- h**6/15 - 7*h**5/80 - h**4/24 - 11*h. Let r(f) = 0. Calculate f.
-1, -2/3, 0
Let u(g) be the first derivative of 2*g**3/15 + 3*g**2/5 - 9. Factor u(h).
2*h*(h + 3)/5
Suppose 7 = -5*s + 32, 0 = x + 5*s - 30. Let u(v) = -2*v**4 + 4*v**2 - 2. Let g(k) = 3*k**4 - k**3 - 7*k**2 + k + 4. Let i(a) = x*u(a) + 3*g(a). Factor i(d).
-(d - 1)*(d + 1)**2*(d + 2)
Let s = -2 + 5. Suppose -s*k = -5*g + 30, 5*g + 1 = -2*k + 31. Factor 24*v**2 + 0 + g + 16*v**3 + 12*v - 4.
2*(2*v + 1)**3
Let m = 29/6 + -1/3. Determine v so that 6*v**4 + 0 - 6*v**2 + 6*v + m*v**5 - 21/2*v**3 = 0.
-2, -1, 0, 2/3, 1
Let b be 28/21 + (-6)/(-9). Factor -2/7*g**3 - 2/7*g**b + 0*g + 0.
-2*g**2*(g + 1)/7
Let q(j) be the first derivative of 1/600*j**6 + 0*j + 1/100*j**5 - 1/3*j**3 + 0*j**2 - 1 + 1/40*j**4. Let y(m) be the third derivative of q(m). Factor y(h).
3*(h + 1)**2/5
Let d(f) = 6*f**2 + 2*f. Let p(r) = 31*r**2 + 11*r. Let x be (-7)/(-35) - 54/(-5). Let s(m) = x*d(m) - 2*p(m). Find u such that s(u) = 0.
0
Let a(l) be the first derivative of 0*l**3 + 2/65*l**5 + 3 + 0*l**2 - 1/13*l**4 + 0*l. What is c in a(c) = 0?
0, 2
Suppose 5*t - 2*l - 9 = 0, -t = -0*t - 4*l - 9. Find z, given that -3/2*z + t + 1/2*z**2 = 0.
1, 2
Let x be 3 + (-1)/(-2)*6. Let y = -3 + x. Factor 0*a**2 - 1/2*a - 1/4*a**4 + 1/4 + 1/2*a**y.
-(a - 1)**3*(a + 1)/4
Suppose -p + v = -6, -6*v + v - 9 = 2*p. Let r(l) be the first derivative of 0*l**2 + 2/3*l**p + 1/2*l**4 + 3 + 0*l. Factor r(x).
2*x**2*(x + 1)
Suppose 0 = q + 4*q - 10. Let g(l) be the third derivative of -1/36*l**4 + l**q + 0*l + 1/120*l**5 + 1/36*l**3 + 0. Factor g(y).
(y - 1)*(3*y - 1)/6
Let t(f) be the first derivative of 2*f**3/15 - f**2/5 + 12. Factor t(y).
2*y*(y - 1)/5
Suppose 32*f = -4 + 4. Determine w so that f + 0*w + 0*w**3 - 1/4*w**2 + 1/4*w**4 = 0.
-1, 0, 1
Let j(b) = 12*b**3 - 24*b**2 + 27*b. Let t(c) = c**3 - c**2 + c. Let h(w) = -j(w) + 15*t(w). Factor h(u).
3*u*(u - 1)*(u + 4)
Let k = -1 + 1. Suppose k*i = i. Solve i*z**3 + 3 + 4*z**2 + 2*z**3 - 3 = 0 for z.
-2, 0
Let k be (-67)/(-63) + (-8)/(-36). Let r = 41/21 - k. Factor r*c**2 - 2/3*c + 0.
2*c*(c - 1)/3
Let o(w) be the second derivative of 18*w**7/7 + 51*w**6/10 - 213*w**5/20 - 17*w**4/2 + 22*w**3 - 12*w**2 + 26*w. Let o(z) = 0. Calculate z.
-2, -1, 1/4, 2/3
Let m(d) be the first derivative of -d**4/2 - 4*d**3/3 + 7*d**2 - 8*d - 22. Determine h so that m(h) = 0.
-4, 1
Let f(p) be the second derivative of 0*p**3 + 1/30*p**6 - 1/6*p**4 + 0 + 1/20*p**5 - 7*p + 0*p**2. Suppose f(g) = 0. Calculate g.
-2, 0, 1
Suppose -6 + 4 = -c. Solve 0 + 7 + 5 + 4*t**c + 5*t + 11*t = 0.
-3, -1
Let i(u) = -u - 4. Let m be i(-6). Suppose -d**m + 195*d + 4 - 195*d = 0. What is d?
-2, 2
Factor 48 + 24*t**3 + 52*t + 72*t**2 + 67*t - 23*t + 3*t**4.
