rd derivative of y**5/12 + 35*y**4/24 + 25*y**3/3 - 53*y**2. Factor v(j).
5*(j + 2)*(j + 5)
Let j = -20 + 24. Let y(h) be the first derivative of 2 - 1/24*h**j - 1/18*h**3 + 1/12*h**2 + 1/6*h. Factor y(p).
-(p - 1)*(p + 1)**2/6
Let z(t) = t**2 - 8*t. Let g be z(8). Suppose g - 10 = -5*v. Factor 2*u + 1/2*u**2 + v.
(u + 2)**2/2
Let m(l) be the first derivative of -1/20*l**5 + 0*l - l**2 - 2 - 3/8*l**4 - l**3. Find i, given that m(i) = 0.
-2, 0
Suppose -3*m + s + 12 = 0, -4*s = -3*m - 14 + 35. What is l in 1/3*l + 0 + 0*l**m - 2/3*l**2 + 2/3*l**4 - 1/3*l**5 = 0?
-1, 0, 1
Let l be 6/4*104/39. Solve -4/3*r**2 + 0*r**3 + 2/3 + 0*r + 2/3*r**l = 0.
-1, 1
Suppose -30*j = -9*j. Let 0*q + 2/11*q**4 - 2/11*q**2 + 0 + j*q**3 = 0. What is q?
-1, 0, 1
Let g be (0 - 0)/(13 + -12). Factor g + 2/11*x**3 - 2/11*x + 2/11*x**4 - 2/11*x**2.
2*x*(x - 1)*(x + 1)**2/11
Suppose 0 - 1/2*l**4 - l**3 - 1/2*l**2 + 0*l = 0. Calculate l.
-1, 0
Let n = 18/5 + -14/15. Let -2/3*f**5 + 0 + 0*f - 10/3*f**3 + 4/3*f**2 + n*f**4 = 0. What is f?
0, 1, 2
Suppose 2/5*t - 2/5 - 2/5*t**3 + 2/5*t**2 = 0. Calculate t.
-1, 1
Let c(w) be the second derivative of -w**8/36960 + w**7/13860 - w**4/6 - 2*w. Let v(y) be the third derivative of c(y). Factor v(o).
-2*o**2*(o - 1)/11
Let m = 204 + -202. Factor 0*y**4 + 0 - 1/4*y**5 + 1/2*y**3 - 1/4*y + 0*y**m.
-y*(y - 1)**2*(y + 1)**2/4
Let s(q) = -2*q**2. Suppose 13 + 7 = 2*h. Let i(c) = -3*c - 2*c + 4*c + h*c**2. Let r(f) = -2*i(f) - 11*s(f). Factor r(d).
2*d*(d + 1)
Let m(d) = 2*d**3 - 13*d**2 + 13*d - 8. Let a(c) = 2*c**3 - 14*c**2 + 12*c - 8. Suppose 9 = 2*h + 1. Let w(r) = h*m(r) - 3*a(r). Factor w(v).
2*(v - 2)**2*(v - 1)
Let -1/5*b**3 - 3/5*b**2 - 2/5*b + 0 = 0. Calculate b.
-2, -1, 0
Factor 0*g - 2/7*g**3 + 0*g**2 + 0 + 0*g**4 + 2/7*g**5.
2*g**3*(g - 1)*(g + 1)/7
Solve -u**2 - 4*u - 4*u**3 + 5*u**3 + u**2 = 0.
-2, 0, 2
Let a(m) be the second derivative of m**7/189 + m**6/45 + m**5/30 + m**4/54 + m. Factor a(z).
2*z**2*(z + 1)**3/9
Suppose 55 = -3*h - 0*h - f, -2*h - 60 = -4*f. Let b = -39/2 - h. Determine i, given that -3/4*i**5 - 3/4*i + b*i**2 - 1/4*i**4 - 1/4 + 3/2*i**3 = 0.
-1, -1/3, 1
Suppose -2*y = 3*v + 3*y - 10, -2 = 5*v - y. Factor 1/2*s**4 + 0*s - 1/2*s**2 + 0*s**3 + v.
s**2*(s - 1)*(s + 1)/2
Solve -24/19*k**4 + 18/19*k + 20/19*k**2 + 4/19 - 8/19*k**3 - 10/19*k**5 = 0.
-1, -2/5, 1
Factor 1/4*w**3 + 0 + 0*w + 1/4*w**2.
w**2*(w + 1)/4
Let x(b) be the first derivative of -b**4/60 + b**3/15 - b**2/10 - 3*b - 3. Let z(t) be the first derivative of x(t). Factor z(s).
-(s - 1)**2/5
Let r(f) be the first derivative of -1/30*f**6 + 0*f**3 + 0*f**2 - 4 + 0*f**5 + 1/20*f**4 + 0*f. Factor r(u).
