(h).
h*(h + 1)*(h + 2)/9
Factor 2/15*r**2 + 4/5*r + 6/5.
2*(r + 3)**2/15
Let h(g) be the second derivative of -g**5/18 - g**4/6 - 4*g**3/27 + 19*g. Determine c, given that h(c) = 0.
-1, -4/5, 0
Let c be (-54)/(12/(-4)) - 3. Suppose 2*g + 2*n = 7*n + 25, 0 = -g - 3*n - c. Factor 2/3*j**3 - 2/3*j + g + 2/3*j**2 - 2/3*j**4.
-2*j*(j - 1)**2*(j + 1)/3
Let 7/5*n + 4/5 - 1/5*n**3 + 2/5*n**2 = 0. What is n?
-1, 4
Factor -3*h**2 - 24*h**5 - 6*h**3 + 20*h**2 + 27*h**5 - 9*h**4 + 19*h**2 - 24*h.
3*h*(h - 2)**2*(h - 1)*(h + 2)
Let j = -31/12 - -347/60. Factor j*d + 2*d**2 - 8/5.
2*(d + 2)*(5*d - 2)/5
Let h(o) be the third derivative of -3*o**8/280 + 2*o**7/35 - 3*o**6/100 - 6*o**5/25 + o**4/5 - 10*o**2. Determine n, given that h(n) = 0.
-1, 0, 1/3, 2
Suppose n + 4 = 11. Suppose 0 = l + o + 1, -5*l + 18 = -o - n. Factor 2/7*w**3 + 0 + 0*w + 2/7*w**l - 4/7*w**2.
2*w**2*(w - 1)*(w + 2)/7
Suppose 3*d = 2 + 19. Determine x, given that -1 - 60*x**2 - 2*x + d - 7*x = 0.
-2/5, 1/4
Let j be (3/36)/((-9)/(-90708)). Let m = -839 + j. What is q in -m*q**3 - 4/3*q - 2/9 - 2*q**2 = 0?
-1, -1/4
Let o(b) be the third derivative of 0*b**3 + 0 - b**2 - 1/45*b**5 + 2/945*b**7 + 1/24*b**4 - 1/540*b**6 + 0*b + 1/3024*b**8. Let o(n) = 0. What is n?
-3, 0, 1
Let c(f) be the second derivative of 2*f + 2/9*f**3 + 1/6*f**4 + 0 - 1/3*f**2. Factor c(b).
2*(b + 1)*(3*b - 1)/3
Let x(b) be the first derivative of -b**3/3 + 20*b**2 - 400*b + 50. Factor x(v).
-(v - 20)**2
Solve 2/3*n + 0 + 2/3*n**3 - 4/3*n**2 = 0.
0, 1
Let s = 278 + -3056/11. Determine d, given that 0 + 0*d**2 - s*d**3 + 2/11*d = 0.
-1, 0, 1
Let z(f) be the first derivative of -2/3*f**3 + 2 - 1/4*f**4 + 0*f - 1/2*f**2. Find q, given that z(q) = 0.
-1, 0
Let i(s) be the first derivative of s**8/1344 - s**7/210 + s**6/80 - s**5/60 + s**4/96 - 3*s**2/2 + 2. Let j(q) be the second derivative of i(q). Factor j(z).
z*(z - 1)**4/4
Let h(m) be the second derivative of 3*m**5/100 - m**4/20 - m**3/10 + 3*m**2/10 - 4*m. Factor h(d).
3*(d - 1)**2*(d + 1)/5
Suppose 9 = 5*n + 24. Let p(w) = -3*w + 3*w**3 + 2*w**2 - 6*w**2 - 6*w**3. Let c(r) = -2*r**3 - 2*r**2 - 2*r. Let u(y) = n*p(y) + 5*c(y). Solve u(o) = 0 for o.
0, 1
Let b(o) be the second derivative of 18*o**2 - 4*o**3 + 0 - 5*o + 1/3*o**4. Factor b(f).
4*(f - 3)**2
Let d(n) = -3*n**4 - n**3 + 2*n**2 + n. Let z(l) = l**4 - l**3 + l. Suppose i - 6 = -5. Let g(u) = i*z(u) + d(u). Factor g(m).
-2*m*(m - 1)*(m + 1)**2
Let d = -5/52 - -11/13. Find s, given that d*s**5 - 3 - 75/4*s**2 - 21/4*s**4 + 57/4*s**3 + 12*s = 0.
1, 2
Let s be (6/2 + 0)/3. Let d(m) = -1. Let k(v) = -2*v**2 + 4*v - 7. Let b(a) = s*k(a) - 5*d(a). Factor b(l).
-2*(l - 1)**2
Let x be 1/3 - (-2)/(-3). Let m = 1/3 - x. Factor 0 + m*o**3 + 2/9*o + 2/9*o**4 + 2/3*o**2.
