3 - 15*h**2 + 1/390*h**5. Factor n(v).
2*v*(v - 2)/13
Determine m, given that -90*m + 51*m - 15*m**3 + 19*m**2 + 35*m**2 = 0.
0, 1, 13/5
Let d(m) = 4*m**3 - 21*m**2 + 29*m + 5. Let w(l) = -2 + 7 + 1 - 5. Let p(b) = 4*d(b) - 44*w(b). Factor p(v).
4*(v - 3)*(v - 2)*(4*v - 1)
Factor -1/4*v**4 + 0 + 0*v**2 - 1/4*v**3 + 0*v.
-v**3*(v + 1)/4
Factor 79/3*r**2 - 4/3 - 16/3*r + 91/3*r**3.
(r + 1)*(7*r - 2)*(13*r + 2)/3
Let w(p) be the third derivative of -p**9/3780 - p**8/168 - 5*p**7/126 - 13*p**4/24 - 10*p**2. Let v(g) be the second derivative of w(g). Factor v(f).
-4*f**2*(f + 5)**2
Let r(n) be the first derivative of -5*n**4/32 - 3*n**3/8 + 21*n**2/8 - n + 174. Factor r(f).
-(f - 2)*(f + 4)*(5*f - 1)/8
Let s(n) be the third derivative of 1/140*n**7 + 0*n**6 - 3/40*n**5 + 1/8*n**4 + 0*n - n**2 + 0 + 0*n**3. Determine g, given that s(g) = 0.
-2, 0, 1
Suppose -4*t + 29 = 1. Let l = t - 4. Suppose -3 - 2 + 9*z - 9*z**2 + l*z**3 + 1 + 1 = 0. What is z?
1
Let l = -10573 - -74020/7. Factor 3/7*r**2 - 3/7*r**3 + 15/7*r + l.
-3*(r - 3)*(r + 1)**2/7
Let g(a) be the first derivative of -a**3/3 - 3*a**2/2 - 2*a - 7. Let l be g(-2). Factor 1/5*n**3 - 1/5*n**2 + l + 0*n.
n**2*(n - 1)/5
Let t(k) = 4*k**2 - 1. Let o(c) = -14*c**2 + c + 18. Let y(i) = 5*o(i) + 15*t(i). Determine n so that y(n) = 0.
-5/2, 3
Let l(t) be the first derivative of -t**4/4 - t**3/3 + 6*t**2 + 216. Let l(u) = 0. Calculate u.
-4, 0, 3
Let i(g) be the first derivative of g**6/3 - 38*g**5/5 + 9*g**4 + 29. Solve i(k) = 0.
0, 1, 18
Let i(s) = s**2 + 4*s + 7. Let t be i(-3). Factor t*o**2 - 560*o**4 - 62*o**2 - 64*o**2 + 7*o**2 + 440*o**3 + 10*o.
-5*o*(4*o - 1)**2*(7*o - 2)
Let q(o) = o**2 - 68*o + 795. Let r be q(15). Factor 4/7*n**4 - 8/7*n**3 + r*n + 4/7*n**2 + 0.
4*n**2*(n - 1)**2/7
Let f be (-2)/16 - (-750)/240. Let o(v) = -v**2 + 4*v - 1. Let j be o(1). Factor -8/3*g - 2/3*g**4 - 8/3 + 4/3*g**f + j*g**2.
-2*(g - 2)**2*(g + 1)**2/3
Let o(t) be the first derivative of -8*t**6/3 - 98*t**5/5 - 35*t**4 - 16*t**3/3 + 418. Find g, given that o(g) = 0.
-4, -2, -1/8, 0
Let u be 206/112 + (-373)/2984. Find i such that -6/7*i**2 + u - 6/7*i = 0.
-2, 1
Suppose 1291*p - 12 = -4*u + 1290*p, 2*u = 4*p + 24. Factor 2*d**3 - 4/3 + 2/3*d**2 - 2*d + 2/3*d**u.
2*(d - 1)*(d + 1)**2*(d + 2)/3
Let c(l) = 9*l**2 - 4*l + 5. Let f be c(1). Let d be (-212)/(-36) - f/2. Suppose 0 - 2/3*p**4 + 0*p**3 + 0*p + d*p**2 + 2/9*p**5 = 0. Calculate p.
-1, 0, 2
Let m = 525 - 523. Let o(k) be the second derivative of -1/60*k**5 + 1/18*k**4 - 5*k + 0 + 1/18*k**3 - 1/3*k**m. Find z such that o(z) = 0.
-1, 1, 2
Suppose 0 = -5*j - 3*j. Let t(c) = -c + 4. Let m be t(j). Solve 5*p**m + p**5 + 4*p**4 - 8*p**4 = 0.
