 derivative of -a**4/54 - a**3/9 - 2*a**2/9 - 5*a. Suppose i(u) = 0. What is u?
-2, -1
Let d(k) = -5*k**4 - k**3 + 4*k**2 + 3*k. Let p(y) = -4*y**4 + 4*y**2 + 2*y. Suppose 0 = -2*u - 5*u + 21. Let q(z) = u*p(z) - 2*d(z). Factor q(l).
-2*l**2*(l - 2)*(l + 1)
Let d be 108/(-90) - 290/(-75). Suppose d*g - 2/3*g**2 + 0 = 0. What is g?
0, 4
Let i(k) = -k + 7. Let b be i(6). Suppose 4*j - 10 = -j. Factor -9*v + 9*v - v**2 - b + 2*v**j.
(v - 1)*(v + 1)
Let f(b) = 3*b**2 + 4*b + 5. Let w(i) = -i**2 - 2*i - 2. Let g(m) = -4*f(m) - 10*w(m). Factor g(t).
-2*t*(t - 2)
Solve 0 - 1/2*k**4 + 0*k**2 - 3/4*k**3 + 1/4*k = 0.
-1, 0, 1/2
Let z(n) be the first derivative of n**6/40 + n**5/20 - 2*n**2 - 3. Let k(r) be the second derivative of z(r). Factor k(w).
3*w**2*(w + 1)
Let j be 10*(0 + 2 + -1). Suppose 0 = 5*r + j, 0*r = k - 3*r - 15. Factor -9*a**3 + 3*a**2 - 3*a**5 + 0*a**3 + 0*a**5 + k*a**4.
-3*a**2*(a - 1)**3
Factor -6/7*t**2 + 0 - 2/7*t**3 + 0*t.
-2*t**2*(t + 3)/7
Let m be 0/(-2) + -2 - (-150)/72. Let s(f) be the second derivative of f + 0*f**2 - m*f**4 - 1/6*f**3 + 0. Factor s(d).
-d*(d + 1)
Let c(f) = -f**3 - f - 1. Let u(q) = -5*q**3 + 5*q**2 - 6*q - 6. Let h(g) = -6*c(g) + u(g). Factor h(t).
t**2*(t + 5)
Let l(j) = j - 4. Let p be l(9). Factor -2*d**5 - 5*d**5 - 2*d**4 + 9*d**p.
2*d**4*(d - 1)
Suppose 15*f - 100 = -10*f. Find q such that 3/4*q**f - 9/4*q**3 + 0*q**2 + 3*q + 0 = 0.
-1, 0, 2
Let g(w) = w + 6. Let z be g(-4). Find n such that 4*n**5 - 4*n**5 - 3*n**5 + n**3 + z*n**3 = 0.
-1, 0, 1
Let d = -13/110 - -3/22. Let n(z) be the second derivative of -d*z**5 + 1/11*z**2 - 1/165*z**6 + 0*z**4 + 2/33*z**3 + 0 + 3*z. Factor n(i).
-2*(i - 1)*(i + 1)**3/11
Let w(b) be the second derivative of -b**6/5 + b**5 - 2*b**4 + 2*b**3 - b**2 - 18*b. Let w(c) = 0. What is c?
1/3, 1
Solve -4/3*h**4 + 2*h**2 + 0 + 10/3*h**3 + 0*h = 0.
-1/2, 0, 3
Let h(q) = -q**4 - q**3 - q**2 - q - 1. Let c(f) = -6*f**4 - 12*f**3 - 12*f**2 - 6*f - 3. Let i(s) = c(s) - 3*h(s). Suppose i(r) = 0. Calculate r.
-1, 0
Let k be 6 - 3 - (-111)/12. Let p = -12 + k. Factor 0 + 1/4*z + 0*z**2 - p*z**3.
-z*(z - 1)*(z + 1)/4
Let n(w) be the second derivative of 0*w**2 - 1/15*w**4 + 0*w**3 - 9/50*w**5 - w + 0. Factor n(c).
-2*c**2*(9*c + 2)/5
Let o = -16 + 19. Let w(m) be the first derivative of -1/3*m - 1/15*m**5 + 2 + 0*m**4 + 0*m**2 + 2/9*m**o. Let w(u) = 0. What is u?
-1, 1
Let r(j) be the first derivative of j**5/390 + j**4/39 + 4*j**3/39 - 5*j**2/2 + 4. Let a(g) be the second derivative of r(g). Factor a(d).
2*(d + 2)**2/13
Factor 0*s**3 - s - 3*s**3 - 2*s**5 + s**5 + 5*s**3.
-s*(s - 1)**2*(s + 1)**2
Suppose 6 + 27*c**4 + 21*c - 21*c**3 + 5*c**3 - 5*c**3 - 33*c**2 = 0. Calculate c.
