0, 4
Let y(u) be the third derivative of -u**8/168 - u**7/210 + u**6/40 + 51*u**2. Find k, given that y(k) = 0.
-3/2, 0, 1
Let z be -3 - ((-96)/10)/3. Let b = 3/29 + 14/145. Find a such that -2/5*a**3 - z*a**4 + b*a**2 + 0 + 2/5*a = 0.
-2, -1, 0, 1
Suppose 5*h - 15 = -0*h. Suppose -m - 17 = -h*d, -d - 3*d + 3*m + 26 = 0. Let -6*c - 6*c + d*c**2 + 8 + 3*c**2 - 4 = 0. Calculate c.
1/2, 1
Let n(h) be the first derivative of 9 + 0*h + 1/10*h**4 - 4/45*h**3 + 0*h**2 - 2/75*h**5. Factor n(m).
-2*m**2*(m - 2)*(m - 1)/15
Let t(o) = -20*o**4 + 105*o**2 + 70*o. Let f(i) = -3*i**4 + 15*i**2 + 10*i. Let q(c) = 15*f(c) - 2*t(c). Factor q(m).
-5*m*(m - 2)*(m + 1)**2
Let r(a) be the first derivative of -a**6/24 - 9*a**5/20 - 3*a**4/2 - 5*a**3/3 - 24. Suppose r(g) = 0. What is g?
-5, -2, 0
Let h(y) = 5*y + 47. Let k be h(-9). Suppose -r + 4 = -k*m, -r = -4*r - m + 5. Factor z + 5/7*z**3 - 1/7*z**4 - 9/7*z**r - 2/7.
-(z - 2)*(z - 1)**3/7
Factor 32/9 - 20/9*u + 2/9*u**2.
2*(u - 8)*(u - 2)/9
Let m(k) be the first derivative of 35 - 5/14*k**2 + 1/21*k**3 - 6/7*k. Factor m(h).
(h - 6)*(h + 1)/7
Let o(t) be the second derivative of t**4/20 - 9*t**3/10 + 8*t - 2. Factor o(x).
3*x*(x - 9)/5
Let i(b) be the first derivative of -b**6/72 + 5*b**4/24 - 3*b**3 - 6. Let u(c) be the third derivative of i(c). What is d in u(d) = 0?
-1, 1
Let p = -5 + 21. Let g be p/6 - (-7)/21. Suppose d**g + 0*d**2 - 1 + 0 - d - d**2 + 2*d**2 = 0. What is d?
-1, 1
Let q = -3120 + 3122. Suppose 0 + 2/5*k - 2/5*k**q + 2/5*k**4 - 2/5*k**3 = 0. What is k?
-1, 0, 1
Let z be (-156)/(-455)*35/15. Suppose -2/5*p**3 + z*p + 0 + 2/5*p**2 = 0. What is p?
-1, 0, 2
Let l(d) be the second derivative of 0 - 1/9*d**3 - 13/60*d**5 + 6*d + 0*d**2 + 11/36*d**4 + 2/45*d**6. Factor l(x).
x*(x - 2)*(x - 1)*(4*x - 1)/3
Let a be 473/(-4) + (12 - 15). Let c = a - -122. Find n such that -5/2*n**4 + 0*n + c*n**5 + 9/4*n**3 + 0 - 1/2*n**2 = 0.
0, 1/3, 1, 2
Let j(k) = k**2 + 2*k + 1. Let x be j(-3). Suppose 210*u + 24 = 214*u. Let n(c) = -c**2 - 2*c - 1. Let i(b) = b**2 + b. Let q(w) = u*i(w) + x*n(w). Factor q(z).
2*(z - 2)*(z + 1)
Factor 1/7*j**3 + 0*j - 1/7*j**5 - 1/7*j**4 + 0 + 1/7*j**2.
-j**2*(j - 1)*(j + 1)**2/7
Let h(b) be the second derivative of -b**7/12600 - b**4/2 - 17*b. Let n(r) be the third derivative of h(r). Factor n(j).
-j**2/5
Let x = 8/25 + -3/25. Let b(d) be the first derivative of 0*d**3 - 3 + 0*d**2 + 1/4*d**4 + x*d**5 + 0*d. Solve b(s) = 0 for s.
-1, 0
Suppose 6*z - 2*z - 91 = -5*a, 5*z - 2*a - 122 = 0. Suppose z = 5*v - 46. What is d in 2 - v*d**2 - 20 + 14*d + 8*d + 8*d + 2*d**3 = 0?
1, 3
Let u(r) be the first derivative of -2/21*r**3 + 0*r - 8 + 0*r**2 - 2/35*r**5 + 1/7*r**4. Factor u(k).
-2*k**2*(k - 1)**2/7
Let a(h) be the first derivative of h**4/14 - 4*h**3/21 + h**2/7 - 12. Suppose a(g) = 0. What is g?