-1, 0
Let x(a) be the third derivative of -a**5/20 - 13*a**4/24 + 35*a**2. Let o(l) = -3*l**2 - 14*l. Let w(d) = -4*o(d) + 5*x(d). Find v, given that w(v) = 0.
-3, 0
Let r(w) = -w**2 - 7*w - 10. Let v be r(-4). Suppose -109*y - 4 + 118*y - 3*y**2 - v = 0. Calculate y.
1, 2
Suppose 12*d - 5 = -4*t + 13*d, 0 = 3*d - 9. Determine w, given that 32/3 - 16*w - 2/3*w**3 + 6*w**t = 0.
1, 4
Let z(a) = 57*a - 1423. Let f be z(25). Determine w so that 0*w - 2/5*w**f - 32/5*w**5 + 0 + 14/5*w**3 - 16/5*w**4 = 0.
-1, 0, 1/4
Let x(j) = -4*j - 31. Let y be x(-9). Factor -22*q**2 - 15*q**y + 22*q**2 + 10*q**3 - 5*q**4.
-5*q**3*(q + 1)*(3*q - 2)
Let v(k) be the second derivative of k**7/14 + 4*k**6/5 + 39*k**5/20 - 11*k**4/2 - 16*k**3 + 48*k**2 - 251*k. What is u in v(u) = 0?
-4, -2, 1
Let s = -835 - -837. Let m(y) be the second derivative of 9/5*y**5 - y**3 + 7/10*y**6 - 8*y + 0*y**s + 0 + 3/4*y**4. Factor m(c).
3*c*(c + 1)**2*(7*c - 2)
Let n(t) be the second derivative of 2*t**7/21 - 4*t**6/15 - t**5/5 + 2*t**4/3 - 104*t. Factor n(l).
4*l**2*(l - 2)*(l - 1)*(l + 1)
Let u(t) = t**4 - t**2 + t - 1. Let s(l) = -4*l**3 + 2*l**2 + 8*l**4 + 7*l**3 - 17*l + 19*l + 7*l**3 - 6. Let v(r) = s(r) - 4*u(r). Factor v(n).
2*(n + 1)**3*(2*n - 1)
Solve 882 + 1/2*k**2 - 42*k = 0.
42
Let j(w) be the first derivative of -3*w + 1/2*w**2 - 1/12*w**4 - 1/20*w**5 + 1 + 1/6*w**3. Let f(p) be the first derivative of j(p). Factor f(g).
-(g - 1)*(g + 1)**2
Let b(r) be the first derivative of -r**4 + 272*r**3/3 - 2312*r**2 + 325. Factor b(t).
-4*t*(t - 34)**2
Let k = -44979 - -314854/7. Factor 0*t**3 + 0 + 0*t**2 + 0*t - k*t**5 - 6/7*t**4.
-t**4*(t + 6)/7
Let j(k) be the third derivative of k**8/40320 + k**7/1260 + k**6/90 + k**5/15 - 9*k**2. Let p(s) be the third derivative of j(s). Factor p(t).
(t + 4)**2/2
Let a(d) be the second derivative of 2*d**6/15 + 8*d**5/7 + 65*d**4/21 + 40*d**3/21 - 24*d**2/7 - 14*d - 2. Let a(g) = 0. Calculate g.
-3, -2, -1, 2/7
Let p be 8/10*15/6. Let l(x) = x + 18. Let w be l(-16). Factor w*o + o - 6*o**3 + o**5 + p*o**5.
3*o*(o - 1)**2*(o + 1)**2
Factor 5*u**4 - 42*u**3 + 62*u**3 - 2*u**2 + 17*u**2 + 0*u**2.
5*u**2*(u + 1)*(u + 3)
Let a(t) be the second derivative of t**7/945 - t**6/270 + t**4/54 - t**3/27 + 6*t**2 - 8*t. Let g(q) be the first derivative of a(q). Solve g(f) = 0.
-1, 1
Let r = 6 - 3. Suppose -7 = -2*g - 1. Find p such that -7*p**5 + 2*p**4 + 0*p**3 + g*p**3 - r*p**3 = 0.
0, 2/7
Let y = -13/21 + 53/63. Let w(r) be the first derivative of y*r**3 + 4/3*r**2 - 8 + 8/3*r. Suppose w(l) = 0. Calculate l.
-2
Let i(l) = l**2 - l - 1. Let f(c) = 3*c**2 - 8. Let m(g) = -f(g) + 4*i(g). What is k in m(k) = 0?
2
Let x(d) be the first derivative of d**4/2 - 82*d**3/3 - 42*d**2 - 223. Suppose x(h) = 0. What is h?