2*o*(o + 1)**3/9
Solve g**3 + 16*g**2 + 0*g**2 + 2*g**3 + 21*g + 9 - g**2 = 0.
-3, -1
Let v be ((-3)/(-14))/((-3)/63*-6). Factor 3/4*d**2 + 0*d - v.
3*(d - 1)*(d + 1)/4
Let b = 1206/1057 + 2/1057. Determine d so that b + 12/7*d + 20/7*d**4 - 4*d**2 - 12/7*d**3 = 0.
-1, -2/5, 1
Suppose -38 = -8*g + 2. Solve -1/2*b + b**3 - 1/2*b**g + 0*b**2 + 0*b**4 + 0 = 0 for b.
-1, 0, 1
Suppose 0 = i + 5*m + 1 - 8, 3*m - 5 = -i. Factor 1/4*q**4 + 0*q + 0 - 3/4*q**3 + 1/2*q**i.
q**2*(q - 2)*(q - 1)/4
Let h(n) be the second derivative of n**6/15 + 3*n**5/10 + n**4/2 + n**3/3 - 19*n. Factor h(d).
2*d*(d + 1)**3
Let -36*c + 3*c**4 - 6*c**3 - 39*c + 81*c - 3*c**2 = 0. What is c?
-1, 0, 1, 2
Find y, given that 0*y + 0 + 3/5*y**4 - 3/5*y**2 + 0*y**3 = 0.
-1, 0, 1
Let h(b) be the first derivative of -3*b**5/5 + 3*b**4/4 + b**3 - 3*b**2/2 - 2. What is a in h(a) = 0?
-1, 0, 1
Let q(n) = 13*n**2 - 24*n + 31. Let i(r) = 4*r**2 - 8*r + 10. Suppose -1 = -4*o - 9. Let k(t) = o*q(t) + 7*i(t). Let k(y) = 0. What is y?
2
Let w = -1759/16 + 110. Let i(j) be the first derivative of 2 - 1/8*j**2 + 1/4*j - 1/12*j**3 + w*j**4. Solve i(m) = 0.
-1, 1
Suppose j + 0 - 2 = 0. Let y(s) be the first derivative of 1 + 3/5*s**j - 1/5*s**4 - 2/5*s - 4/15*s**3 + 6/25*s**5 - 1/15*s**6. Factor y(g).
-2*(g - 1)**4*(g + 1)/5
Suppose 42*c - 39*c = 12. Let g(z) be the first derivative of 1/2*z**2 + c + 0*z + 1/3*z**3. Factor g(q).
q*(q + 1)
Let i(w) be the third derivative of w**6/240 + w**5/20 + 5*w**4/48 - 5*w**2. Suppose i(c) = 0. What is c?
-5, -1, 0
Let q(t) = -3*t**2 - 7*t + 2. Let s(r) = r + 3. Let m be s(-7). Let x(f) = -4*f**2 - 8*f + 2. Let b(p) = m*x(p) + 5*q(p). Factor b(n).
(n - 2)*(n - 1)
Let z = 209 - 119. Suppose -71 + 3*l**3 - 9*l - 27*l**2 - 10 + z*l = 0. Calculate l.
3
Let q be (-1)/7 + (-522)/(-126). Factor 4*d**2 - d**5 - 2 - 6*d**3 + d**q - 3*d**4 - d + 8*d**3.
-(d - 1)**2*(d + 1)**2*(d + 2)
Let a(x) be the second derivative of 4*x + 0 + 1/27*x**3 + 0*x**2 + 1/90*x**5 - 1/27*x**4. Factor a(l).
2*l*(l - 1)**2/9
Let t = 1839/4 - 457. Factor -1/2 - 9/2*c**2 - 9/4*c**3 - t*c.
-(c + 1)*(3*c + 1)*(3*c + 2)/4
Let 2/7*w - 4/7 - 2/7*w**3 + 4/7*w**2 = 0. What is w?
-1, 1, 2
Let f(a) be the first derivative of -3*a**4/8 - 3*a**3/2 + 6*a - 22. Factor f(p).
-3*(p - 1)*(p + 2)**2/2
Let x(l) be the third derivative of l**8/5040 + l**7/2520 - l**6/540 + l**3/6 - 5*l**2. Let r(o) be the first derivative of x(o). Factor r(s).
s**2*(s - 1)*(s + 2)/3
Let d(p) = -p**3 - 14*p**2 - 15*p - 26. Let z be d(-13). Solve 0 + 1/4*a**4 + 1/2*a - 3/4*a**2 + z*a**3 = 0 for a.
-2, 0, 1
Let k(m) be the first derivative of -m**5/150 - m**4/30 + m**3/5 - 3*m**2 - 8. Let f(a) be the second derivative of k(a). Factor f(g).
