 + h**5/50 + h**4/45 - 7*h + 3. Let s(o) be the first derivative of q(o). Determine b so that s(b) = 0.
-1, 0, 2
Let c(o) be the second derivative of -10*o**7/21 - 17*o**6/6 - 7*o**5 - 55*o**4/6 - 20*o**3/3 - 5*o**2/2 + 6*o. Find h, given that c(h) = 0.
-1, -1/4
Let h(d) be the second derivative of d**7/168 - d**6/40 + 3*d**5/80 - d**4/48 + 9*d. Factor h(s).
s**2*(s - 1)**3/4
Factor -2/9*g**4 + 2/9*g + 0 - 2/9*g**3 + 2/9*g**2.
-2*g*(g - 1)*(g + 1)**2/9
Factor 0*t - 1/6*t**4 + 1/6*t**2 - 1/6*t**5 + 0 + 1/6*t**3.
-t**2*(t - 1)*(t + 1)**2/6
Suppose 4*h + o = h + 22, -h + 4*o = 10. Suppose 0 = h*i - i - 10. Factor 4 + 11*b**2 + b**i - 16*b**4 + 8*b**3 + 2*b**5 + 4*b**5 - 8*b - 6*b.
2*(b - 1)**3*(b + 1)*(3*b - 2)
Let u(m) be the third derivative of m**5/270 - m**4/54 - 5*m**2. Factor u(k).
2*k*(k - 2)/9
Let l(g) = -2*g**5 + 3*g**4 + 12*g**3 + 5*g**2 + 3*g + 3. Let r(f) = -5*f**5 + 10*f**4 + 36*f**3 + 16*f**2 + 8*f + 8. Let z(q) = -8*l(q) + 3*r(q). Factor z(x).
x**2*(x + 2)**3
Let s be 63/405*3/4. Let i(k) be the second derivative of -1/4*k**4 + 0 - 2*k - s*k**5 - 1/45*k**6 - 1/6*k**2 - 5/18*k**3. Find y, given that i(y) = 0.
-1, -1/2
Suppose n = -n + 3*y, -5*n = y. Let r(j) be the third derivative of -1/180*j**5 + 0*j + 0 + 0*j**4 - 2*j**2 + n*j**3. Factor r(k).
-k**2/3
Let j(k) = -k**3 + 7*k**2 + 2*k + 4. Let p be j(7). Suppose -2*t = -0*t - 2. Factor -10*h**2 - p*h - 5 + t - 4*h**2.
-2*(h + 1)*(7*h + 2)
Let l(r) = -r**3 + r**2 - r. Let n(u) = -u**5 + u**4 + 4*u**3 - 2*u**2 - 10*u. Let j(c) = -2*l(c) + n(c). Determine s so that j(s) = 0.
-2, -1, 0, 2
Let d(q) be the first derivative of 2*q**6 - 7*q**5 + 8*q**4 - 2*q**3 - 2*q**2 + q - 7. Determine n, given that d(n) = 0.
-1/3, 1/4, 1
Let d(i) be the third derivative of -2/9*i**3 + 5/36*i**4 - 2*i**2 - 1/45*i**5 - 1/504*i**8 + 0 + 4/315*i**7 + 0*i - 1/45*i**6. Solve d(g) = 0 for g.
-1, 1, 2
Factor -14*h**2 + 4*h**3 + 11*h**2 + 2*h**3 + 6*h**2.
3*h**2*(2*h + 1)
Let d(g) = g**3 + 3*g**2 - 4. Let q be d(-3). Let o be 6/q*1*-4. Let -2*m**2 + o*m**4 + 24*m**3 - 24*m**4 + 3*m - 4*m - 3*m = 0. Calculate m.
-1/3, 0, 2/3, 1
Let w(x) be the first derivative of x**4/7 - 20*x**3/21 + 16*x**2/7 - 16*x/7 - 40. Solve w(k) = 0.
1, 2
Let m = -355/2 + 178. Factor m*p**3 + 0 - p**2 + 0*p.
p**2*(p - 2)/2
Let o = 121 + -118. Suppose 8/3*r - 2/3 + 8/3*r**o - 4*r**2 - 2/3*r**4 = 0. What is r?
1
Let u(g) = -21*g**3 - 9*g**2 - 11*g - 11. Let s(r) = -4*r**3 - 2*r**2 - 2*r - 2. Let k = 10 - 8. Let n(x) = k*u(x) - 11*s(x). Factor n(b).
2*b**2*(b + 2)
Let h = 32 + -59. Let b(u) = -1002*u**3 - 1392*u**2 - 456*u - 39. Let y(g) = -77*g**3 - 107*g**2 - 35*g - 3. Let t(p) = h*y(p) + 2*b(p). Factor t(m).