-u**3*(u - 1)*(u + 1)/5
Let m be (19 + 1098/(-54))*(-6)/4. Suppose -1/5*t - 2/5*t**m + 2/5 + 1/5*t**3 = 0. Calculate t.
-1, 1, 2
Find k such that 30/7*k**5 + 8/7*k - 38/7*k**3 + 8/7*k**2 + 0 - 8/7*k**4 = 0.
-1, -2/5, 0, 2/3, 1
Let q(b) be the first derivative of 1/108*b**4 + 0*b + 0*b**3 - 1 + 1/270*b**5 + b**2. Let j(c) be the second derivative of q(c). Let j(t) = 0. Calculate t.
-1, 0
Let l(n) be the second derivative of -1/45*n**6 + 0*n**2 + 0 - 1/10*n**5 - 2/9*n**3 + 3*n + 1/63*n**7 + 5/18*n**4. Suppose l(q) = 0. What is q?
-2, 0, 1
Factor -214*u - 15*u**4 + 13*u**3 + 3*u**5 + 12*u**2 + 190*u + 5*u**3.
3*u*(u - 2)**3*(u + 1)
Solve 2/3*s**2 + 0 - s + 1/3*s**3 = 0.
-3, 0, 1
Let c(d) = -d**3 - d**2 - d + 1. Let h(g) = -2*g**3 - 74*g**2 + 642*g - 574. Let f(k) = 4*c(k) - h(k). Factor f(j).
-2*(j - 17)**2*(j - 1)
Let m = -255 + 517/2. Suppose -1 + 4*y - 23/4*y**2 + m*y**3 - 3/4*y**4 = 0. What is y?
2/3, 1, 2
Suppose -5*o + 3*o - 72 = 0. Let l be (2/(-3))/(8/o). Factor l*x - 2*x**2 - 3*x.
-2*x**2
Factor 6 + 8*z**2 + 20*z - 5*z + 3*z**3 + z**2 + 3*z**2.
3*(z + 1)**2*(z + 2)
Let q(k) be the second derivative of 5*k**4/12 - 5*k**2/2 + 10*k. Determine s so that q(s) = 0.
-1, 1
Determine v so that 0 + 4/9*v**2 - 2/9*v**3 - 2/9*v = 0.
0, 1
Let p(r) be the second derivative of -3*r**4/28 - r**3/14 + 6*r. Factor p(c).
-3*c*(3*c + 1)/7
Let x(z) be the third derivative of z**9/211680 + z**8/35280 + z**7/17640 + z**5/60 + z**2. Let g(w) be the third derivative of x(w). Factor g(u).
2*u*(u + 1)**2/7
Suppose -4*k - 130 = -2*b, 0*k - b = k + 25. Let y = k + 33. Factor -2/3*g + 2/9*g**y + 4/9 + 0*g**2.
2*(g - 1)**2*(g + 2)/9
Let g(p) = 9*p**3 - 9*p. Let l(n) = -n**3 + n. Let m(o) = g(o) + 6*l(o). Suppose m(x) = 0. What is x?
-1, 0, 1
Let y(d) be the second derivative of -d**5/80 - d**4/16 + 3*d**3/8 - d**2/2 + 11*d. Let h(u) be the first derivative of y(u). Find a such that h(a) = 0.
-3, 1
Let m(w) be the third derivative of 3*w**8/224 - w**7/20 + 3*w**6/80 + 3*w**5/40 - w**4/8 - w**2. Factor m(s).
3*s*(s - 1)**3*(3*s + 2)/2
Let s = 2 + 0. Suppose q**2 + q - 2*q - 2*q**s + 2*q = 0. What is q?
0, 1
Let l be (((-60)/(-18))/5)/2. Let j = 8 - 6. Solve -1/3 - l*t**j + 2/3*t = 0.
1
Factor -18*c**3 + 19*c**2 + 17*c**2 - 4*c**4 - 56*c**2 - 6*c.
-2*c*(c + 1)*(c + 3)*(2*c + 1)
Suppose 10*q - 5*q = 10. Find w, given that 0*w**2 - q*w**4 - w**2 - 5*w**2 + w**3 + 2*w + 5*w**3 = 0.
0, 1
Let y(a) be the second derivative of 2*a**6/75 - a**5/25 - a**4/15 + 2*a**3/15 + 24*a. Solve y(p) = 0 for p.
-1, 0, 1
Let b = -200/3 + 1412/21. Solve b*q**2 + 0 + 2/7*q**3 - 6/7*q = 0 for q.
-3, 0, 1
Let a(i) be the third derivative of 1/240*i**5 + 0*i - 1/12*i**3 + 0 + i**2 - 1/96*i**4. Find j such that a(j) = 0.
