1)**3*(n + 1)/3
Let j(h) be the first derivative of -h**4/2 + 2*h**3 - 3*h**2 + 2*h - 5. Suppose j(a) = 0. Calculate a.
1
Let x(o) = -o**2 + 31*o - 84. Let n be x(3). Factor -y - 1/4*y**3 + y**2 + n.
-y*(y - 2)**2/4
Suppose -3*y - 3*t + 9 = 0, 6*y - 3*y + 5*t = 15. Factor y - 20/3*j**2 - 2/3*j - 50/3*j**3.
-2*j*(5*j + 1)**2/3
Let i = 573/4 + -143. Factor 0 + i*o - o**2.
-o*(4*o - 1)/4
Let r be (-4)/10*-2*5. What is h in 1/3 - 4/3*h + 4/3*h**3 - h**r + 2/3*h**2 = 0?
-1, 1/3, 1
Let a(l) = l. Let x be a(2). Let u(i) be the second derivative of 1/5*i**x - 2*i + 1/20*i**5 + 0 - 2/15*i**4 + 1/30*i**3. Factor u(s).
(s - 1)**2*(5*s + 2)/5
Let u(l) be the first derivative of l**6/3 - 6*l**5/5 - l**4/2 + 14*l**3/3 - 8*l - 7. Solve u(s) = 0.
-1, 1, 2
Let s = 58/3 - 19. Let m(f) be the first derivative of 1/3*f**2 + 2 - s*f - 1/9*f**3. Suppose m(r) = 0. What is r?
1
Let w(x) = x**3 - 3*x**2 - 4*x + 4. Let v be w(4). Factor -2*p + 2*p**2 + v*p - p**2 - p.
p*(p + 1)
Let h(k) be the first derivative of -3/2*k**2 - 9/4*k**4 + 2 + 0*k - 3*k**3 - 3/5*k**5. Factor h(y).
-3*y*(y + 1)**3
Factor 0*r**2 + 4/3*r**3 + 2/3*r**4 + 0 + 0*r.
2*r**3*(r + 2)/3
Let t(d) be the third derivative of -d**5/240 + d**4/24 - d**3/6 + 17*d**2. Factor t(x).
-(x - 2)**2/4
Let b be (10/25)/(2/160). Let j be 2*1 - (-8)/b. Factor -j*v**2 + 3/2 + 9/4*v - 3/2*v**3.
-3*(v - 1)*(v + 2)*(2*v + 1)/4
Suppose 0 = 7*r - 4*r - 6. Let f(b) be the third derivative of -1/96*b**4 + 1/240*b**5 + 0 - 1/840*b**7 - b**r + 1/480*b**6 + 0*b + 0*b**3. Solve f(p) = 0.
-1, 0, 1
Let a be 0 + 1 + -2 + 0. Let r(f) = f**2 - 1. Let d be r(a). Factor d*x + 1/4*x**4 + 0*x**2 + 0 - 1/4*x**3.
x**3*(x - 1)/4
Solve -3*q**2 + 0 - q - 13/4*q**3 - 1/4*q**5 - 3/2*q**4 = 0.
-2, -1, 0
Factor -46/3*z + 80/3*z**2 - 14/3*z**3 - 20/3.
-2*(z - 5)*(z - 1)*(7*z + 2)/3
Let u(y) be the second derivative of 3/16*y**4 - 1/16*y**5 + 0 + 2*y + 1/120*y**6 - 7/24*y**3 + 1/4*y**2. Factor u(k).
(k - 2)*(k - 1)**3/4
Factor -4/3*y**4 + 1/3*y**5 + 2*y**3 - 4/3*y**2 + 0 + 1/3*y.
y*(y - 1)**4/3
Suppose -2*o = b + 10, 0*o = -5*b + 2*o + 10. Suppose 0 + 64/9*a**3 + b*a - 154/9*a**4 - 8/9*a**2 + 98/9*a**5 = 0. What is a?
0, 2/7, 1
Let o(j) be the second derivative of j**8/13440 - j**7/1680 + j**6/480 - j**5/240 + j**4/4 - 3*j. Let d(a) be the third derivative of o(a). Factor d(w).
(w - 1)**3/2
Let b be ((-30)/(-55))/(16/14). Let l = 8/11 - b. Determine p so that 0*p**3 + 1/4*p**5 + 0*p**2 + l*p**4 + 0 + 0*p = 0.
-1, 0
Let r(y) = 3*y**3 - 2*y + 1. Let q be r(1). Suppose -11 + 1 = -q*f. Determine h so that -2*h**5 + h**f + h**2 + h**4 + h**3 - 2*h**4 = 0.
-1, 0, 1
Let u = 18 + -14. Let -5*y + y + 3 + u*y**2 - 7 + 2*y**3 + 2*y**3 = 0. What is y?
