 + 2*n**4/15 + 4*n**3/15 + 108*n**2. Factor x(w).
2*(w + 1)*(w + 2)**2/5
Let o = 10990 - 10986. Factor 8/3*y**2 - 4/3*y**5 + 16/3*y**o + 0*y - 20/3*y**3 + 0.
-4*y**2*(y - 2)*(y - 1)**2/3
Let i = -406 + 1625/4. Let f(g) be the first derivative of -1/4*g**5 - 1 + 5/8*g**4 + 5/8*g**2 - 5/6*g**3 + 1/24*g**6 - i*g. Determine r so that f(r) = 0.
1
Let c(b) be the third derivative of b**8/2352 + 2*b**7/735 - 11*b**6/420 - b**5/105 + b**4/8 + 305*b**2. Suppose c(n) = 0. What is n?
-7, -1, 0, 1, 3
Factor -428/5*h**2 - 4/5*h**3 + 0 + 432/5*h.
-4*h*(h - 1)*(h + 108)/5
Factor -1/10*q**3 - 3/5*q**2 - 9/10*q + 0.
-q*(q + 3)**2/10
Let a(n) be the second derivative of 0 + 0*n**2 + 1/60*n**6 + 0*n**3 - 1/16*n**5 + 5/168*n**7 - 1/24*n**4 - 23*n. Determine u so that a(u) = 0.
-1, -2/5, 0, 1
Let b(t) = -23*t**2 - 1172*t - 116427. Let a(f) = 7*f**2 + 391*f + 38809. Let m(j) = -10*a(j) - 3*b(j). Let m(z) = 0. What is z?
-197
Let h(w) be the first derivative of -3*w**5/40 - 39*w**4/4 - 1403*w**3/4 - 1989*w**2/2 - 7803*w/8 + 257. Find s such that h(s) = 0.
-51, -1
Suppose 0 - 32/3*m**3 - 24*m + 28*m**2 + 4/3*m**4 = 0. What is m?
0, 2, 3
Let g(l) = -60*l**4 - 75*l**3 - 10*l**2 - 10. Let o(i) = -90*i**4 - 113*i**3 - 15*i**2 - 16. Let p(s) = -8*g(s) + 5*o(s). Let p(b) = 0. Calculate b.
-1, -1/6, 0
Let b(a) be the first derivative of a**5 - 15*a**4/4 - 5*a**3/3 + 15*a**2/2 - 88. Find h, given that b(h) = 0.
-1, 0, 1, 3
Suppose -9 = -0*k - 3*k. Suppose -k = -v, -5*x - 2*v + 60 = 3*v. Factor 0*i**3 + i**2 + 8 + i**3 - x - i + 0*i**2.
(i - 1)*(i + 1)**2
Let z(m) be the second derivative of -4*m**5/5 - m**4/3 + 6*m + 2. Let z(t) = 0. What is t?
-1/4, 0
Let l(q) be the third derivative of 1/288*q**4 + 0*q**3 - 1/360*q**5 + 0 + 0*q + 1/1440*q**6 - 37*q**2. Determine b so that l(b) = 0.
0, 1
Let m(o) = 2 + 0 - 20*o - o**2 + 3 + 4*o. Let j be m(-16). Let 2/9*h**j + 2/9 + 2/9*h**4 - 4/9*h**2 + 2/9*h - 4/9*h**3 = 0. What is h?
-1, 1
Let o(n) = 3*n**2 + 74*n - 19. Let a be o(-25). Let v(f) be the second derivative of 0*f**2 + 1/6*f**3 + a*f + 1/24*f**4 + 0. What is l in v(l) = 0?
-2, 0
Let d = 36 + -33. Suppose -6*b - 6*b + 2*b**2 + 4*b + d + 5 = 0. Calculate b.
2
Let y(w) be the second derivative of -5/12*w**4 + 5/2*w**2 - 28*w + 0*w**3 + 0. Find j such that y(j) = 0.
-1, 1
Let q(y) be the third derivative of y**5/120 - y**4/12 + y**3/3 - 52*y**2. Solve q(l) = 0 for l.
2
Let o(s) = -2*s - 6. Let k be o(-4). Let c be (10/(-3))/(-5) + k/(-5). Factor -14/15*b**2 + 0 - 2/15*b**5 - c*b - 2/3*b**4 - 6/5*b**3.
-2*b*(b + 1)**3*(b + 2)/15
Let s(w) be the second derivative of -1/14*w**4 + 9/14*w**2 + 0 - 7*w + 5/14*w**3. Solve s(d) = 0 for d.
-1/2, 3
Let p(r) = r**4 + r**3. Let c(x) = 25*x**4 + 105*x**3 - 305*x**2 + 105*x + 490. Let i(a) = -c(a) + 30*p(a). Suppose i(z) = 0. What is z?