3*(m + 1)*(5*m + 1)**2
Let g(v) be the third derivative of v**5/90 - v**4/36 + 6*v**2. Find s such that g(s) = 0.
0, 1
Solve -3/2*s**2 - 3*s - 3/2 = 0 for s.
-1
Let r(g) = g**2 + 3*g + 4. Suppose 0*v - 3 = 4*v - c, v - 23 = 5*c. Let o be r(v). Solve 64/5*t + 48/5*t**o + 16/5*t**3 + 32/5 + 2/5*t**4 = 0 for t.
-2
Factor -l - 14*l**2 - 2*l - 6*l**2 - 2*l.
-5*l*(4*l + 1)
Let 1/2*x**2 + 1/2*x + 0 = 0. Calculate x.
-1, 0
Let a = -41 - -41. Let a + s**2 + 1/2*s**3 + 0*s = 0. Calculate s.
-2, 0
Let i(h) = -4*h**2 + 4*h - 6. Let w(x) = 4*x - 4*x**2 - 11 - 3*x**2 + 3*x. Let t(q) = 11*i(q) - 6*w(q). Factor t(g).
-2*g*(g - 1)
Let z(t) = 3*t**3 + 3*t**2 - t + 1. Let p(a) = -a - 6. Let f(m) = m + 5. Let d(c) = 7*f(c) + 6*p(c). Let g(r) = -d(r) - z(r). What is l in g(l) = 0?
-1, 0
Determine b so that 0*b + 0 - 8/11*b**3 - 8/11*b**2 - 2/11*b**4 = 0.
-2, 0
Let p(d) be the third derivative of -d**5/40 - 7*d**2. Factor p(y).
-3*y**2/2
Factor 3*y + 2*y + 17*y**2 - 12*y**2.
5*y*(y + 1)
Let i be (-1)/(2/(-4)) - -3. Factor -i*y**3 + 2*y**3 + 2*y**3 - 24*y - y**3 - 12*y**2 - 16.
-2*(y + 2)**3
Let r(w) be the first derivative of -1/4*w**4 - 1/8*w**2 - 1/4*w**3 - 1/8*w**5 - 1/40*w**6 - 2*w - 4. Let h(p) be the first derivative of r(p). Factor h(d).
-(d + 1)**3*(3*d + 1)/4
Let y(d) be the second derivative of 27*d**7/14 - 12*d**6 + 391*d**5/20 - 31*d**4/3 + 2*d**3 - 4*d. Solve y(x) = 0 for x.
0, 2/9, 1, 3
Let z(r) be the second derivative of -4*r + 0*r**3 + 0 - 1/4*r**4 + 3/2*r**2. Factor z(k).
-3*(k - 1)*(k + 1)
Let f(j) be the third derivative of -j**8/26880 + j**6/2880 + j**4/12 + 3*j**2. Let b(g) be the second derivative of f(g). Factor b(v).
-v*(v - 1)*(v + 1)/4
Solve -1/5*p**2 + 1/5*p + 2/5 = 0 for p.
-1, 2
Let x(f) be the first derivative of -3*f**5/5 - 21*f**4/4 - 18*f**3 - 30*f**2 - 24*f - 5. Suppose x(i) = 0. Calculate i.
-2, -1
Let f(l) = l. Let w be f(2). Find c such that -4 + 5*c**w - c**2 + 4*c + 4 = 0.
-1, 0
Let u(x) be the first derivative of -x**6/45 + x**5/30 - x + 1. Let l(h) be the first derivative of u(h). Let l(j) = 0. Calculate j.
0, 1
Let y be (-104)/(-16) + 1 + -6. Solve -1 - y*p - 1/2*p**2 = 0.
-2, -1
Let y(g) be the second derivative of -g**6/40 - g**5/20 + 7*g**2/2 + 6*g. Let d(f) be the first derivative of y(f). Factor d(c).
-3*c**2*(c + 1)
Let y(l) be the first derivative of l**5/120 + l**2/2 - 2. Let t(b) be the second derivative of y(b). Factor t(c).
c**2/2
Let f(w) be the first derivative of -w**6/360 - w**5/60 + w**3 + 3. Let n(g) be the third derivative of f(g). Factor n(r).
-r*(r + 2)
Suppose -2 = 2*d - 8. Let g be 10/95 - (-220)/76. Factor 0*o**2 - d*o - o**2 + o + o**g.
o*(o - 2)*(o + 1)
Let g(i) be the third derivative of 0*i**3 - 1/96*i**4 + 1/210*i**7 + 0*i - 2*i**2 + 1/60*i**5 - 1/1344*i**8 + 0 - 1/80*i**6. Factor g(a).