-1, -2/9, 1
Let v(x) = -x. Let q be v(-7). Suppose -2*a - 15 = -q*a. Let 0 + 0*u + 1/2*u**2 - 1/2*u**4 + 0*u**a = 0. What is u?
-1, 0, 1
Let q(m) = 144*m. Let l be q(3). Suppose -52*a**4 - l*a**2 - 134*a**3 - 82*a**3 + 4*a**4 - 324*a - 4*a**5 = 0. What is a?
-3, 0
Let i(v) be the first derivative of -v**4/36 - v**3/27 + v**2/18 + v/9 - 1. Solve i(o) = 0.
-1, 1
Let k(z) be the second derivative of -z**4/4 - 3*z**3 - 27*z**2/2 - 13*z. Determine c so that k(c) = 0.
-3
Let n(x) be the third derivative of 0*x + 0 - 1/20*x**5 + 11/72*x**4 - 1/9*x**3 + 3*x**2. Factor n(i).
-(i - 1)*(9*i - 2)/3
Let w(i) = 2*i**2 - 4*i + 2. Let x(t) = 3*t**2 - 8*t + 5. Let z(r) = -9*w(r) + 4*x(r). Let s(l) = l**2 - 1. Let c(p) = -2*s(p) - z(p). Solve c(b) = 0.
0, 1
Let d(q) be the first derivative of 4*q**3/3 - 16*q + 11. Factor d(x).
4*(x - 2)*(x + 2)
Factor 3*w**4 + 3*w**5 + 6*w - 5*w**3 + 7*w**3 - 11*w**3 - 3*w**2.
3*w*(w - 1)**2*(w + 1)*(w + 2)
Solve 2/9*y**3 - 2/9*y**5 + 2/3*y**4 + 0*y + 0 - 2/3*y**2 = 0 for y.
-1, 0, 1, 3
Let x = 109 + -106. Find u, given that 0 + 14/5*u**2 + 4/5*u - 8/5*u**x = 0.
-1/4, 0, 2
Let u(c) be the first derivative of 3 - 1/4*c**2 + 0*c + 1/4*c**5 - 9/16*c**4 + 7/12*c**3 - 1/24*c**6. Factor u(p).
-p*(p - 2)*(p - 1)**3/4
Let b(t) be the third derivative of t**11/332640 + t**10/75600 + t**9/60480 + t**5/30 - 2*t**2. Let x(a) be the third derivative of b(a). Factor x(w).
w**3*(w + 1)**2
Factor 3*q**5 + 4*q**4 + 2*q**4 + 3*q**3 + 0*q**3.
3*q**3*(q + 1)**2
Factor -1/3*r**3 + 8/3*r**2 - r**4 - 4/3*r + 0.
-r*(r - 1)*(r + 2)*(3*r - 2)/3
Factor -2/3*d**3 + 0*d**2 + 4/3 + 2*d.
-2*(d - 2)*(d + 1)**2/3
Factor -1/7*h**2 - 4/7 + 4/7*h.
-(h - 2)**2/7
Let p(q) be the first derivative of q**4/72 - q**3/36 - 6*q + 1. Let z(a) be the first derivative of p(a). Factor z(l).
l*(l - 1)/6
Factor -25*w**2 - 5*w**4 + 0*w**2 + 5*w**2 + 20*w**3.
-5*w**2*(w - 2)**2
Find k such that -4/7*k**3 - 4/7*k**4 + 4/7*k**2 + 4/7*k + 0 = 0.
-1, 0, 1
Suppose -3*u + 15 = 2*u. Factor -1/2*v**5 + 0*v + 0*v**2 - v**4 + 0 - 1/2*v**u.
-v**3*(v + 1)**2/2
Suppose -4*g = -4, -12 = -5*h - 5*g + 3. Find r, given that -8/5*r**2 - 2/5*r**3 - h*r - 4/5 = 0.
-2, -1
Factor 12 - 7*f - 21*f + 3*f**2 + 13*f.
3*(f - 4)*(f - 1)
Let i(f) be the first derivative of -26/3*f**3 + 10*f**4 + 2*f**2 - 2 - 18/5*f**5 + 0*f. Factor i(m).
-2*m*(m - 1)**2*(9*m - 2)
Let o(h) be the third derivative of -h**6/120 + h**5/30 - 4*h**2. Factor o(l).
-l**2*(l - 2)
Let y = -75 + 77. What is u in -2/7*u + 4/7 - 6/7*u**y = 0?
-1, 2/3
Suppose 0 = -3*j + 12 - 3. Let i(f) be the first derivative of -f**2 - 2*f + 1 + 2/3*f**j + 1/2*f**4. Find p such that i(p) = 0.
-1, 1
Factor 13*t**2 + t**2 - 3*t**2 + 4*t**2 + 6*t.