-1, 2, 7
Suppose 49*q = -24*q. Factor q*u + 0*u**2 + 1/7*u**3 + 1/7*u**5 + 0 - 2/7*u**4.
u**3*(u - 1)**2/7
Let m(d) be the second derivative of 2*d**6/75 - 6*d**5/25 - 8*d**4/15 + 4*d**3/5 + 14*d**2/5 + 451*d. Solve m(g) = 0.
-1, 1, 7
Suppose 0 = -19*v + 16*v + 678. Let i = -2484/11 + v. Let 14/11*o**2 - 8/11*o**5 + 26/11*o**4 + 0 - 30/11*o**3 - i*o = 0. Calculate o.
0, 1/4, 1
Let c(r) be the third derivative of 0*r**3 - 1/15*r**5 - 8*r**2 + 0*r - 1/60*r**6 + 0 - 1/12*r**4. Factor c(n).
-2*n*(n + 1)**2
Suppose -4*v + 3*i = 7, 4*v + 3*i - 3 = 20. Suppose v*w = 5*r - 8, 5*r = -5*w + 18 - 3. Factor 4/5*x**r - 2/5*x + 0 + 2/5*x**5 - 4/5*x**4 + 0*x**3.
2*x*(x - 1)**3*(x + 1)/5
Let d(j) = 3*j**3 - 6 + j**4 + 3*j**4 + j**5 + 1 + 2. Let f(x) = 2*x**5 + 7*x**4 + 5*x**3 - 5. Let m(y) = 5*d(y) - 3*f(y). Factor m(u).
-u**4*(u + 1)
Let -1/11*c**2 - 7/11 - 8/11*c = 0. Calculate c.
-7, -1
Let w(l) = l. Let r(c) = 2*c**4 + 3*c**3 - 2*c**2 - 2*c. Let h(a) = -r(a) - 2*w(a). Factor h(k).
-k**2*(k + 2)*(2*k - 1)
Let w = -3443 - -3443. Let 2/9*s**2 + w + 8/9*s = 0. Calculate s.
-4, 0
Let a(c) be the first derivative of 1/9*c**2 + 0*c - 7 + 1/27*c**3. Let a(z) = 0. What is z?
-2, 0
Let l(w) be the first derivative of w**8/1680 + w**7/168 + 29*w**3/3 + 17. Let y(x) be the third derivative of l(x). Factor y(q).
q**3*(q + 5)
Let n(a) be the second derivative of -29929*a**4/72 - 173*a**3/9 - a**2/3 + 239*a. Suppose n(m) = 0. What is m?
-2/173
Suppose -5*b = 5*f + 20, -4 = 2*b + 4*f + 8. Let w be (-9)/18*(b/(-6) - 1). Factor -w*d**2 - 4/3*d - 1.
-(d + 1)*(d + 3)/3
Find p such that -725/9*p - 46/3*p**3 - 1/9*p**5 + 125/3 + 19/9*p**4 + 470/9*p**2 = 0.
1, 3, 5
Let v(z) be the second derivative of -z**7/462 + 7*z**6/330 - 19*z**5/220 + 25*z**4/132 - 8*z**3/33 + 2*z**2/11 - 27*z. Determine t so that v(t) = 0.
1, 2
Let o = 2807 - 2757. Let t(r) be the first derivative of 500/3*r + 5 + 20/3*r**3 - o*r**2 - 1/3*r**4. Factor t(a).
-4*(a - 5)**3/3
Factor 0 + 2/7*w**2 - 62/7*w.
2*w*(w - 31)/7
Let o(d) = -22*d**2 + 178*d - 16. Let u be o(8). Find z, given that u + 2/19*z**2 + 12/19*z = 0.
-6, 0
Let a(o) be the third derivative of -o**8/378 + o**7/35 + 43*o**6/540 - 19*o**5/270 - 13*o**4/36 - 8*o**3/27 + 5*o**2. Determine h, given that a(h) = 0.
-1, -1/4, 1, 8
Let v(h) be the second derivative of h**6/720 - h**5/360 - h**2/2 + 11*h. Let x(g) be the first derivative of v(g). Factor x(s).
s**2*(s - 1)/6
Factor 4/5*d**2 - 336/5 - 332/5*d.
4*(d - 84)*(d + 1)/5
Suppose 4 = 69*c - 203. Let z(f) be the second derivative of 0 - 3*f + 0*f**2 + 1/3*f**4 + 1/5*f**5 + 0*f**c. Determine u so that z(u) = 0.
-1, 0
Let t(b) be the first derivative of -b**5 + 35*b**4/4 + 40*b**3/3 + 34. Determine p so that t(p) = 0.