-1, 1
Suppose 5*u - 2*q - 15 = 9, 0 = 4*u - 5*q - 26. Let o = -1 + u. Factor 24*j**2 - 18*j + 1 + j**3 - 1 + 4 - 11*j**o.
-2*(j - 1)**2*(5*j - 2)
Factor -2/11*x + 1/11 + 1/11*x**2.
(x - 1)**2/11
Suppose 3*x + 3*m = 6, 3*m - 10 = 3*x - 7*x. Let h be (x/(-21))/(6/(-9)). Suppose -2/7*w**3 + h*w**2 + 0 + 0*w = 0. Calculate w.
0, 1
Let g be (-7 - 1)/(24/(-6) - -1). Factor 8*w**2 - g*w**3 + 16/3 + 1/3*w**4 - 32/3*w.
(w - 2)**4/3
Suppose -8*w**2 + w**2 - 5*w**2 + 8*w**2 - 4 - 8*w = 0. What is w?
-1
Let -2*d**2 + 0 - 2*d - 1/2*d**3 = 0. What is d?
-2, 0
Let h = -5 + 5. Suppose 4*v + 5*o = -h*o + 13, v + 2 = 4*o. Factor 0 + 2/7*u**v + 0*u + 2/7*u**3.
2*u**2*(u + 1)/7
Let x(v) be the third derivative of v**7/630 - v**5/30 + v**4/9 - 7*v**3/6 - 3*v**2. Let p(u) be the first derivative of x(u). Suppose p(y) = 0. Calculate y.
-2, 1
Suppose -3*y + 5*h + 31 = 0, -3*y + h + 7 = -4. Let v be y + 3 + 6/2. Determine m, given that -4*m**2 - 4 - m**4 + 4*m**3 - 4*m + v + m**2 = 0.
-1, 1, 2
Let w(j) be the first derivative of -j**6/42 - j**5/35 + 5. Solve w(v) = 0 for v.
-1, 0
Let f = -53/2 + 27. Let w be ((-9)/(-15))/((-2)/(-10)). Factor 3/2*x**w + 0*x - 1/2*x**2 + 0 + f*x**5 - 3/2*x**4.
x**2*(x - 1)**3/2
Let u(r) be the third derivative of -r**7/8820 - r**6/2520 - r**4/8 + 2*r**2. Let y(q) be the second derivative of u(q). Find l, given that y(l) = 0.
-1, 0
Let a(k) = -24*k**2 + 60*k - 104. Let p(t) = 14 + 9 + 2*t**2 + 3*t**2 - 12*t - 2. Let z(b) = 3*a(b) + 14*p(b). Factor z(q).
-2*(q - 3)**2
Let z(j) = -8*j**2 + 9*j + 4. Suppose -2*g + r = -44 - 5, 0 = -g - 5*r + 41. Let l(n) = -n - 2*n**2 + 2*n + 1 + n. Let p(t) = g*l(t) - 6*z(t). Factor p(o).
-2*(o + 1)*(2*o - 1)
Let h(i) be the first derivative of -2*i**3/21 + 4*i**2/7 - 6*i/7 + 17. Let h(w) = 0. What is w?
1, 3
Let f = 2255 - 20159/9. Suppose -5*r - 5 = 0, 3*r - 3 = -4*m + 10. Factor -f*g + 16/9 + 250/9*g**m + 140/3*g**2 - 550/9*g**3.
2*(g - 1)*(5*g - 2)**3/9
Let u(f) be the third derivative of 5*f**7/14 + 3*f**6/4 - 111*f**5/20 + 17*f**4/2 - 6*f**3 - 35*f**2. Factor u(l).
3*(l - 1)*(l + 3)*(5*l - 2)**2
Let i(k) be the third derivative of -1/30*k**4 - 3*k**2 + 1/100*k**5 - 2/15*k**3 + 0 + 0*k. What is h in i(h) = 0?
-2/3, 2
Suppose 70 = -3*u + u - 3*g, -2*u + 5*g = 38. Let s = u - -40. Factor -7*t - 3*t**2 + 2 - 5*t + s*t**2 + 2*t.
2*(t - 1)*(4*t - 1)
Let d(k) be the third derivative of k**5/270 + k**4/108 - 2*k**3/9 - 27*k**2. Let d(u) = 0. Calculate u.
-3, 2
Let l(m) be the first derivative of -2*m**3/33 + m**2/11 - 1. Factor l(y).
-2*y*(y - 1)/11
Let z(p) be the second derivative of -p**5/60 + p**4/36 + p**3/18 - p**2/6 + 5*p. Factor z(h).
-(h - 1)**2*(h + 1)/3
Let y(p) = -4*p - 10. Let d be y(-8). Let h be d/7 + (-8)/56. Factor -1/6 + 1/6*z**2 - 1/6*z**h + 1/6*z.