3*t*(5*t + 2)
Let h(y) be the second derivative of -y**6/360 + y**3/3 + y. Let c(w) be the second derivative of h(w). Find a, given that c(a) = 0.
0
Let f(n) be the second derivative of -n**6/105 + n**5/70 + n**4/14 - 5*n**3/21 + 2*n**2/7 - n + 25. Determine d so that f(d) = 0.
-2, 1
Let j(z) = -5*z**2 + 5*z - 2. Let q(c) = 9*c**2 - 10*c + 3. Let t(g) = -11*j(g) - 6*q(g). Suppose t(f) = 0. What is f?
-4, -1
Let r(c) be the third derivative of 0*c + 3/4*c**6 + 0 - 4/5*c**5 + 0*c**3 - 5/21*c**7 + 2*c**2 + 1/3*c**4. Suppose r(j) = 0. What is j?
0, 2/5, 1
Suppose -4/3*q - 1/3 + 5/3*q**2 = 0. Calculate q.
-1/5, 1
Let r(i) = 2*i**2 + i - 1. Let q be r(1). Let y(l) be the first derivative of -1/8*l**4 + 0*l + 1/12*l**3 + 1/20*l**5 + 0*l**q - 4. Find p such that y(p) = 0.
0, 1
Let x = 5 - 5. Factor -d**2 + x - 1/3*d - 2/3*d**3.
-d*(d + 1)*(2*d + 1)/3
Let o(k) be the third derivative of -k**8/43680 + k**7/16380 - k**4/3 - 8*k**2. Let w(m) be the second derivative of o(m). Factor w(h).
-2*h**2*(h - 1)/13
Let n(j) be the first derivative of j**6/30 - j**5/5 + j**4/4 + 2*j**3/3 - 2*j**2 - j + 1. Let t(m) be the first derivative of n(m). Let t(d) = 0. What is d?
-1, 1, 2
Let k(a) be the second derivative of -a**6/10 - 33*a**5/5 - 363*a**4/2 - 2662*a**3 - 43923*a**2/2 + 2*a. Factor k(s).
-3*(s + 11)**4
Let x(q) be the third derivative of q**7/315 + q**6/30 + 13*q**5/90 + q**4/3 + 4*q**3/9 - 7*q**2. Determine r so that x(r) = 0.
-2, -1
Suppose 2/3*n**5 - 2/3*n**4 - 4/3*n**3 + 4/3*n**2 - 2/3 + 2/3*n = 0. What is n?
-1, 1
Let r(m) be the first derivative of -2*m**5/45 + m**4/6 - 5. Let r(a) = 0. Calculate a.
0, 3
Suppose -2*r + 6*r = -2*r. Let y(l) be the third derivative of 1/525*l**7 + 0*l**3 + r*l + 0 + 1/150*l**6 - 3*l**2 + 1/150*l**5 + 0*l**4. Factor y(o).
2*o**2*(o + 1)**2/5
Let d be (0 + -3)/((-39)/65). Suppose 10 + 5 = d*s. Factor 0*w**2 + 0 + 1/4*w**s - 1/4*w.
w*(w - 1)*(w + 1)/4
Let l(k) = -k**4 - 31*k**3 - 67*k**2 - 48*k. Let s(h) = 8*h**4 + 216*h**3 + 468*h**2 + 336*h. Let g(u) = -20*l(u) - 3*s(u). Determine p so that g(p) = 0.
-3, -2, 0
Let p(q) be the third derivative of q**7/630 + q**6/90 + q**5/45 + 5*q**2. Determine f so that p(f) = 0.
-2, 0
Let q(u) = u - 4. Let b be q(6). Suppose 3*k - 7 = b. Factor 2*w + 5*w**3 + 0*w - 3*w**k + 4*w**2.
2*w*(w + 1)**2
Let r(f) be the second derivative of 1/75*f**6 + 1/5*f**3 + 0 - 2/5*f**2 + 4*f + 1/30*f**4 - 3/50*f**5. Suppose r(n) = 0. Calculate n.
-1, 1, 2
Let n be 5/6 - 6/12. Find z, given that 2/3*z - n*z**2 - 1/3 = 0.
1
Let w = 9 - 4. Factor 0*y**2 + y - 2*y**2 - 3*y**5 - y**4 + 2*y**w + 3*y**4.
-y*(y - 1)**3*(y + 1)
Let x = 4 - 2. Let b(m) = 5*m**3 - 2*m**2 + 2*m. Let d be b(1). Factor -d*r - x - r + 2*r - 2*r**2.
-2*(r + 1)**2
Let w(m) = -m**3 + 5*m**2 + 11*m - 26. Let f be w(6). Factor -8/3*v - 8/3*v**3 - 2/3 - 2/3*v**4 - f*v**2.
