t + 1)
Let y(f) be the third derivative of f**5/60 - 588*f**2. Factor y(c).
c**2
Let x(t) be the first derivative of 3/2*t + 1/18*t**3 - 1/2*t**2 + 2. Suppose x(o) = 0. Calculate o.
3
Let u = -11 + 15. Let j(f) = -f**2 + 3*f - f + 8*f**3 + f**u - 13*f**3 + 3*f. Let a(h) = -h**4 + 4*h**3 + h**2 - 4*h. Let w(t) = 3*a(t) + 2*j(t). Factor w(m).
-m*(m - 2)*(m - 1)*(m + 1)
Let c(i) be the first derivative of 2/9*i**3 - 8 + 4/3*i**2 + 0*i. Factor c(b).
2*b*(b + 4)/3
Let r = 50 - 15. Let x be (4/(-5))/((-7)/r). Find a such that -6*a - 3 - 9*a**4 + 17*a**2 - 5*a**2 + x*a**3 + 5*a**3 - 3*a**3 = 0.
-1, -1/3, 1
Let x(z) = -23*z**4 - 23*z**3 - 393*z**2 - 1768*z - 2693. Let o(t) = 2*t**4 - t**3 - 1. Let r(s) = 22*o(s) + 2*x(s). Factor r(v).
-2*(v + 4)**2*(v + 13)**2
Let c = 26 + -23. Factor 3/4*d - 3/4*d**c + 3/2*d**2 - 3/2.
-3*(d - 2)*(d - 1)*(d + 1)/4
Let j be (1 - 22/18)/((-10)/(-15)). Let i = 1/6 - j. Factor 1/2*f**3 - 1/2*f - i*f**2 + 1/2*f**4 + 0.
f*(f - 1)*(f + 1)**2/2
Let a(p) be the second derivative of -p**6/6 + p**5/2 + 5*p**4/3 - 5*p**3/3 - 15*p**2/2 - p - 1. Find f such that a(f) = 0.
-1, 1, 3
Let h(x) = -x**4 + 7*x**3 + x**2 - 2*x. Let s(k) = k**4 + k**3 - k**2 - 2*k. Let t = 69 + -68. Let m(l) = t*h(l) + 5*s(l). Factor m(n).
4*n*(n - 1)*(n + 1)*(n + 3)
Let w be (-4)/22 - (-194)/(-22). Let u = 12 + w. Factor -u*j**3 - 5*j**2 - 4*j**2 - 9*j**4 + 6 + 3*j + 12*j**4.
3*(j - 2)*(j - 1)*(j + 1)**2
Let j(q) = 4*q**2 + 72*q - 82. Let v(f) = -17*f**2 - 286*f + 330. Let k(z) = 9*j(z) + 2*v(z). Solve k(u) = 0.
-39, 1
Let m(b) be the third derivative of -b**7/42 + 3*b**6/8 - 7*b**5/12 - 75*b**4/8 - 70*b**3/3 + 3*b**2 + 80*b. Find p such that m(p) = 0.
-1, 4, 7
Solve -20*y + 204*y**2 - 40*y**3 - 3*y**4 + 12*y**5 + 37*y**3 - 73*y**4 - 81*y**3 - 36*y = 0.
-2, 0, 1/3, 1, 7
Let c(j) be the third derivative of -j**6/80 + 7*j**5/8 + 183*j**2. Factor c(s).
-3*s**2*(s - 35)/2
Let c be 2 - 1 - ((-1071)/34)/21. Factor -2 - c*z - 1/2*z**2.
-(z + 1)*(z + 4)/2
Let k(d) be the first derivative of -2*d**3/51 - 16*d**2/17 - 56*d/17 + 426. Solve k(g) = 0 for g.
-14, -2
Let p = -318 - -318. Determine k, given that -2/17*k**2 + p*k + 0 + 2/17*k**4 + 0*k**3 = 0.
-1, 0, 1
Let q(o) be the first derivative of 0*o - o**3 + 7 + 27/28*o**4 - 3/7*o**2. Solve q(w) = 0 for w.
-2/9, 0, 1
Factor -12*o - 28*o**3 + 9 + 4*o**3 - 38*o**2 - o**3 - 3*o**4 + 5*o**3.
-(o + 1)*(o + 3)**2*(3*o - 1)
Let u(l) be the first derivative of l**4 + 32*l**3 - 216*l**2 + 448*l - 560. Factor u(x).
4*(x - 2)**2*(x + 28)
Let t(b) be the second derivative of -b**6/195 + b**5/65 + b**4/78 - 2*b**3/39 - 141*b. Let t(a) = 0. What is a?
-1, 0, 1, 2
Suppose 769 - 814 = -15*o. Let f(g) be the first derivative of -2*g**2 + 8/3*g**o - g**4 + 8 + 0*g. Suppose f(q) = 0. Calculate q.
