s + 2/3*s**3. Find p such that t(p) = 0.
-1, 2
Let d(g) = g**3 - 6*g**2 + 7*g + 9. Let o be d(3). Let q(s) be the first derivative of -9*s + o*s**2 + 5 - 1/3*s**3. Factor q(m).
-(m - 3)**2
Let z be ((2 - (-16)/(-24))/(-10))/(-4). Let t(g) be the second derivative of z*g**6 + 1/4*g**4 + 7*g + 1/5*g**5 - 2/3*g**3 + 0 - 2*g**2. Factor t(b).
(b - 1)*(b + 1)*(b + 2)**2
Let c be -2 + 2/(32/34). Let v be (-6)/(-16)*((-50)/(-50))/((-3)/(-2)). Factor c*f**3 + 0*f + v*f**2 + 0.
f**2*(f + 2)/8
Let j(m) be the third derivative of 0 + 1/132*m**4 + 2/33*m**3 - 1/330*m**5 + 0*m - 15*m**2. Determine n so that j(n) = 0.
-1, 2
Let b = -28 - -30. Suppose 3*y = b*y + 4*y. Factor r**3 - 1/2*r**4 + 1/2*r**2 + y - r.
-r*(r - 2)*(r - 1)*(r + 1)/2
Let r = -6594 + 6597. Let -7/6*o**3 + 1/2*o + r - 13/6*o**2 - 1/6*o**4 = 0. Calculate o.
-3, -2, 1
Suppose 0 = -2*m + 3*a + 57, -2*a + 27 = m - 3*a. Let w = 26 - m. Let n + w*n - n - n**2 + 2 + 1 = 0. Calculate n.
-1, 3
Suppose -4*v - 5*b - 14 = -6*v, b = 2*v + 2. Let l be v/(-36)*(0 - -3 - 1). Factor l*n**3 - 1/6*n - 1/2*n**2 + 1/2.
(n - 3)*(n - 1)*(n + 1)/6
Suppose 11*s = 9*s - 2. Let x be (130/52)/(s/1 - -4). Factor -4/3*a + x*a**2 - 2/3.
(a - 2)*(5*a + 2)/6
Factor -10/13*n**4 + 2/13*n**5 - 8/13*n**2 + 16/13*n**3 + 0*n + 0.
2*n**2*(n - 2)**2*(n - 1)/13
Let j(o) be the first derivative of 12/7*o**2 - 4/7*o + 9 - 4/21*o**3 - 64/35*o**5 - 24/7*o**4. What is i in j(i) = 0?
-1, 1/4
Let l(z) be the first derivative of z**7/112 + z**6/80 + 2*z + 10. Let x(g) be the first derivative of l(g). Factor x(o).
3*o**4*(o + 1)/8
Solve 0*q + 1/2*q**2 - 5/4*q**4 + 0 + 3/4*q**3 = 0.
-2/5, 0, 1
Let m(a) be the third derivative of 0*a**5 + 0*a + 0 + 0*a**4 + 0*a**3 + 2/105*a**7 + 1/15*a**6 + 12*a**2. Suppose m(h) = 0. Calculate h.
-2, 0
Solve 1375*x**2 - 1381*x**4 - 292*x + 121*x**5 - 843*x**3 + 1337*x**4 + 15 + 9 - 341*x**2 = 0.
-3, 2/11, 1, 2
Let x = 14057/1509 - -9/503. Factor -16/3*d**4 + 4/3*d + 0 - 8/3*d**2 - x*d**3.
-4*d*(d + 1)**2*(4*d - 1)/3
Factor 8/7*r + 0 - 2/7*r**3 + 8/7*r**2 - 2/7*r**4.
-2*r*(r - 2)*(r + 1)*(r + 2)/7
Let y = -76 + 80. Let k be y + ((-45)/(-35) - 5). Factor -2/7*d**3 + k*d + 2/7 - 2/7*d**2.
-2*(d - 1)*(d + 1)**2/7
Let d(x) be the third derivative of -x**6/240 - x**5/20 - 11*x**4/48 - x**3/2 + 12*x**2. Factor d(y).
