- 3/2*s**4 - 1/30*s**6 - 7/20*s**5 - 7*s. Factor w(t).
-(t + 1)*(t + 2)**3
Let g(i) be the third derivative of i**8/1344 - i**7/56 - 19*i**6/480 + 43*i**5/240 + 13*i**4/16 + 4*i**3/3 - 249*i**2. Factor g(q).
(q - 16)*(q - 2)*(q + 1)**3/4
Suppose c = -3*t - 2*c + 33, 23 = 4*t - 3*c. Suppose -2*y = -t*y + y. Factor 0*k - 2/5*k**2 + y + 2/5*k**3.
2*k**2*(k - 1)/5
Let v(u) = 3*u**3 - 15*u**2 + 21*u - 12. Suppose -3*b + 6*b = -9. Let z(k) = -3*k**3 + 15*k**2 - 21*k + 13. Let r(w) = b*z(w) - 4*v(w). Factor r(x).
-3*(x - 3)*(x - 1)**2
Let q(j) be the third derivative of j**7/105 - j**6/30 - 2*j**5/5 + 3*j**4/2 + 9*j**3 - 557*j**2. Let q(w) = 0. Calculate w.
-3, -1, 3
Let a(r) be the third derivative of r**7/735 + r**6/60 - r**5/21 - 4*r**4/21 + 233*r**2. Factor a(u).
2*u*(u - 2)*(u + 1)*(u + 8)/7
Factor 7*o + 32*o**2 - 35*o**2 - 37*o - 48.
-3*(o + 2)*(o + 8)
Let o(r) be the first derivative of 10/3*r**3 + 0*r**2 + 7 + 0*r + 5/4*r**4. Determine i, given that o(i) = 0.
-2, 0
Let a(c) = 5*c - 2. Let x be (-1)/((-15)/(-9) - 2). Let t be a(x). Solve 12*g**2 + t*g**3 + 5*g**5 - 4*g**5 + 4*g + 6*g**4 + 0*g**5 = 0 for g.
-2, -1, 0
Let s(i) be the third derivative of 1/3*i**3 + 0 + 1/240*i**6 - 6*i**2 + 0*i - 1/40*i**5 + 0*i**4. What is a in s(a) = 0?
-1, 2
Let y(u) = u - 3. Let m(f) = -2*f**2 + 6*f + 2. Let p(q) = -m(q) - 6*y(q). Suppose p(i) = 0. Calculate i.
2, 4
Factor 1/8*c**2 + 0 + 31/8*c.
c*(c + 31)/8
Suppose -5*p = p - 30. Find k such that -25*k**2 + 29*k**5 - 15*k**2 - 100*k**3 - 8*k**5 + 24*k**p - 30*k**4 = 0.
-2/3, 0, 2
Let g(c) be the second derivative of -1/100*c**5 + 1/12*c**4 + 20*c - 7/30*c**3 + 3/10*c**2 + 0. Factor g(r).
-(r - 3)*(r - 1)**2/5
Let g(k) be the third derivative of 0*k + 2/455*k**7 - 12*k**2 - 1/2184*k**8 - 7/390*k**6 + 8/195*k**5 - 3/52*k**4 + 0 + 2/39*k**3. Find t such that g(t) = 0.
1, 2
Suppose -18*r + 2*r**5 + 6*r - 52 + 45*r**3 - 2*r**5 - 92 + 120*r**2 - 6*r**4 - 3*r**5 = 0. Calculate r.
-3, -2, 1, 4
Suppose 0 = -28*v - 1 + 29. Solve 3/4*u**2 - v - 1/4*u**4 - 1/2*u**3 + u = 0 for u.
-2, 1
Let q = -46 - -49. Factor -12*l**4 + 43*l + 16 + l**q + 16*l**4 + 5*l + 23*l**3 + 52*l**2.
4*(l + 1)**2*(l + 2)**2
Let l(f) be the third derivative of f**6/660 + 2*f**5/165 - f**4/132 - 4*f**3/33 + 4*f**2 - 5. Let l(s) = 0. Calculate s.
-4, -1, 1
Let v(o) be the second derivative of -o**6/165 + 3*o**5/55 - o**4/66 - 8*o**3/11 - 16*o**2/11 - 120*o. Determine p so that v(p) = 0.
-1, 4
Let m(w) = 123*w**3 - w**2 - 2. Let o be m(-2). Let z = o + 4976/5. Factor -z*l**4 - 4/5*l**3 - 22/5*l**5 + 0*l**2 + 0 + 0*l.
-2*l**3*(l + 1)*(11*l + 2)/5
Suppose -s + 5*i + 26 = 0, -2*i + 16 = 2*s - 3*i. Factor 3*c**2 - 12*c - 2*c**2 - 9*c + s + 26*c.