0, 1
Suppose 5*s - 16 - 14 = 0. Let i(q) be the first derivative of 7/2*q**2 + 2*q + 4/5*q**5 - s - 2*q**3 - 7/4*q**4. Solve i(j) = 0 for j.
-1, -1/4, 1, 2
Let r(s) be the first derivative of -s**6/180 + 7*s**5/30 - 49*s**4/12 - 9*s**3 - 4. Let m(i) be the third derivative of r(i). Suppose m(y) = 0. What is y?
7
Let t(p) = -p - 3. Let c be t(-3). Suppose 3*l + 0*l - 3 = c. Factor -1 + l - 3*i**2 + i**4 + 2*i.
i*(i - 1)**2*(i + 2)
Let x(n) be the third derivative of -n**6/120 - 2*n**5/3 - 100*n**2. Factor x(f).
-f**2*(f + 40)
Let w(k) = -2*k**3 + k**2 - 4*k - 1. Let j(p) = p**3 - p**2 + 3*p + 1. Let s = 6 - 4. Let i(d) = s*w(d) + 3*j(d). Determine g, given that i(g) = 0.
-1, 1
Let f(b) = -15*b**2 - 248*b + 563. Let c(l) = -5*l**2 - 83*l + 188. Let h(i) = -7*c(i) + 2*f(i). Factor h(q).
5*(q - 2)*(q + 19)
Solve -12/7 + 34/7*c - 2/7*c**5 + 8/7*c**4 + 0*c**3 - 4*c**2 = 0 for c.
-2, 1, 3
Let c = -83049/533 - -3572/41. Let n = c + 69. Determine g, given that 0 + 10/13*g**3 - n*g**2 + 0*g + 14/13*g**4 = 0.
-1, 0, 2/7
Determine f so that 3/4*f**2 - 3/4 - 1/4*f + 1/4*f**3 = 0.
-3, -1, 1
Let o = -254 + 325. Let q = 143/2 - o. Suppose -q + 0*x**2 - 1/4*x**3 + 3/4*x = 0. What is x?
-2, 1
Let d(o) = 72*o - 214. Let r be d(3). Let b(i) be the third derivative of 1/24*i**4 - 1/60*i**6 + 0*i**3 + 0*i + 0 + 3*i**r - 1/60*i**5. Solve b(k) = 0 for k.
-1, 0, 1/2
Factor 5*v - 8*v**3 + 12*v**2 - 15*v + v + 5*v**3.
-3*v*(v - 3)*(v - 1)
Suppose -2*x = 0, -4*u - 10 = -9*u + 5*x. Factor 18*w**2 + 14*w**3 - 8*w**3 - 8*w**u.
2*w**2*(3*w + 5)
Let j(k) be the second derivative of k**7/84 + 19*k**6/180 + 19*k**5/120 - 43*k**4/72 - 11*k**3/18 + 2*k**2 + 15*k - 12. Suppose j(t) = 0. What is t?
-4, -3, -1, 2/3, 1
Let a(z) = -40*z**2 + 2*z + 22. Let k = 16 - 32. Let t(j) = 13*j**2 - j - 7. Let b(s) = k*t(s) - 5*a(s). Factor b(r).
-2*(r - 1)*(4*r + 1)
Let t(x) be the third derivative of 0*x + 0*x**4 + 0*x**3 + 0 - 1/80*x**5 + 4*x**2 - 1/280*x**7 - 1/80*x**6. Factor t(h).
-3*h**2*(h + 1)**2/4
Let z(c) be the second derivative of 27*c**5/100 - 3*c**4/2 + 14*c**3/5 - 12*c**2/5 + 74*c. Factor z(g).
3*(g - 2)*(3*g - 2)**2/5
Let w = 5151/1472 - -1/1472. Solve w*m**4 + 0 - 1/2*m**2 + 0*m + m**3 + 2*m**5 = 0 for m.
-1, 0, 1/4
Factor 31 - 16 + 24*a**2 + 6*a**2 - a**3 + 63*a + 17.
-(a - 32)*(a + 1)**2
Let n be 1 + -1 + (24 - 20). Let z be (n - 21/6)/(3/2). Factor -z*w + 2/3 - 1/3*w**2.
-(w - 1)*(w + 2)/3
Let r be (-3 - -10 - -1) + -3. Factor -r*p**2 + 3*p + 4*p + p**3 - 2 + 1 - 2.
(p - 3)*(p - 1)**2
Let q be (-2)/(30/(-7) - -4). Factor -20*g + q*g**2 + 810 - 794 - 3*g**2.
4*(g - 4)*(g - 1)
Let c(f) be the first derivative of 0*f + 1/3*f**2 + 12 + 0*f**3 - 1/6*f**4. Factor c(v).