-(y + 1)*(y + 2)*(y + 3)/2
Let u(g) be the third derivative of g**6/540 - g**5/54 + 2*g**4/27 - 4*g**3/27 - 176*g**2 + 4*g. Factor u(h).
2*(h - 2)**2*(h - 1)/9
Suppose 0 = -8*o - 11 + 27. Let z(f) be the second derivative of 1/40*f**5 + 1/24*f**4 - 1/12*f**3 - 5*f + 0*f**o + 0 - 1/60*f**6. Factor z(m).
-m*(m - 1)**2*(m + 1)/2
Suppose -29*d + 79 = -95. Let h(b) be the first derivative of 0*b + 0*b**3 + 49/18*b**d + 1/3*b**4 + 28/15*b**5 - 5 + 0*b**2. Let h(n) = 0. What is n?
-2/7, 0
Let w(s) = -s**2 - 7*s - 13. Let f be w(-6). Let m = f + 23/3. Let 0 - 2/3*y + 2/3*y**3 - m*y**2 + 2/3*y**4 = 0. Calculate y.
-1, 0, 1
Let o be 174/(-145)*(-5)/3. Let d(t) be the first derivative of -10 - 2/5*t**4 + 0*t - 2/5*t**o - 2/25*t**5 - 2/3*t**3. Factor d(l).
-2*l*(l + 1)**2*(l + 2)/5
Factor -264/5 + 4/5*s**2 + 4*s.
4*(s - 6)*(s + 11)/5
Let c(o) be the third derivative of 0 - 1/120*o**5 + 1/3*o**3 + 0*o**4 + 0*o - 2*o**2. Find s such that c(s) = 0.
-2, 2
Let y(w) = w**2 + w. Let p be y(-2). Suppose p*t + 2*t = 0. Factor -2*a - a**5 + t*a**3 - a**5 + 4*a**3.
-2*a*(a - 1)**2*(a + 1)**2
Suppose 4*p - 4*j + 76 = 0, 9*p + 3*j + 127 = 4*p. Let i = p - -62. Factor -1 + 8*b - 43*b**2 + i*b**2 - 3.
-4*(b - 1)**2
Let s(v) = -2*v - 19. Let g be s(-9). Let f be (g + -1)*(36/(-8) + 2). Factor 0*p - 2/5*p**4 + 0*p**2 + 1/5*p**f + 1/5*p**3 + 0.
p**3*(p - 1)**2/5
Let g(t) = -3*t - 2 + 1 + 2*t + 0. Let r be g(-4). Find a such that -3*a**r + a**2 + 3*a**4 - a**2 + a**2 - a**5 = 0.
0, 1
Let u be ((-4)/3)/(7/((-105)/10)). Solve 12*n - 135 - 117 - 6*n**u - 3*n**3 + 276 = 0 for n.
-2, 2
Let a(b) be the third derivative of -b**5/130 - 7*b**4/39 - 3*b**3/13 + 108*b**2. Factor a(c).
-2*(c + 9)*(3*c + 1)/13
Suppose 7*u + 12 = 26. Let n be 0 - (-4 - -4)/u. Find j such that -2/7*j**2 + 2/7*j**5 + 0 + n*j + 6/7*j**3 - 6/7*j**4 = 0.
0, 1
Let n(z) = 15*z**2 + 5*z - 16. Let p(o) = 15*o**2 + 5*o - 18. Let x(q) = -4*n(q) + 3*p(q). Solve x(m) = 0.
-1, 2/3
Let n = 15759/7 - 2250. Suppose -10/7*y**2 + 3/7*y**3 + n*y - 2/7 = 0. What is y?
1/3, 1, 2
Find w, given that -2/7*w**2 - 24/7*w + 90/7 = 0.
-15, 3
Let u(o) = -o**2 - 8*o + 12. Let p be u(-9). Factor -3*x**2 - 2*x**2 - 4 + 10*x - 3*x**2 + x**3 + x**p.
2*(x - 2)*(x - 1)**2
Let k(i) = -2*i + 18. Let t be (9/(-2))/((-6)/12). Let s be k(t). Find y such that -8/9*y**5 - 8/3*y**4 + s - 26/9*y**3 - 2/9*y - 4/3*y**2 = 0.