3*(t + 2)**4
Let m(x) be the second derivative of -x**4/16 + x**3/8 + 3*x**2/4 + 9*x. Solve m(y) = 0.
-1, 2
Let g be 82/(-42) + 6/3. Let z(x) be the second derivative of -2*x**2 + 1/3*x**4 + g*x**7 + 0 + x**3 + 0*x**6 - 2/5*x**5 - 3*x. Factor z(v).
2*(v - 1)**3*(v + 1)*(v + 2)
Let c(m) be the second derivative of 2*m**7/7 - 13*m**6/10 + 33*m**5/20 - m**4/2 + 6*m. Let c(s) = 0. What is s?
0, 1/4, 1, 2
Let r(t) be the second derivative of -t**7/630 + t**6/360 + 2*t**2 + 3*t. Let q(y) be the first derivative of r(y). Factor q(v).
-v**3*(v - 1)/3
Suppose -3*c**2 - 4*c**3 + 19*c**2 - 56*c + 32 - 2*c**2 + 14*c**2 = 0. Calculate c.
1, 2, 4
Let u(o) be the first derivative of o**4/18 + 2*o**3/9 + o**2/3 - 3*o + 2. Let a(h) be the first derivative of u(h). Factor a(j).
2*(j + 1)**2/3
Let a be (2/(-84))/((-6)/18). Let x(c) be the second derivative of -1/3*c**6 + 0*c**4 + 5/6*c**3 + 0 - a*c**7 - c + c**2 - 1/2*c**5. Factor x(o).
-(o + 1)**4*(3*o - 2)
Let a(g) = -g**3 - 4*g**2 - 3*g. Let d be a(-4). Suppose -w = 2*w + n - 6, -3*n - d = -w. Let 3*u**2 - 2*u**2 + 0*u**3 + u**w + 0*u**3 = 0. Calculate u.
-1, 0
Let u(c) be the first derivative of 4*c**4 - 32*c**3/3 + 10*c**2 - 4*c - 19. Factor u(b).
4*(b - 1)*(2*b - 1)**2
Let m(a) be the second derivative of a**6 + 7*a**5/4 - 5*a**4/12 - 5*a**3/3 - 4*a. Determine l so that m(l) = 0.
-1, -2/3, 0, 1/2
Let b(z) be the third derivative of z**9/15120 - z**7/840 - z**6/360 + z**4/6 + 4*z**2. Let c(w) be the second derivative of b(w). Suppose c(h) = 0. What is h?
-1, 0, 2
Let o(w) = -10*w**2 + 15*w + 25. Let n(f) = -5*f**2 + 8*f + 13. Let t(r) = 5*n(r) - 3*o(r). Solve t(s) = 0 for s.
-1, 2
Let p(u) = -3*u**2 + 27*u - 12. Let a(g) be the second derivative of g**4/12 - 11*g**3/6 + 5*g**2/2 + 8*g. Let v(q) = 12*a(q) + 5*p(q). Factor v(t).
-3*t*(t - 1)
Suppose 15*w = 42*w. Determine n, given that -2/5*n**4 - 8/5*n**2 + 8/5*n**3 + w*n + 0 = 0.
0, 2
Let z(k) be the first derivative of 4 - 3 + 0*k**3 - 3*k**2 - k**3. Find a, given that z(a) = 0.
-2, 0
Let q(z) be the first derivative of 3*z**4/28 + 4*z**3/7 + 15*z**2/14 + 6*z/7 - 5. Factor q(b).
3*(b + 1)**2*(b + 2)/7
Let f(u) = -2*u - 2*u**2 - 2*u + 1 - 6. Let c(d) = -2*d**2 - 4*d - 6. Let y be 32/(-6) - (-4)/(-6). Let n(m) = y*f(m) + 5*c(m). Factor n(o).
2*o*(o + 2)
Let l(a) = -a**2 - 5*a - 4. Let x be l(-3). Find j, given that -x - 3*j**2 + 1 - j**4 + 5*j**2 = 0.
-1, 1
Let q(m) = -5*m**3 + 6*m**2 + 12*m - 6. Let h(b) = 2*b**3 - 7*b**2 + 6*b**2 - b**2 - 4*b + 2. Let d(z) = -14*h(z) - 4*q(z). Factor d(t).
-4*(t - 1)*(t + 1)*(2*t - 1)
Find o, given that 0*o**2 + 1/4*o**4 + 0 - 1/4*o**3 + 0*o = 0.
0, 1
Factor 0*g**2 + 4/7 + 2/7*g**3 - 6/7*g.
2*(g - 1)**2*(g + 2)/7
Let y be (-2)/15 - (-7)/21. Let f(t) be the first derivative of t + 0*t**2 + 2 - 2/3*t**3 + 0*t**4 + y*t**5. Factor f(j).
