z such that r(z) = 0.
0, 1/3, 1
Let v(o) = 4*o**4 - 14*o**3 + 16*o**2 - 6*o. Let j(h) = -9*h**4 + 29*h**3 - 31*h**2 + 11*h. Let f(r) = -2*j(r) - 5*v(r). Factor f(k).
-2*k*(k - 4)*(k - 1)**2
Let n = 448 - 448. Factor 1/4*l**3 + n + 0*l**2 - 1/4*l.
l*(l - 1)*(l + 1)/4
Let q(n) be the first derivative of -n**5/25 + n**3/15 - 3. Find j, given that q(j) = 0.
-1, 0, 1
Let z(g) be the second derivative of 1/14*g**3 - 1/14*g**4 + 1/35*g**6 - 1/98*g**7 + 0*g**5 + 0 + 0*g**2 + 3*g. Factor z(m).
-3*m*(m - 1)**3*(m + 1)/7
Let b = 1 + 7. Factor 8*n + 0*n**2 + b*n + n**2 - 17*n.
n*(n - 1)
Suppose -4*k + 19 = -3*b, 3*k = -5*b + 1 + 6. Factor -4*j**3 + 0*j**3 + 3*j**3 + 3*j**4 + k*j**3.
3*j**3*(j + 1)
Factor 0 - d - 3/2*d**3 + 5/2*d**2.
-d*(d - 1)*(3*d - 2)/2
Let t(b) be the second derivative of 0*b**3 + 0*b**2 - 1/6*b**4 + 0 - b + 4/5*b**5 - 16/15*b**6. Determine n so that t(n) = 0.
0, 1/4
Suppose d**4 - 4*d**4 - 2*d**2 - 3*d + 9*d + 11*d**2 = 0. What is d?
-1, 0, 2
Let v(w) = -w**3 + 4*w**2 + 6*w - 2. Let r be v(5). Let t = -1333 + 1333. Solve t*u + 0 + 0*u**r - 1/4*u**4 + 1/4*u**2 = 0.
-1, 0, 1
Let u(c) = 3*c**3 - 12*c**2 - 15*c - 6. Let r(k) = -8*k**3 + 24*k**2 + 30*k + 12. Let d(q) = -3*r(q) - 7*u(q). Factor d(v).
3*(v + 1)**2*(v + 2)
Let m(n) be the first derivative of -n**5/70 - n**4/21 - 4*n - 1. Let g(l) be the first derivative of m(l). Factor g(k).
-2*k**2*(k + 2)/7
Let w(q) be the second derivative of q**5/35 - 2*q**3/7 + 4*q**2/7 - 5*q - 4. Factor w(t).
4*(t - 1)**2*(t + 2)/7
Factor 0 - 1/4*g**2 + 1/4*g**5 - 1/4*g**3 + 0*g + 1/4*g**4.
g**2*(g - 1)*(g + 1)**2/4
Let l be (-3)/9*0/((-12)/(-3)). Let j(x) be the second derivative of -1/48*x**4 - 1/120*x**6 + 1/40*x**5 + 0 + 2*x + l*x**3 + 0*x**2. Factor j(k).
-k**2*(k - 1)**2/4
Let n = 9 + -15. Let f = n - -8. Factor 7*q - 18 - f*q**2 + 0*q + 3*q + 2*q.
-2*(q - 3)**2
Let z(g) = -g**3 + 6*g**2 + 8*g - 4. Let b be z(7). Factor 5*y**3 - b*y**3 - 29*y + 0 + 6*y**2 + 35*y + 2.
2*(y + 1)**3
Factor -340*z + 348*z + 13*z**2 + 63*z**2.
4*z*(19*z + 2)
Let x(f) be the third derivative of -9*f**2 + 0 + 0*f**3 + 1/240*f**5 + 0*f**4 + 0*f. Factor x(d).
d**2/4
Let r(f) = 8*f**4 - 17*f**3 + f**2 + 8*f. Let n(l) = -2*l**4 + 4*l**3 - 2*l. Let d be (1 - -14)*(-6)/10. Let g(p) = d*n(p) - 2*r(p). Let g(i) = 0. Calculate i.
-1, 0, 1
Let y = 1663/11 + -151. Factor 2/11*l**4 - y*l**2 + 0*l**3 + 0 + 0*l.
2*l**2*(l - 1)*(l + 1)/11
Let z(f) be the third derivative of 0*f + 0 + 0*f**3 + 1/240*f**6 + 4*f**2 - 1/60*f**5 + 1/48*f**4. Solve z(w) = 0 for w.
0, 1
Suppose 3*j - 20 = -2*j + 3*o, j + 4*o = 4. Let p(m) = -2*m**2 + 11*m. Let f be p(5). Factor -8*x**f + 5/2*x**2 + 5/2*x - 1/2 - 20*x**j - 25/2*x**3.