0, 1
Let a = -3/800 + 4009/2400. Factor 1/3*p**5 + 3*p**3 + 2/3*p - 7/3*p**2 + 0 - a*p**4.
p*(p - 2)*(p - 1)**3/3
Let z be ((561/(-6))/17)/((-2)/28). Let d be 3/(-1) - z/(-14). Let 0 - 4*c**4 - 2*c**5 - d*c**3 + 0*c - 1/2*c**2 = 0. What is c?
-1, -1/2, 0
Suppose 5*b + d - 6*d = -95, -4*d + 13 = -b. Let p be 10/12 + -2*7/b. Let -3 - p*g + 3/2*g**2 = 0. What is g?
-1, 2
Let p(r) = -r**3 - 7*r**2 - 6*r - 2. Let c(a) = 1. Let m(b) = -4*c(b) - 2*p(b). Factor m(l).
2*l*(l + 1)*(l + 6)
Factor -56*n - n**2 + 98 - 29*n**2 - 3*n**3 + 10*n**2 - 63*n - 20*n**2.
-(n + 7)**2*(3*n - 2)
Let o be -8*(-1)/(-2) + 6. Factor q + 3*q**o + 4*q + q + 0*q.
3*q*(q + 2)
Factor 0*w**3 + 0*w**2 + 0*w + 0 - 1/2*w**4.
-w**4/2
Let i**5 + 1764 + 330*i**3 - 15*i**2 - 157*i**2 + 9*i**4 - 5*i**5 + 2173*i - 247*i**2 - 9145*i = 0. Calculate i.
-6, 1/4, 7
Let n(k) = 685*k + 2060. Let h be n(-3). Determine f so that -3*f + 2*f**2 + 11/3*f**3 + 0 - 4/3*f**h - 4/3*f**4 = 0.
-3/2, 0, 1
Determine u so that 0 - 3/5*u - 3/5*u**2 = 0.
-1, 0
Let r(l) be the third derivative of l**8/252 - 2*l**7/105 + l**6/90 + l**5/15 - l**4/9 - 102*l**2. Suppose r(x) = 0. What is x?
-1, 0, 1, 2
Let a = 9272/9 - 1028. Factor 4/9 + 0*j**2 + 10/9*j - 2/3*j**5 - 20/9*j**3 - a*j**4.
-2*(j + 1)**4*(3*j - 2)/9
Let c(j) = -11*j - 1. Let r be c(-1). Let u = r - 8. Factor g**u + 0 - 5 + 4.
(g - 1)*(g + 1)
Let o(p) be the second derivative of 9/2*p**2 + 0 + 9*p - 1/4*p**4 + p**3. Find l such that o(l) = 0.
-1, 3
Let m(d) be the second derivative of 128*d**4/3 + 160*d**3 + 225*d**2 + 433*d. Factor m(o).
2*(16*o + 15)**2
Factor 5*l**5 - l**2 - 28*l**4 - l**2 - 4*l**5 + 3*l**3 + 6*l**2 - 4*l + 24*l**4.
l*(l - 2)**2*(l - 1)*(l + 1)
Let s be ((-9)/15)/((-1)/((-4)/(-22)) - -4). Factor -s*u**2 - 1/5*u - 1/5*u**3 + 0.
-u*(u + 1)**2/5
Let i(r) be the second derivative of r**4/48 - r**3/24 + 2*r + 8. Factor i(q).
q*(q - 1)/4
Let h(m) = -3*m**4 + 20*m**3 - 90*m**2 - 172*m - 95. Let c(r) = 2*r**4 - 19*r**3 + 84*r**2 + 173*r + 95. Let w(v) = 4*c(v) + 3*h(v). Factor w(b).
-(b - 5)*(b + 1)**2*(b + 19)
Let i(o) be the second derivative of -3*o**5/20 + o**4/2 - 2*o + 12. Let i(r) = 0. What is r?
0, 2
Let q = 35 - 31. Let j(s) be the second derivative of 1/18*s**4 + 0 + q*s + 1/9*s**3 - 2/3*s**2. Factor j(l).
2*(l - 1)*(l + 2)/3
Let t(l) be the second derivative of 0 - 1/8*l**3 - 1/80*l**5 + 8*l - 5/48*l**4 + 9/8*l**2. Factor t(i).
-(i - 1)*(i + 3)**2/4
Let y(q) be the third derivative of -q**8/1848 + 2*q**7/1155 + 2*q**6/165 - 8*q**5/165 - 4*q**4/33 + 32*q**3/33 + 75*q**2. Factor y(m).
-2*(m - 2)**3*(m + 2)**2/11
Let p be (-6)/(-12) + 6/4. Factor 25 + 60*f**2 + 85*f - 22*f**3 + 99*f**2 - 53*f**p + 13*f**4 + 80*f**3 + f**5.