(j - 1)**2*(j + 1)**2
Let x(y) = -y**4 - y**3 - y**2 - y + 1. Let i(k) = 2*k**4 + 8*k**3 + 8*k**2 + 2*k - 5. Let a(o) = i(o) + 5*x(o). Solve a(g) = 0.
-1, 0, 1
Suppose 5*b = -3*q + 20, -4*b - 12 = -q + 6. Let 4*g**3 - 7*g**3 + 5*g**3 + 8*g**2 + q*g + 4 = 0. What is g?
-2, -1
Let f(y) be the second derivative of -12*y**2 + 0 - 26/3*y**3 + 5/3*y**4 - 8*y. Factor f(l).
4*(l - 3)*(5*l + 2)
Let k be 2/(-1*(-4)/6). Factor -2 - 22*t**2 - 4*t**3 + t - t**3 - 7*t**k - 13*t.
-2*(t + 1)*(2*t + 1)*(3*t + 1)
Let h(s) = -s**4 - s**3 - s**2 + s - 1. Let d(w) = -w**4 - 13*w**3 + 13*w**2 - 5*w - 3. Let t(m) = d(m) - 3*h(m). Factor t(z).
2*z*(z - 2)**2*(z - 1)
Factor 4/7*a**2 + 0 + 2/7*a**3 + 2/7*a.
2*a*(a + 1)**2/7
Let l(y) = -6*y**5 - 20*y**4 - 40*y**3 - 40*y**2 - 22*y - 2. Let a(o) = o**5 + o - 1. Let p(g) = 2*a(g) + l(g). Factor p(w).
-4*(w + 1)**5
Let b(t) be the second derivative of -t**6/60 + 3*t**5/20 - t**4/24 - 2*t**3 - 4*t**2 - 12*t. Suppose b(o) = 0. What is o?
-1, 4
Suppose 2*s = -3*u, 5*s = s + 4*u. Factor -2/3*a - 2/3*a**3 + 4/3*a**2 + s.
-2*a*(a - 1)**2/3
Let f be 2/28*14/24. Let j(g) be the third derivative of -f*g**4 - g**2 + 0*g**3 + 0 - 1/60*g**5 + 0*g. What is b in j(b) = 0?
-1, 0
Let 3 + 6*n - 26*n**3 + 6*n**3 - 3*n**4 + 14*n**3 = 0. What is n?
-1, 1
Let v(k) = -8*k**4 - 4*k**3 - 2*k**2 + 2. Let j(f) = -f**5 + 9*f**4 + 3*f**3 + 2*f**2 - 3. Let a(c) = -2*j(c) - 3*v(c). What is z in a(z) = 0?
-1, 0
Let c(d) be the first derivative of -1/100*d**5 + 0*d**2 + 1/15*d**4 - 2 - 2/15*d**3 - 2*d. Let b(u) be the first derivative of c(u). Factor b(p).
-p*(p - 2)**2/5
Let a = 709423/7 + -101141. Let v = -204 + a. Factor -2/7*z**2 - v + 8/7*z.
-2*(z - 2)**2/7
Suppose 4/5*w**3 + 0 + 2/5*w**2 - 2/5*w**4 - 4/5*w = 0. Calculate w.
-1, 0, 1, 2
Let v = 85/62 - -4/31. Let n be (-10)/(-8) + (-2)/8. Factor -v*b - n - 1/2*b**2.
-(b + 1)*(b + 2)/2
Let q be (24/14)/((-2)/(-7)). Let u(k) be the third derivative of 1/54*k**5 + 1/945*k**7 + 0*k + k**2 - 1/54*k**4 + 0 + 0*k**3 - 1/135*k**q. Factor u(y).
2*y*(y - 2)*(y - 1)**2/9
Let c(l) be the first derivative of -2*l**3/27 + 9. Let c(n) = 0. Calculate n.
0
Let z(r) = 7*r**2 - r - 11. Let h(m) = 10*m**2 - m - 17. Let p(u) = -5*h(u) + 8*z(u). Determine d so that p(d) = 0.
-1/2, 1
Let b = 1/52 + 3/13. Let a be -1*(-7)/(-4) + 2. Determine w, given that a*w**2 + 0 - b*w = 0.
0, 1
Determine p, given that 3/2*p**2 + 0 + 3/2*p**3 + 0*p = 0.
-1, 0
Factor 5/3*w**4 - 5/3*w**5 + 0 + 10/3*w - 25/3*w**2 + 5*w**3.
-5*w*(w - 1)**3*(w + 2)/3
Let t be ((-14)/28)/(1/(-42)). Let j = -21 + t. Solve j - 7/5*w**3 + w**2 + 2/5*w = 0 for w.
-2/7, 0, 1
Let a be (-10)/20*(1 + -1). Let r(u) be the second deri