-(x + 1)**3*(4*x - 1)**2/2
Let s(q) = q**2 + q. Let c(k) = -3*k**3 + 2*k**3 - 3 - 8*k**3 - 12*k + 15 - 21*k**2. Let v(l) = c(l) - 12*s(l). What is j in v(j) = 0?
-2, 1/3
Find m, given that 12*m**4 + 2*m**2 - 4 - 12*m - 2*m**2 + 0*m**2 + 4*m**5 + 8*m**3 - 8*m**2 = 0.
-1, 1
Suppose 14 = -5*k - 26. Let f be (k/(-12))/(8/6). What is x in 1/4*x**3 - f*x**2 + 0 + 1/4*x = 0?
0, 1
Let p = 23132/6755 + 4/965. Factor 48/7*m**3 - 3/7 - p*m**2 - 3*m.
3*(m - 1)*(4*m + 1)**2/7
Suppose -14 = -8*h + 2. Let d(t) be the first derivative of -1 + 2/3*t + 2/3*t**h + 2/9*t**3. Suppose d(z) = 0. Calculate z.
-1
Factor -1/6*j**2 - 1/6 - 1/3*j.
-(j + 1)**2/6
Let f(j) be the first derivative of -5 + 0*j + 2/9*j**3 + 1/3*j**2. Factor f(c).
2*c*(c + 1)/3
Let n(b) be the second derivative of b**7/210 - 2*b**6/75 + b**5/25 - 4*b. Factor n(h).
h**3*(h - 2)**2/5
Suppose u + 4*f = -2*u + 20, -2*f = -5*u - 10. Solve 9/5*j**3 + 3/5*j**4 + 3/5*j + 9/5*j**2 + u = 0 for j.
-1, 0
Factor 4*j**2 + 10 - 17 + 31 + 20*j.
4*(j + 2)*(j + 3)
Suppose 5*h = 15, 0*y + 5*h - 49 = -2*y. Let l be 12/102 + 32/y. Factor -3*f**3 + 1/3 + 5/3*f + f**l.
-(f - 1)*(3*f + 1)**2/3
Let x(l) be the second derivative of -l**7/14 + l**6/5 - l**4/2 + l**3/2 + 7*l. Find s, given that x(s) = 0.
-1, 0, 1
Let r(v) be the second derivative of v**6/45 + v**5/15 + v**4/18 - 18*v. Solve r(z) = 0.
-1, 0
Let n = 382 + -382. What is d in 0*d + n + 1/3*d**4 + 0*d**3 - 1/3*d**2 = 0?
-1, 0, 1
Suppose 2*t = 4 - 0. Suppose t = 2*z - z. Solve 5*y**2 - 4*y**2 + y**2 + 2 - 6*y + z*y = 0.
1
Let f(j) be the first derivative of j**3 + 1 - 1/4*j**4 - 3/2*j**2 + j. Factor f(y).
-(y - 1)**3
Let f(h) be the second derivative of 0*h**2 + 0 - 1/10*h**6 + 0*h**4 + 0*h**3 - 1/14*h**7 + 0*h**5 + 2*h. Solve f(s) = 0 for s.
-1, 0
Factor -6*v**4 - 40*v - 20*v**2 + 11*v**4 + 5*v**3 + 5*v**3.
5*v*(v - 2)*(v + 2)**2
Let c(z) = 160*z**3 - 60*z**2 - 44*z. Let o(s) = 29*s**3 - 11*s**2 - 8*s. Let k(j) = -5*c(j) + 28*o(j). Factor k(b).
4*b*(b - 1)*(3*b + 1)
Let a(j) be the third derivative of 0 - 1/168*j**8 + 1/15*j**5 + 1/20*j**6 + 0*j**3 + 0*j - 2*j**2 + 0*j**4 + 0*j**7. Solve a(d) = 0 for d.
-1, 0, 2
Let s = 3461/20 - 173. Let t(x) be the third derivative of -s*x**6 - 1/15*x**5 + 2*x**2 + 0*x + 0*x**3 + 0 + 0*x**4 + 2/105*x**7. Suppose t(k) = 0. What is k?
-1/2, 0, 2
Let c(b) be the third derivative of b**5/240 - b**4/48 + 8*b**2. Factor c(z).
z*(z - 2)/4
Let u be (20/75)/((30/25)/6). Factor -2/3*c + 4/3 + 2/3*c**3 - u*c**2.
2*(c - 2)*(c - 1)*(c + 1)/3
Let i(o) be the second derivative of -o**6/1080 - o**3 - 9*o. Let p(r) be the second derivative of i(r). Factor p(q).
-q**2/3
Let c = 107 - 105. Let z(q) be the third derivative of 1/6*q**5 + 0*q**3 - 2*q**c + 0 + 0*q - 1/12*q**4 - 1/15*q**6. Find m such that z(m) = 0.