-a*(a - 1)**4/4
Let p(j) = -3*j**2 - 23*j + 16. Let n(c) = 2*c**2 - 3*c - 8*c + 0*c - 3*c**2 + 8. Let f(b) = -14*n(b) + 6*p(b). Solve f(q) = 0.
2
Let x(v) be the first derivative of 4*v**3/3 - 6. What is q in x(q) = 0?
0
Let g = -20268/11 - -1844. Factor 6/11*d + 4/11 - 4*d**3 - 10/11*d**5 - 36/11*d**4 - g*d**2.
-2*(d + 1)**4*(5*d - 2)/11
Suppose -590*s = -588*s. Factor -1/2*v**4 + 0*v**2 + 0*v + 0 + s*v**3.
-v**4/2
Let t be (-3)/(-2)*(-10)/(-3). Suppose b + 4*b = 20, -t*d - 5*b = -35. Factor -4*f**d - 2*f**4 - 3 + 0 + 5 - f + 5*f.
-2*(f - 1)*(f + 1)**3
Let b(j) be the second derivative of -j**7/490 + j**5/140 + 5*j**2/2 + 3*j. Let u(w) be the first derivative of b(w). Factor u(x).
-3*x**2*(x - 1)*(x + 1)/7
Let s(n) be the first derivative of n**3/8 + 3*n**2/2 - 27*n/8 + 48. Find b such that s(b) = 0.
-9, 1
Let j(t) be the third derivative of -t**11/332640 + t**9/60480 + t**5/20 - t**2. Let g(u) be the third derivative of j(u). Factor g(m).
-m**3*(m - 1)*(m + 1)
Let w(f) = -f**2 + 9*f - 14. Let z be w(7). Let g be (-1)/3 - (-26)/42. Suppose -6/7*n**4 + g*n + 6/7*n**2 - 2/7*n**3 + z = 0. What is n?
-1, -1/3, 0, 1
Let w(k) = k - 6. Let i be w(-2). Let m be i/(-20)*5 - 2. Factor -1/2*o**2 - o + m.
-o*(o + 2)/2
Suppose -1/6 + 1/6*x + 1/6*x**2 - 1/6*x**3 = 0. What is x?
-1, 1
Suppose 5*b + 31 - 6 = 0, -3 = -4*q - b. Let j = 4 - 2. Let q*g**j - g**2 + 0*g**2 + g = 0. Calculate g.
-1, 0
Let v = -2 + 0. Let s(y) = y + 2. Let r be s(v). Solve 30*j**2 + 20*j**2 + 8 - 40*j + r = 0.
2/5
Let t(k) be the third derivative of 2/21*k**3 - 1/84*k**4 + 0 - 1/210*k**5 - 5*k**2 + 0*k. Factor t(u).
-2*(u - 1)*(u + 2)/7
Let x(w) = -5*w**2 - 2*w + 2. Let b be x(-2). Let m be (-10)/b*(-12)/(-15). What is k in m*k + 0 - 2/7*k**2 = 0?
0, 2
Determine t so that 0 - 3*t**2 - 342*t + 348*t + 2 - 5 = 0.
1
Suppose 3 + 802*c + 9*c**4 - 802*c + 6*c**5 - 6*c**3 - 12*c**2 = 0. What is c?
-1, 1/2, 1
Let c(g) = -g**2 + g. Let n(r) = -2*r**2 + 77*r - 320. Let b(d) = 3*c(d) + n(d). Factor b(i).
-5*(i - 8)**2
Let m be ((-12)/(-63))/(1*(-10)/(-35)). Factor 2/3 - 1/3*k**3 + 1/3*k - m*k**2.
-(k - 1)*(k + 1)*(k + 2)/3
Suppose 2*p - 4*p + 2 = -2*c, -4*p - c = -19. Let n(d) = 2*d**2 - 2*d - 22. Let a be n(4). Solve 1/4*f**p + 0 - 1/4*f**a - 1/2*f**3 + 1/2*f = 0 for f.
-1, 0, 1, 2
Let j(l) be the second derivative of -l**6/2520 - l**5/140 - 3*l**4/56 + l**3/2 + 2*l. Let c(n) be the second derivative of j(n). Factor c(g).
-(g + 3)**2/7
Let r(y) be the third derivative of -1/2*y**3 + 2*y**2 - 1/8*y**4 + 0 + 1/20*y**5 + 0*y + 1/40*y**6. Determine p, given that r(p) = 0.
-1, 1
Let k(p) = 3*p**5 - 3*p**4 - 3*p**3 - 19*p**2 - 11*p. Let t(y) = -y**5 + y**4 + y**3 + 5*y**2 + 3*y. Let d(u) = 6*k(u) + 22*t(u). Factor d(m).
-4*m**2*(m - 1)**2*(m + 1)
Let j(