-2*(g - 1)*(g + 3)/5
Let z(o) = 3*o**2 - 60*o + 18. Let u(c) = -c**2 + 17*c - 5. Let a(r) = 18*u(r) + 5*z(r). Determine j, given that a(j) = 0.
0, 2
Suppose 6*a = a + 15. Suppose 4*d + a - 11 = 0. Determine k, given that -8/9*k - 2/9 - 8/9*k**d + 4/9*k**3 + 4/9*k**5 + 10/9*k**4 = 0.
-1, -1/2, 1
Let u = 9 - 13. Let q(k) = k**3 + 4*k**2 + 2. Let r be q(u). Factor 0 + 0*g + 0*g**3 + 1/2*g**4 - 1/2*g**r.
g**2*(g - 1)*(g + 1)/2
Let k(l) be the second derivative of l**6/1440 + l**5/240 + l**4/96 - l**3/2 - 3*l. Let w(i) be the second derivative of k(i). Factor w(a).
(a + 1)**2/4
Let u(f) = f**4 - f**3 - f**2 - 1. Let s(w) = 20*w**4 - 25*w**3 - 20*w**2 - 25. Let h(r) = s(r) - 25*u(r). Solve h(q) = 0 for q.
-1, 0, 1
Let v = 299/123 - 4/41. Let j = -6/5 + 28/15. Factor -k**3 + j + 2/3*k**2 + v*k.
-(k - 2)*(k + 1)*(3*k + 1)/3
Let h(l) = l**5 - 11*l**3 + l + 3. Let c(u) = -u**5 + 23*u**3 - u - 7. Let z(s) = 3*c(s) + 7*h(s). Factor z(d).
4*d*(d - 1)**2*(d + 1)**2
Let j be (68/(-6))/((-6)/9). Suppose 0*u = -2*r - 5*u - j, -4*u = -2*r + 28. Suppose -2*l**4 - r*l**3 - 2/5 - 4*l**2 - 2*l - 2/5*l**5 = 0. Calculate l.
-1
Let b(f) be the first derivative of f**4/36 + f**3/18 - f + 5. Let c(l) be the first derivative of b(l). Let c(x) = 0. What is x?
-1, 0
Suppose -4*d - d - 2*r + 10 = 0, -5*d + 10 = -3*r. Let -1/4 + a - 3/4*a**d = 0. Calculate a.
1/3, 1
Factor -4*k**4 + 2*k**3 - 8*k**4 + 6*k**3.
-4*k**3*(3*k - 2)
Let y(l) be the third derivative of -2*l**2 - 2/3*l**4 + 1/30*l**5 + 16/3*l**3 + 0*l + 0. Factor y(d).
2*(d - 4)**2
Let h(l) be the second derivative of 0*l**2 - 3*l - 1/40*l**5 - 1/180*l**6 - 1/24*l**4 + 0 - 1/36*l**3. Solve h(v) = 0.
-1, 0
Let v be 6/10 - 2/5. Factor 1/5 + v*u**2 - 2/5*u.
(u - 1)**2/5
Let w(t) = 6*t - 6. Let i(b) = -b**2 - 18*b + 19. Let o(l) = -4*i(l) - 14*w(l). Factor o(h).
4*(h - 2)*(h - 1)
Let y be (-80)/(-18) + -2 - 2. Solve -y*d + 2*d**3 + 0 - 10/9*d**4 - 14/9*d**5 + 10/9*d**2 = 0.
-1, 0, 2/7, 1
Let a(n) be the first derivative of n**6/21 + 2*n**5/35 - 3*n**4/14 - 2*n**3/21 + 2*n**2/7 - 11. Solve a(k) = 0.
-2, -1, 0, 1
Let z(t) be the first derivative of -t**5/80 + t**4/12 - 5*t**3/24 + t**2/4 + t - 1. Let d(q) be the first derivative of z(q). Factor d(r).
-(r - 2)*(r - 1)**2/4
Suppose 0 = -4*h + 12 - 0. Suppose 5*x - x - h = -y, 5*x - 5*y = -15. Suppose 4/5*t**4 + 2/5*t + x*t**3 - 2/5*t**5 + 0 - 4/5*t**2 = 0. Calculate t.
-1, 0, 1
Suppose 7*t - 3*t = 2*y - 4, 0 = 4*t. Let 1/4*z**y - 1/2*z + 1/4 = 0. Calculate z.
1
Let f be 48/(-60)*10/(-4). Solve 1/2*p**f + 0 + 1/2*p = 0 for p.
-1, 0
Let d(q) = -2*q**4 + 2*q**3 - q**2 + 5*q + 5. Let f(y) = -y**4 + y**3 + y**2 + y + 1. Let w(c) = -d(c) + 5*f(c). Find g, given that w(g) = 0.
-1, 0, 2
Let b(s) be the second derivative of s**5/70 - 2*s**4/21