-(z - 1)**2*(z + 1)/6
Let a(l) be the third derivative of -l**6/24 - l**5/4 - 5*l**4/12 + 7*l**2. Factor a(p).
-5*p*(p + 1)*(p + 2)
Let m(c) = c**3 + 7*c**2 + 7*c + 6. Let t be m(-6). Solve t + 3/4*i**2 + 3/4*i = 0.
-1, 0
Suppose -15/4 - 21/4*d**2 - 33/4*d - 3/4*d**3 = 0. What is d?
-5, -1
Let -2 + 19/9*a - 1/9*a**2 = 0. What is a?
1, 18
Let j(d) = d**2 + 3. Let s be j(0). Factor -f**2 + 3*f**4 + s*f - f - 8*f**2 + 4*f.
3*f*(f - 1)**2*(f + 2)
Suppose 4*b - 17 = -0*k + 3*k, -2*b + 19 = -5*k. Factor 3*u - 4*u**b - 2*u**2 + 3*u**2.
-3*u*(u - 1)
Let v = 11 + -11. Let d(p) be the second derivative of -p - 1/12*p**4 + v + 0*p**2 + 1/6*p**3. Solve d(r) = 0 for r.
0, 1
Let w(u) be the first derivative of -9*u**6/10 + 63*u**5/25 + 3*u**4/10 - 4*u**3 + 12*u**2/5 + 14. Determine c, given that w(c) = 0.
-1, 0, 2/3, 2
Suppose 0 = -5*y - 0*i - 5*i + 45, -9 = -y + 2*i. Suppose 0*o + y = o + 3*r, -3*o + 2*r - 6 = 0. Factor 2*s**3 - 3*s**3 + 2*s**4 + o*s**4 - s**5.
-s**3*(s - 1)**2
Let q(d) be the first derivative of 0*d + 1/84*d**4 + 0*d**2 - 1/3*d**3 - 2 + 0*d**5 - 1/1260*d**6. Let f(c) be the third derivative of q(c). Factor f(o).
-2*(o - 1)*(o + 1)/7
Let v(t) be the third derivative of t**10/30240 - t**9/3780 + t**8/1344 - t**7/1260 + t**4/8 - 5*t**2. Let n(x) be the second derivative of v(x). Factor n(g).
g**2*(g - 2)*(g - 1)**2
Let u(l) be the second derivative of 0*l**6 + 0*l**4 + 2*l - 1/21*l**3 + 1/35*l**5 + 0*l**2 - 1/147*l**7 + 0. Factor u(f).
-2*f*(f - 1)**2*(f + 1)**2/7
Let b(i) be the first derivative of -i**3 - 3*i**2/2 + 18*i + 8. Determine s, given that b(s) = 0.
-3, 2
Let f(i) be the third derivative of 0 + 0*i + 0*i**3 + 1/1155*i**7 + i**2 + 0*i**4 - 1/330*i**5 - 1/1848*i**8 + 1/660*i**6. Find b, given that f(b) = 0.
-1, 0, 1
Let f(s) be the third derivative of -s**5/450 + s**4/45 - 4*s**3/45 + 2*s**2. Find k, given that f(k) = 0.
2
Let k(f) be the first derivative of 2*f**3/33 - 2*f**2/11 - 6*f/11 - 8. Factor k(l).
2*(l - 3)*(l + 1)/11
Factor -2/9*g**2 - 18 - 4*g.
-2*(g + 9)**2/9
Let -6*h + 4*h**2 + 8/3 - 2/3*h**3 = 0. Calculate h.
1, 4
Let v = 365 - 1085/3. Let -4/3*y**3 + 0 + 4/3*y - v*y**2 + 10/3*y**4 = 0. What is y?
-1, 0, 2/5, 1
Let r be (-8)/(-32) - (-2)/12. Let s = 1/4 + r. Factor 0*u**3 - 2/3*u**5 + s*u + 0 - 4/3*u**2 + 4/3*u**4.
-2*u*(u - 1)**3*(u + 1)/3
Let a = 36 - 34. Let t(j) be the third derivative of 0*j**3 - 1/45*j**5 + 2*j**a + 1/72*j**6 - 1/315*j**7 + 0 + 0*j + 1/72*j**4. Suppose t(u) = 0. Calculate u.
0, 1/2, 1
Suppose -2*x + h - 2 = -3*x, 3*h = 0. Let v be x + 0 - (-24)/(-18). Find a such that 2/3 + 1/3*a - v*a**2 - 1/3*a**3 = 0.
-2, -1, 1
Let f(x) be the first derivative of x**5/15 + x**4/4 + 2*x**3/9 + 5. Find g, given that f(g) = 0.
-2, -1, 0
Let z be (-5)/(5/2) + (-28)/(-7). Let 2*l 