(c + 2)*(c + 3)
Let l = -1723 + 1726. Factor 0*v**l + 3/5*v**2 + 0 + 0*v - 3/5*v**4.
-3*v**2*(v - 1)*(v + 1)/5
Let g(b) = 7*b**2 + b - 1. Let s be g(1). Suppose -101 = -s*w + 32. Suppose -w*f - f**2 + 9*f - 4*f**2 = 0. Calculate f.
-2, 0
Factor 1323*c**3 + 11328*c + 8568*c**2 - 1029/2*c**4 + 4608.
-3*(c - 6)*(7*c + 8)**3/2
Let j(p) be the third derivative of p**8/3528 - p**7/245 + p**6/84 + 5*p**5/126 - 13*p**2 - 1. Find u, given that j(u) = 0.
-1, 0, 5
Let c = -451 + 456. Let n(a) be the third derivative of 0 + 0*a**6 + 0*a**4 + 1/3*a**3 + c*a**2 + 1/105*a**7 + 0*a - 1/15*a**5. Factor n(t).
2*(t - 1)**2*(t + 1)**2
Let y be 3 - ((-3094)/(-2028) + (-10)/(-12)). Let s(b) be the third derivative of 0*b - y*b**3 - 2/195*b**5 - 5*b**2 + 0 + 5/39*b**4. Factor s(d).
-2*(2*d - 5)**2/13
Let y = -4/4689 - -25012/4689. Find c, given that 588*c**4 + 1108/3*c**2 + y + 1064*c**3 - 304/3*c = 0.
-1, 2/21
Let z = -6031/3 - -2011. Factor 4*q + z*q**2 + 10/3.
2*(q + 1)*(q + 5)/3
Let h(y) be the third derivative of y**8/392 + 53*y**7/735 + 3*y**6/10 + 3*y**5/7 - y**4/84 - 5*y**3/7 - 6*y**2 - 36. What is s in h(s) = 0?
-15, -1, 1/3
Let l(p) be the second derivative of p**7/490 - p**6/140 + p**4/28 - p**3/14 - 7*p**2/2 - 10*p. Let v(w) be the first derivative of l(w). Factor v(b).
3*(b - 1)**3*(b + 1)/7
Suppose -219*g + 207 = -56*g - 282. Factor -2*a + 16/15 + 2/15*a**g + 4/5*a**2.
2*(a - 1)**2*(a + 8)/15
Factor 3/5*o**5 + 0 + 0*o**3 - 6/5*o**4 - 3/5*o + 6/5*o**2.
3*o*(o - 1)**3*(o + 1)/5
Let c be (-160)/6*8/(-5). Let a(t) = 2*t**3 + 54*t**2 + 144*t + 3. Let q be a(-24). Factor -8*l**2 + 2/3*l**q - c + 32*l.
2*(l - 4)**3/3
Let t be (6 - 3) + -1 + -1 + 2. Let g be t/(-2) + 27*4/40. Factor 0*s**3 + 0 + 4/5*s - 2/5*s**4 + g*s**2.
-2*s*(s - 2)*(s + 1)**2/5
Let d(l) be the second derivative of 2*l**6/75 + 3*l**5/25 - l**4/15 - 2*l**3/5 - 156*l. Suppose d(g) = 0. What is g?
-3, -1, 0, 1
Let w(p) = 6*p**4 - 18*p**3 - 3*p**2 - 3*p + 3. Let c(s) = 11*s**4 - 36*s**3 - 5*s**2 - 5*s + 5. Let n(u) = 3*c(u) - 5*w(u). Let n(i) = 0. Calculate i.
0, 6
Let a(n) = n**2 - 3*n - 3. Let r be a(6). Factor -z**2 - 11*z**2 + 2 - 5 - r*z.
-3*(z + 1)*(4*z + 1)
Let c(q) be the second derivative of -q**6/10 + 87*q**5/20 + 15*q**4/2 - 49*q + 1. Let c(p) = 0. What is p?
-1, 0, 30
Let s(j) be the third derivative of 23*j**2 - 1/30*j**6 + 0*j**3 + 0*j**4 + 0*j + 0 + 1/15*j**5. Find z, given that s(z) = 0.
0, 1
Let a(g) be the third derivative of -g**5/60 - 23*g**4/12 - 15*g**3/2 + 36*g**2 + 1. Factor a(j).
-(j + 1)*(j + 45)
Let l = 2044 + -2037. Let a(h) be the third derivative of 2*h**2 + 0 + 0*h**3 - 1/20*h**5 + 0*h + 1/70*h**l - 1/40*h**6 + 1/8*h**4. Solve a(b) = 0 for b.
-1, 0, 1
Let n = 698 - 1020. Let x = -175 - n. Suppose 4*f**3 - 139 + 16*f**2 + 20*f + x + 0*f = 0. What is f?