(f + 1)**3*(f + 5)**2
Let f(q) be the third derivative of -q**8/6720 - q**7/840 + 2*q**5/15 + 18*q**2. Let y(c) be the third derivative of f(c). Factor y(s).
-3*s*(s + 2)
Let m(l) be the third derivative of l**7/42 - l**6/6 - 5*l**5/2 + 85*l**4/6 - 175*l**3/6 - 6*l**2 + 9*l. Factor m(h).
5*(h - 7)*(h - 1)**2*(h + 5)
Suppose -315 = -9*z - 54*z. Factor 2/3*c**2 + 0 + 14/3*c**4 + 0*c + 2*c**z + 10/3*c**3.
2*c**2*(c + 1)**2*(3*c + 1)/3
Let b(n) be the second derivative of -27*n**5/40 + 35*n**4/4 + 97*n**3/4 + 27*n**2/2 + 91*n. Factor b(o).
-3*(o - 9)*(o + 1)*(9*o + 2)/2
Let m(l) be the third derivative of l**8/24 + 2*l**7/21 - 5*l**6/12 - 4*l**5/3 - l**4 - 124*l**2. Suppose m(u) = 0. Calculate u.
-2, -1, -3/7, 0, 2
Let k(s) be the first derivative of -8*s**5/5 - 15*s**4/2 - 32*s**3/3 - 3*s**2 + 4*s + 98. Determine g so that k(g) = 0.
-2, -1, 1/4
Let -264*b**3 + 0*b + 13*b**2 - 8*b**4 - 19*b + 73*b**2 - 3*b + 184*b**3 = 0. What is b?
-11, 0, 1/2
Let i be (-2)/(-4)*(-3 + 7). Find v such that 0*v**i - 3*v**2 - 2*v**3 + 11*v**2 - 8*v = 0.
0, 2
Let j = 3507 - 3504. Let a = -414 - -6214/15. Determine t so that 0 - 2/5*t**2 + a*t**j + 0*t + 2/15*t**4 = 0.
-3, 0, 1
Let q(h) = -5*h**2 - 53*h - 6. Let u(d) = 7*d**2 + 53*d + 8. Let n(v) = -4*q(v) - 3*u(v). Factor n(t).
-t*(t - 53)
Let n(d) be the third derivative of d**8/112 + d**7/35 - d**6/20 - 2*d**5/5 - 7*d**4/8 - d**3 - 4*d**2 + 2. Factor n(x).
3*(x - 2)*(x + 1)**4
Let k = -6 + 9. Suppose -k*q + 2 = -7. Factor -u**3 - q + 1 - 7*u**3 + 6*u**4 - 4*u**2 + 8*u.
2*(u - 1)**2*(u + 1)*(3*u - 1)
Let y = 1638 + -1635. Let q(v) be the first derivative of 3 + 0*v + 1/13*v**2 - 2/39*v**y. Solve q(k) = 0 for k.
0, 1
Let c(t) = -t**2 + 20*t + 45. Let h be c(22). Let g(p) = 4*p**2 - 16*p + 15. Let l be g(h). Factor -4/9*r**l + 8/9*r**2 - 4/9*r + 0.
-4*r*(r - 1)**2/9
Factor 5/3*o**2 - 1/3*o**3 - o - 3.
-(o - 3)**2*(o + 1)/3
Let o(r) be the second derivative of r**7/10080 - r**6/360 + r**5/40 + 10*r**4/3 - r. Let s(b) be the third derivative of o(b). Suppose s(d) = 0. What is d?
2, 6
Suppose 2*h + 5*v + 1 = 0, 5*h + v - 18 = -9. Factor -2/5*y**h + 8/5*y - 6/5.
-2*(y - 3)*(y - 1)/5
Let n(d) = 8*d**2 + 2*d + 1. Let z be n(-1). Let y(i) = -i**2 - 8*i + 12. Let q be y(-9). Factor -o**q + o + o**2 - z*o + 8*o.
-o*(o - 2)*(o + 1)
Suppose -4*r = -12, 4*r - 6 = 6*i - 8*i. Let b be (8/28 - i) + 10/(-35). Factor -4/5*z**2 + 0 + 0*z - 2/5*z**b.
-2*z**2*(z + 2)/5
Let o = 4872 - 4869. Suppose 2*t - 1/4*t**5 - 1/4*t**2 + 5/4*t**4 - 7/4*t**o - 1 = 0. Calculate t.
-1, 1, 2
Let r be 4 - (2/(-1) - -4). Find z such that z**2 + 16*z - 32 - 2*z**2 + 0*z**r - z**2 = 0.
4
Let q(l) be the first derivative of -l**6/1800 + l**4/30 + 5*l**3 + 14. Let k(b) be t