-2*v*(v - 1)*(v + 1)/3
Suppose 5*p - 32 = -22. Let n(w) be the second derivative of 1/50*w**5 + 0*w**3 + 4/5*w**p - 1/10*w**4 + 0 + w. Factor n(c).
2*(c - 2)**2*(c + 1)/5
Factor -18/5*k + 16/5 + 2/5*k**2.
2*(k - 8)*(k - 1)/5
Let d(g) be the first derivative of -g**7/35 + 3*g**6/40 - g**4/8 + 4*g**2 + 4. Let b(k) be the second derivative of d(k). Factor b(t).
-3*t*(t - 1)**2*(2*t + 1)
Find j, given that -24*j + 10 - 5/2*j**2 = 0.
-10, 2/5
Let s(g) = -g**3 + 49*g**2 - 129*g - 414. Let n be s(46). Find p, given that 2*p**3 + 2/3*p + n - 2*p**2 - 2/3*p**4 = 0.
0, 1
Factor 25/2*p + 57 + 1/2*p**2.
(p + 6)*(p + 19)/2
Factor 5/2*c**3 + 57/2*c - 9 - 16*c**2.
(c - 3)**2*(5*c - 2)/2
Let u be (-50)/(-40) - 9/12. Factor 0 - 1/2*k - u*k**2.
-k*(k + 1)/2
Let f(j) = j - 12. Let b be f(12). Suppose l - 4 + 2 = b. Factor 14*x**3 + 14*x**3 + 9*x**4 - 24 + 90*x**l + 36*x + 23*x**3.
3*(x + 2)**3*(3*x - 1)
Let u(a) = -8*a**3 + 60*a**2 - 118*a + 24. Let k(m) = -8*m**3 + 62*m**2 - 116*m + 24. Let h(d) = -3*k(d) + 2*u(d). Factor h(f).
2*(f - 6)*(f - 2)*(4*f - 1)
Suppose -5*t + 3*l = -25 + 4, 16 = 4*t - 2*l. Suppose 16 - 8*g**t - 18*g**2 + 32*g - 2*g**4 - 2*g**4 + 30*g**2 = 0. What is g?
-2, -1, 2
Let h(q) = q**3 + q**2. Let p(z) = 4*z**4 + z**4 + 10*z + 1 + 20*z**2 + 10*z**3 - 6 + 0. Let b(v) = 20*h(v) - p(v). Factor b(k).
-5*(k - 1)**3*(k + 1)
Let w(l) be the second derivative of -4/11*l**2 + 0 - 1/66*l**4 + 5/33*l**3 - 30*l. Factor w(i).
-2*(i - 4)*(i - 1)/11
Suppose -l = -2*d, 4*d + 3 = -3*l - 27. Let v be (-2 + 7)*l/(-10). Factor -7*u**5 - 20*u**4 + 25*u**4 - u**3 + v*u**3.
-u**3*(u - 1)*(7*u + 2)
Let l = -1127687 + 12414022/11. Let o = 861 - l. Solve 2/11*b - o*b**2 - 2/11*b**3 + 6/11 = 0.
-3, -1, 1
Suppose -4*x - 29 = -41. Suppose -x*z - 3 = -5*s + 15, 1 = s + 2*z. Solve 0 + 0*o - 2/5*o**4 + 0*o**s + 2/5*o**2 = 0 for o.
-1, 0, 1
Let u be 25/(-30)*((-2)/5 + -4). Let s(g) be the second derivative of -6*g - u*g**3 - 8/3*g**4 - 7/10*g**5 + 0 - 2*g**2. Determine r so that s(r) = 0.
-1, -2/7
Let j be 174/624 - ((-2)/(-80) - (-29)/290). Factor -8/13*s - j*s**2 - 8/13.
-2*(s + 2)**2/13
Let w(i) be the third derivative of -5*i**8/168 - 17*i**7/105 + 23*i**6/20 - 11*i**5/6 - i**4/3 + 4*i**3 + 192*i**2. Suppose w(g) = 0. What is g?
-6, -2/5, 1
Let v(w) be the first derivative of -2*w**5/45 - 10*w**4/9 - 154*w**3/27 + 242*w**2/9 - 77. Factor v(b).
-2*b*(b - 2)*(b + 11)**2/9
Find m such that -5/3*m + 4/3*m**2 + 2/3 - 1/3*m**3 = 0.
1, 2
Let u = -49 + 72. Suppose u*h - 24*h = 0. Factor 0*a + 1/6*a**2 + h.
a**2/6
Let f be 4 - (2 + -2) - 3. Let s(g) = g**3 + g. Let x(o) = -27*o**5 + 126*o**4 - 216*o**3 + 156*o**2 - 57*o + 6. Let c(d) = f*x(d) + 6*s(d). Solve c(z) = 0.
1/3, 1, 2
Let j(f) be the third derivative of -1/6*f**4 + 0*f + 0 + 0*f**3 - 