-2, -1
Let p(s) be the second derivative of s**7/30 + s**6/5 + 29*s**5/100 + s**4/10 + 6*s - 4. Let p(z) = 0. Calculate z.
-3, -1, -2/7, 0
Let x be 5/1 - (4 + -2). Let p(f) be the second derivative of 0 - 9*f + 1/3*f**4 + 0*f**2 + 1/20*f**5 + 1/2*f**x. Factor p(c).
c*(c + 1)*(c + 3)
Let u(n) be the first derivative of -3/8*n**2 + 3/16*n**4 - 17 + 1/2*n**3 - 3/10*n**5 + 0*n. Let u(a) = 0. What is a?
-1, 0, 1/2, 1
Suppose -10 = p + 4*p. Let f be (30/(-45))/(p/9). What is t in -t**2 - 47*t**3 - 6*t + 8*t**2 + 50*t**f + 0*t**2 = 0?
-3, 0, 2/3
Let t be 14/6 - (-2)/(-6). Suppose -3*f - t = -4*f. Solve 0*k**4 + 7*k**4 + 0*k**f + 3*k**3 - 3*k**2 - 4*k**4 - 3*k = 0.
-1, 0, 1
Let t be (-8)/(-132)*(-11 + (14 - 0)). Factor 0 - t*k**2 + 4/11*k.
-2*k*(k - 2)/11
Let c(g) be the second derivative of 4*g**2 + 1/10*g**5 + g**4 - 6*g + 3*g**3 + 0. Factor c(k).
2*(k + 1)**2*(k + 4)
Suppose -5*n + 41 = -14. Let a(l) = -l + 4. Let d be a(2). Factor -z**2 - 10*z + 11*z**3 - n*z**3 + 2*z**3 + 2*z**4 - 4 - 5*z**d.
2*(z - 2)*(z + 1)**3
Let s(y) be the first derivative of 1/2*y**2 + 1/6*y**3 - 3/2*y + 24. Find h, given that s(h) = 0.
-3, 1
Solve -53*c**3 + 2 + 46*c + 4*c**2 + 9*c**3 - 990*c**5 - 26*c**4 + 988*c**5 + 20 = 0 for c.
-11, -1, 1
Let x(k) = k + 1. Let d(j) = -j**2 + 33*j - 255. Let n(y) = -4*d(y) + 4*x(y). Factor n(q).
4*(q - 16)**2
What is v in 4*v**4 + 2*v**2 + 0*v**3 - 5*v**3 + 45*v**5 - 46*v**5 = 0?
0, 1, 2
Let k(x) = 2*x**4 - 8*x**3 - 10*x**2 - 10*x. Let i = 89 - 99. Let r(c) = -c**3 - c**2 - c. Let f(y) = i*r(y) + k(y). Find u such that f(u) = 0.
-1, 0
Let r = 7560 - 7555. Let 1/2*c**r + 0 + 0*c - c**2 - 1/2*c**3 + c**4 = 0. What is c?
-2, -1, 0, 1
Let h(o) be the first derivative of 30 + 0*o + 1/6*o**4 + 1/3*o**2 - 4/9*o**3. Solve h(k) = 0 for k.
0, 1
Let i(o) = -5*o**3 + 45*o**2 + 5*o + 15. Let q(y) = y**2 - y - 3. Let u(x) = i(x) + 5*q(x). Factor u(m).
-5*m**2*(m - 10)
Let d(x) be the first derivative of -5*x**6/6 - 7*x**5 - 45*x**4/2 - 100*x**3/3 - 20*x**2 - 38. Let d(y) = 0. Calculate y.
-2, -1, 0
What is h in -4 + 1/4*h**3 + 0*h**2 - 3*h = 0?
-2, 4
Let t be 7 + (1 - 6) - 0 - 0. Let g(w) be the first derivative of 3/4*w**t + 0*w + 1/2*w**3 - 3/10*w**5 - 3/8*w**4 + 3. Suppose g(d) = 0. Calculate d.
-1, 0, 1
Let o(m) = 15*m**2 + 17*m + 11. Suppose 16 = -4*p + 4*j, -p = -4*j + 2 + 5. Let w(t) = -14*t**2 - 18*t - 10. Let u(h) = p*w(h) - 2*o(h). Solve u(d) = 0.
-1, -2/3
Let x(p) be the first derivative of -p**4 + 4/15*p**5 + 4*p - 24 + 1/9*p**6 - 16/9*p**3 + 5/3*p**2. Solve x(r) = 0.
-3, -1, 1, 2
Solve 12*a**2 - 4*a**3 + 16*a**2 - 4*a + 0*a**3 + 3*a**3 + 5*a**3 - 28 = 0.
-7, -1, 1
Let a(f) be the third derivative of 5*f**8/144 + 4*f**7/105 + f**6/90 + 28*f**2 + 4. Factor a(d).
d**3*(5*d + 2)