-1, 2
Let v = 10 - 7. Let f(s) be the third derivative of 1/60*s**5 + 0*s**v + 0*s**4 + 0 + 0*s + 2*s**2. Factor f(g).
g**2
Factor -3*x**2 + 5*x**2 + 132*x**3 - 260*x**3 + 126*x**3.
-2*x**2*(x - 1)
Let m(v) = -v**2 + v - 6. Let z be m(0). Let h be (1 + 2)*z/(-9). Factor 2*w**2 - 2 - h + 2*w**4 - 6*w + 0*w**2 + 0 + 6*w**3.
2*(w - 1)*(w + 1)**2*(w + 2)
Let d(c) be the second derivative of c**8/2100 - c**7/600 + c**6/900 + c**5/600 + c**3/6 - 3*c. Let s(n) be the second derivative of d(n). Factor s(b).
b*(b - 1)**2*(4*b + 1)/5
Let w(o) = -7*o**3 + 12*o**2 - 3*o - 2. Let m(v) = 14*v**3 - 24*v**2 + 6*v + 4. Let l(q) = -6*m(q) - 13*w(q). Factor l(j).
(j - 1)**2*(7*j + 2)
Let n(p) be the first derivative of p**4/5 + 32*p**3/15 - 2*p**2/5 - 32*p/5 + 30. Solve n(h) = 0.
-8, -1, 1
Suppose 0 = u + 4*u. Let i(x) be the third derivative of u*x + x**2 + 1/100*x**6 + 0 + 1/150*x**5 + 1/840*x**8 + 0*x**4 + 0*x**3 + 1/175*x**7. Factor i(k).
2*k**2*(k + 1)**3/5
Determine m, given that 0*m + 2/9 - 2/9*m**2 = 0.
-1, 1
Let x(s) = -s**3 - 2*s**2 + s + 2. Let z be x(-1). Let i(a) be the first derivative of -2 + 4/15*a**3 - 1/5*a**2 + z*a - 1/10*a**4. Factor i(c).
-2*c*(c - 1)**2/5
Suppose 27 = 15*h - 3. Determine g, given that 2*g - 1/2*g**2 - h = 0.
2
Let h(f) = -f**3 + 11*f + 0*f + 10*f**2 + 0*f. Let y be h(11). Factor -1/3*s**3 + 1/3*s**5 + 0*s + y + 0*s**2 + 0*s**4.
s**3*(s - 1)*(s + 1)/3
Let x(o) be the third derivative of -o**8/280 + o**7/75 - o**6/60 + o**5/150 + 6*o**2. Solve x(a) = 0 for a.
0, 1/3, 1
Let d(h) be the first derivative of -h - 1/2*h**2 - 4 + 1/3*h**3 + 1/4*h**4. Factor d(j).
(j - 1)*(j + 1)**2
Let m(o) be the first derivative of -o**3/36 - o**2/24 + o/6 - 40. Find c such that m(c) = 0.
-2, 1
Let r(w) be the third derivative of w**8/84 + 2*w**7/35 + w**6/30 - w**5/5 - w**4/3 - 3*w**2. Let r(j) = 0. What is j?
-2, -1, 0, 1
Let y be 2*(0 - (-1112)/20). Let v = y - 110. Let 2/5*r**4 + 6/5*r**2 - v*r**3 - 2/5*r + 0 = 0. What is r?
0, 1
Suppose c - 4*c + 9 = 0. Let g be 4/2 + -1 + -1. Suppose -1/5*j**4 + g*j**c + 0 + 0*j**2 + 0*j = 0. What is j?
0
Let f be (4/154)/((-123)/21 - -6). Factor -f*s**5 - 10/11*s - 2/11 - 10/11*s**4 - 20/11*s**2 - 20/11*s**3.
-2*(s + 1)**5/11
Let n(z) be the first derivative of -z**5/5 - z**4/4 + 16. Factor n(o).
-o**3*(o + 1)
Let m(f) = -f**5 - f**4 - f + 1. Let d(k) = -21*k**5 - 15*k**4 - 18*k + 18. Let n(v) = d(v) - 18*m(v). Solve n(j) = 0 for j.
0, 1
Let g(o) = 18*o**4 + 5*o**3 - 17*o**2 - 4*o - 7. Let y(m) = 9*m**4 + 3*m**3 - 8*m**2 - 2*m - 3. Let f(w) = -3*g(w) + 7*y(w). Determine d so that f(d) = 0.
-1, -1/3, 0, 2/3
Let u be 14/4 - (6 - 3). Let r(y) be the first derivative of 0*y**2 + u*y**4 + 0*y + 2 + 2/3*y**3. Factor r(z).
2*z**2*(z + 1)
Let f(s) = 20*s**3 - 748*s**2 + 3932*s - 6500. Let r(t) = -3*t**3 + 115*t**2 - 605*t + 1000. Let c(j) = 5*f(j) + 32*r(j