0, 1/4, 1
Let c(v) be the third derivative of v**6/48 - 5*v**4/48 - 35*v**2 - 1. Solve c(q) = 0 for q.
-1, 0, 1
Let x(y) = -5*y**3 + 13*y**2 - 2*y - 6. Let a(f) = -f + 1. Let i = 5 - 7. Let w(c) = i*a(c) - x(c). Factor w(k).
(k - 2)*(k - 1)*(5*k + 2)
Let o = -281439757/927 + 303603. Let x = o + -2/103. Factor 0*q - 2/9 + x*q**2.
2*(q - 1)*(q + 1)/9
Let d(h) be the first derivative of h**4/22 + 4*h**3/33 - h**2/11 - 4*h/11 - 8. Solve d(x) = 0 for x.
-2, -1, 1
Let k(c) be the second derivative of c**7/2016 - 7*c**6/2880 + c**5/240 + 5*c**4/12 + 2*c. Let j(s) be the third derivative of k(s). What is h in j(h) = 0?
2/5, 1
Let x(f) be the second derivative of -f**5/180 + f**4/18 - f**3/6 + 2*f**2/9 + 17*f. Find h such that x(h) = 0.
1, 4
Let i(a) be the first derivative of a**6/3 - 2*a**5 + 9*a**4/2 - 14*a**3/3 + 2*a**2 - 3. Factor i(g).
2*g*(g - 2)*(g - 1)**3
Let p(w) be the first derivative of w**4/54 - w**2/9 + 2*w - 3. Let r(y) be the first derivative of p(y). Factor r(x).
2*(x - 1)*(x + 1)/9
Let y = 2147/5 + -429. Factor 0*d**3 + y*d**4 + 0 + 0*d - 2/5*d**2.
2*d**2*(d - 1)*(d + 1)/5
Let l = 24 - 20. Let r(z) be the third derivative of -1/150*z**5 + z**2 + 0*z**3 + 0*z + 0 + 1/300*z**6 - 1/60*z**l + 1/525*z**7. Factor r(x).
2*x*(x - 1)*(x + 1)**2/5
Suppose 6*u - 3 - 3 = 0. Let 2*j**4 - 5*j - 2*j**2 - u + 4*j + 1 + j**5 = 0. Calculate j.
-1, 0, 1
Let p be (0 - (-2)/4)*-8 + 9. What is w in 0*w**3 + 0 + 2*w**p + 0*w**2 - 2/3*w**4 + 0*w = 0?
0, 1/3
Let g(y) be the third derivative of -1/3*y**3 + 0*y**4 + 1/7*y**7 + 0*y + 0 + 3*y**2 + 1/3*y**5 + 1/3*y**6 + 1/42*y**8. Factor g(l).
2*(l + 1)**4*(4*l - 1)
Let x be (-3)/6 + 15/20. Let u(i) be the first derivative of 1/4*i**2 - x*i**4 + 1 + 1/3*i**3 + 1/12*i**6 - 1/2*i - 1/10*i**5. Find j, given that u(j) = 0.
-1, 1
Let k(p) be the first derivative of -p**6/540 + p**5/90 - p**4/36 + 2*p**3/3 + 2. Let b(g) be the third derivative of k(g). Determine i so that b(i) = 0.
1
Let k(n) be the second derivative of 0*n**3 - 1/18*n**4 + 0*n**2 + 1/15*n**5 - 3*n + 0 - 1/45*n**6. Suppose k(p) = 0. What is p?
0, 1
Suppose -28 = -f - 2*z, f - 2*f = 5*z - 43. Solve -6*u**2 - 24*u**3 - 6*u**4 + 21*u**5 + 18*u**2 - f*u**3 - 6 + 21*u = 0 for u.
-1, 2/7, 1
Let t = 2/41 + 68/287. Factor 6/7*x + t + 4/7*x**2.
2*(x + 1)*(2*x + 1)/7
Let r = 515/2028 + -2/507. Solve -1/4*n**4 + 0 + 0*n + 0*n**3 + r*n**2 = 0 for n.
-1, 0, 1
Let b(f) = f**2 + 10*f + 11. Let p be b(-9). Let j(z) be the first derivative of 2*z**2 + 0*z + 1 + 0 + p*z**3 - 2*z. Factor j(w).
2*(w + 1)*(3*w - 1)
Suppose 3*p + 5*m + 13 = 0, -2*p + 3 = 2*m - m. Let x(a) be the second derivative of 0 - 2*a + 1/7*a**3 + 1/42*a**p + 2/7*a**2. What is u in x(u) = 0?
-2, -1
Let k(z) be the second derivative of z**7/2520 + z**6/360 + z**4/6 + 5*z. Let 