-1, -1/2, 0
Let u(a) be the third derivative of -a**7/1155 - a**6/165 - a**5/110 + a**4/33 + 4*a**3/33 - 36*a**2. Suppose u(b) = 0. Calculate b.
-2, -1, 1
Let a be 1/9 - (7 - 12544/1800). Let l(s) be the first derivative of -2/5*s**2 - 2/15*s**3 + 1/5*s**4 + 0*s + a*s**5 - 6. Factor l(q).
2*q*(q - 1)*(q + 1)*(q + 2)/5
Let w(g) = 3 - 6*g**2 - 9 + 3*g - 1 + g**3 - 3. Let k(t) = -t**3 + 6*t**2 - 4*t + 9. Let f(q) = 6*k(q) + 5*w(q). Factor f(r).
-(r - 4)*(r - 1)**2
Suppose -2*u - 5*b + 10 = 0, -285*b + 289*b = 8. Factor -2/7*t**4 + u + 0*t + 0*t**2 + 4/7*t**3.
-2*t**3*(t - 2)/7
Let x(j) = -735*j**2 - 745*j - 22. Let z(d) = -735*d**2 - 745*d - 25. Let l(a) = -5*x(a) + 4*z(a). Let l(h) = 0. What is h?
-1, -2/147
Let m(f) be the third derivative of -f**5/300 - 3*f**4/40 + 7*f**2 - 3*f. Suppose m(o) = 0. Calculate o.
-9, 0
Suppose -28/5*b**4 - 3/5*b**2 + 19/5*b**3 + 0 + 0*b = 0. What is b?
0, 1/4, 3/7
Let u be -5 + ((-17826)/(-1620) - 6). Let v(s) be the third derivative of 0*s - 1/54*s**4 - u*s**5 - 3*s**2 + 0*s**3 + 0 + 1/540*s**6. Factor v(j).
2*j*(j - 2)*(j + 1)/9
Let c(u) be the first derivative of 5/4*u**4 + 4/5*u**5 + 0*u + 2/3*u**3 + 0*u**2 + 1/6*u**6 - 37. Suppose c(r) = 0. What is r?
-2, -1, 0
Let u(w) = -6*w**2 + 20*w - 54. Let n(d) = -7*d**2 + 20*d - 55. Suppose -3*v + 5*v - 8 = 0. Let y(l) = v*n(l) - 5*u(l). Determine p, given that y(p) = 0.
5
Let q(k) be the third derivative of -25*k**8/84 - 68*k**7/21 + 251*k**6/30 + 76*k**5/15 - 50*k**4/3 - 64*k**3/3 + 23*k**2 + 4. Determine z, given that q(z) = 0.
-8, -2/5, 1
Let i(n) be the second derivative of n**7/105 + 58*n**6/75 + 114*n**5/5 + 3971*n**4/15 + 6859*n**3/15 + 16*n. Suppose i(q) = 0. What is q?
-19, -1, 0
Let c be -6*(-3)/27*3. Let g(l) be the first derivative of -3/16*l**4 + 3 + 9/8*l**c + 0*l**3 - 3/2*l. Factor g(y).
-3*(y - 1)**2*(y + 2)/4
Let h(r) = -r - 5. Let q be h(-9). Suppose -q = -2*p - 0*p. Find l, given that -6*l**4 + 14*l - 2*l**2 - 3*l**3 - p*l**5 - 14*l - 3*l**3 = 0.
-1, 0
Let s(c) be the third derivative of -100/27*c**3 - 1/30*c**6 - 61/270*c**5 + 0 + 42*c**2 + 5/3*c**4 - 1/945*c**7 + 0*c. Solve s(i) = 0 for i.
-10, 1
Let q(d) be the third derivative of -d**6/600 - 2*d**5/75 + 68*d**2. What is i in q(i) = 0?
-8, 0
Let k(w) be the first derivative of 81*w**5/10 + 207*w**4/8 - 457*w**3/3 + 93*w**2 - 20*w + 425. Factor k(u).
(u - 2)*(u + 5)*(9*u -