-1, 0, 42
Let i(c) be the second derivative of 2/15*c**6 + 0*c**2 - 2*c - 6/5*c**5 + 0 - 8/3*c**3 + 3*c**4. Determine q, given that i(q) = 0.
0, 1, 4
Let i(u) = -2*u**2 + 9*u + 11. Let c be i(5). Factor 41*g**3 - 23*g**3 - c*g**2 - 3*g - 21*g**3.
-3*g*(g + 1)**2
Let r(t) be the second derivative of 7*t**5/100 - t**4/4 - 9*t**3/5 + 4*t**2/5 + 422*t. Factor r(g).
(g - 4)*(g + 2)*(7*g - 1)/5
Let s(r) be the first derivative of 2/3*r**2 + 5 + 8/9*r**3 - 4*r - 9/20*r**5 - 5/12*r**4. Let a(g) be the first derivative of s(g). Factor a(b).
-(b + 1)*(3*b - 2)*(9*b + 2)/3
Let r(w) be the second derivative of w**5/4 - 35*w**4/12 + 35*w**3/6 + 75*w**2/2 + 22*w + 4. Factor r(d).
5*(d - 5)*(d - 3)*(d + 1)
Let g(c) be the second derivative of 0 + 1/9*c**3 + 8*c - 1/54*c**4 - 2/9*c**2. Determine n so that g(n) = 0.
1, 2
Let g = 40/13 + -68/39. Let y = 16463 + -16463. Let g*c**3 + 16/9*c + y - 8/3*c**2 - 2/9*c**4 = 0. What is c?
0, 2
Let c(a) = a**2 + 1. Let d(w) = -5*w**4 + 60*w**3 + 219*w**2 + 20*w - 306. Let q(s) = 6*c(s) + d(s). Factor q(h).
-5*(h - 15)*(h - 1)*(h + 2)**2
Let d = 5833/25 - 233. Let t(j) be the first derivative of 0*j - d*j**5 - 1/2*j**4 + 2/5*j**2 + 14/15*j**3 - 4. Determine h, given that t(h) = 0.
-2, -1/4, 0, 1
Let r be (-2)/(-8 + 7) - (-3 + 95/20). Factor q + 0 - 1/2*q**4 - 3/4*q**3 + r*q**5 + q**2.
q*(q - 2)**2*(q + 1)**2/4
Let s be (9/2 - 20/(-10)*4) + 0. Suppose s*h**5 + 5 + 55*h**4 + 65/2*h + 95*h**3 + 80*h**2 = 0. Calculate h.
-1, -2/5
Suppose n + 0*f + 3*f + 7 = 0, -5*f - 49 = -3*n. Let p(a) = -a**3 + 9*a**2 - 4*a - 32. Let y be p(n). Suppose -1/3*l + y - 1/3*l**2 = 0. What is l?
-1, 0
Suppose 0 = 8*s - 11*s + 15*s. Factor -2/3*a**3 - 4/3*a + s + 2*a**2.
-2*a*(a - 2)*(a - 1)/3
Let n(w) be the first derivative of w**4/2 + 18*w**3 + 195*w**2 + 338*w + 330. Determine v so that n(v) = 0.
-13, -1
Suppose 17 = 3*o + 5*h, 5*o - 11*h - 19 = -10*h. Let f(t) = -t - 2. Let s be f(-5). Determine u so that -3*u**4 + 4*u**3 + 3*u**4 - 2*u**s + 2*u**o = 0.
-1, 0
Determine w so that -3/7*w**5 - 45/7 + 3/7*w**4 - 150/7*w**2 + 54/7*w**3 + 141/7*w = 0.
-5, 1, 3
Let z(p) be the first derivative of 2*p**6 + 159*p**5/5 - 141*p**4/4 - 67*p**3 + 129*p**2/2 + 42*p - 226. Let z(a) = 0. Calculate a.
-14, -1, -1/4, 1
Let q(n) = -n**3 + 12*n**2 - 12*n + 14. Let f be q(11). Factor -8*m - 2*m**3 + m**f + 16 + 0 - 7*m**2.
-(m - 1)*(m + 4)**2
Let p(q) be the third derivative of -5/48*q**5 + 0*q**3 - 1/96*q**6 - 5/16*q**4 + 0 + 0*q + 23*q**2. Suppose p(h) = 0. Calculate h.
-3, -2, 0
Let t be (-8)/(-270)*558/124. Factor t*p - 4/15 + 2/15*p**2.
2*(p - 1)*(p + 2)/15
Let a(l) be the second derivative of l**7/840 - l**6/360 + 14*l**3/3 + 12*l. Let s(r) be the second derivative of a(r). Find y, given that s(y) = 0.
0, 1
Let a(p) be the second derivat