-1, 0, 8
Determine d so that -80*d**4 + 124492 - 124492 - 5*d**5 + 180*d**3 = 0.
-18, 0, 2
Suppose 3*l - 23 = -2*f, -f = 234*l - 235*l + 1. Factor -2/11*d + 0 - 10/11*d**5 - 32/11*d**f - 16/11*d**2 - 36/11*d**3.
-2*d*(d + 1)**3*(5*d + 1)/11
Let n(m) be the first derivative of -m**4/24 + m**3/18 + m**2/2 - 46. Determine g so that n(g) = 0.
-2, 0, 3
Let f(v) be the third derivative of v**5/480 + v**4/16 + 5*v**3/12 + 70*v**2 - 3. Determine u so that f(u) = 0.
-10, -2
Let f(b) = 7*b**2 - 2*b - 2. Let i(x) = 8*x**2 - 2*x - 1. Let z(a) = 7*f(a) - 6*i(a). Factor z(q).
(q - 4)*(q + 2)
Let d be 20/(-8) + (-3)/2 - -2. Let q be d/9 + (-217)/(-126). Factor q*x - 1/4*x**2 - 9/4.
-(x - 3)**2/4
Let q = 891 + -631. Factor 232*j + q*j - 338 - 2*j**2 - 440*j.
-2*(j - 13)**2
Let b be (2 + -1)/((-8)/(-280)). Let 67*s**4 - 22*s**4 + 14*s**2 - b*s**4 + 2*s**5 + 18*s**3 + 4*s = 0. Calculate s.
-2, -1, 0
Let -6*m + 1/3*m**3 - 32/3 + 5*m**2 = 0. Calculate m.
-16, -1, 2
Let q(f) be the second derivative of 3/80*f**5 - 1/120*f**6 + 2*f - 1/8*f**3 + 1/4*f**2 + 0 - 1/48*f**4. Factor q(i).
-(i - 2)*(i - 1)**2*(i + 1)/4
Let j(n) be the first derivative of -40*n**2 + 100/3*n**3 - 13 + 16*n. Let j(r) = 0. What is r?
2/5
What is v in 96*v**2 - 1567 + 2*v**5 + 54*v**4 + 148*v**3 - 1569 + 3136 = 0?
-24, -2, -1, 0
Let f be ((-9)/(-24))/(3/24). Let v(x) be the second derivative of -1/105*x**6 + 1/42*x**4 + 0*x**f + 0*x**2 + 1/70*x**5 - 5*x + 0 - 1/147*x**7. Factor v(t).
-2*t**2*(t - 1)*(t + 1)**2/7
Let p = 3 + 1. Let m be (-12 - -13)/((-12)/(-32)). Find t, given that -4/3*t**2 + p*t - m = 0.
1, 2
Let m(q) = 9*q**2 - 33*q + 36. Let c(f) = 16*f**2 - 65*f + 71. Let t(r) = 6*c(r) - 11*m(r). Suppose t(v) = 0. What is v?
-10, 1
Let v(q) = q**2 + 5*q - 80. Let f be v(-12). Factor 3*x**f + 0 + 3/2*x**5 - 3/2*x - 3*x**2 + 0*x**3.
3*x*(x - 1)*(x + 1)**3/2
Let n(v) = 2*v + 2. Let a(f) = 9*f**2 - 471*f + 360. Let t(q) = -a(q) + 15*n(q). Find d, given that t(d) = 0.
2/3, 55
Let u = -1/74 + 204/37. Let -u*w + 3/2 - 2*w**2 = 0. Calculate w.
-3, 1/4
Let v(h) = 14*h**2 + 172*h - 532. Let b(l) = 2*l**2 + 25*l - 76. Let c(q) = 44*b(q) - 6*v(q). Factor c(o).
4*(o - 2)*(o + 19)
Let t be (-33)/429 + (-80)/(-26). Solve -t*j**2 + 15/2*j**3 - 15/2*j + 3 = 0.
-1, 2/5, 1
Let r(a) be the first derivative of a**4/4 + 3*a**3 + 27*a**2/2 - 3*a - 9. Let g(h) be the first derivative of r(h). Find p such that g(p) = 0.
-3
Let l(v) = -3*v**4 + 4*v**3 + 5*v**2 - 8*v + 6. Let h(n) = -7*n**4 + 9*n**3 + 11*n**2 - 16*n + 13. Let m(t) = 2*h(t) - 5*l(t). Factor m(o).
(o - 2)*(o - 1)**2*(o + 2)
Suppose -5*d - 4 = -29. Suppose -4 = -3*l + d. Factor 0*j + 2 + 12*j - 4 + l*j**2 + 11.
3*(j + 1)*(j + 3)
Let d(j) be the third derivat