*(p + 1)/3
Let n(o) be the first derivative of -3*o**8/224 - o**7/35 + o**6/80 + o**5/20 - 2*o**2 - 2. Let t(l) be the second derivative of n(l). Solve t(k) = 0.
-1, 0, 2/3
Let h(l) = l**2 - 4 + 5*l - 1 - 1. Let o be h(-6). Suppose 6*i + 3*i**2 - i**2 + 4 + o*i = 0. Calculate i.
-2, -1
Let b(j) = -j**2 + 4*j - 3. Let l(y) = y**2 - 1. Let x(n) = -b(n) + 4*l(n). Factor x(r).
(r - 1)*(5*r + 1)
Let n = -9/16 + 13/16. Factor n*k**3 + 0 - 1/2*k**2 + 1/4*k.
k*(k - 1)**2/4
Let f(h) = h**2 - h - 1. Let g(n) = n**2 + n. Let b be (4/6)/(5/30). Suppose 3*x - 3 = 3. Let i(u) = b*f(u) + x*g(u). Find q such that i(q) = 0.
-2/3, 1
Let c(g) be the first derivative of -g**8/5880 + g**7/2940 + g**3 - 3. Let n(i) be the third derivative of c(i). Find t, given that n(t) = 0.
0, 1
Suppose -2 = 5*g + 4*d - 4, 3*g = -4*d - 2. Determine m, given that 4/11*m - 10/11*m**g + 6/11*m**3 + 0 = 0.
0, 2/3, 1
Suppose 4 + 2 = 2*w. Determine x, given that -4*x**w + 2*x**2 - 5*x**2 + 3*x**3 = 0.
-3, 0
Let l(j) be the first derivative of -j**6/720 - j**5/60 - j**4/12 - j**3 + 2. Let b(a) be the third derivative of l(a). Factor b(n).
-(n + 2)**2/2
Let n(o) be the first derivative of 1 + 7/4*o**2 + 3/2*o**3 - o. Solve n(j) = 0 for j.
-1, 2/9
Let y = -5 - -8. Suppose 0 = -y*q + q + 4. Factor 2*w - q*w**2 + 6 - 2 + 0.
-2*(w - 2)*(w + 1)
Let u(w) = w**4 - w**3 - w**2 + w - 1. Let m(j) = -2*j**4 + 9*j**3 - 17*j**2 + 15*j - 4. Let p(t) = 4*m(t) + 4*u(t). Factor p(x).
-4*(x - 5)*(x - 1)**3
Let y = 533/4 + -133. Factor 1/2*r**3 + 0 - y*r - 1/4*r**5 + 0*r**4 + 0*r**2.
-r*(r - 1)**2*(r + 1)**2/4
Let s(t) be the second derivative of -t**6/1620 - t**5/180 - 2*t**3/3 - 3*t. Let q(j) be the second derivative of s(j). Let q(d) = 0. Calculate d.
-3, 0
Suppose -2*q - 4 = 2*x, 2*x - 27 = -4*q - 39. Solve 1/5*o**5 + 0*o**x + 1/5*o + 0 - 2/5*o**3 + 0*o**4 = 0.
-1, 0, 1
Let j(p) be the third derivative of 0 + 6*p**2 + 1/8*p**4 + 1/4*p**3 + 0*p + 1/40*p**5. Factor j(g).
3*(g + 1)**2/2
Find u, given that 324/5*u + 162/5*u**2 + 36/5*u**3 + 3/5*u**4 + 243/5 = 0.
-3
Let t(p) be the third derivative of 2/195*p**6 - 6*p**2 + 2/195*p**5 + 0*p + 1/273*p**7 + 1/2184*p**8 + 0*p**4 + 0*p**3 + 0. Let t(v) = 0. What is v?
-2, -1, 0
Let f = -41 - -41. Solve f*h + 1/3 + 2/3*h**3 - h**2 = 0 for h.
-1/2, 1
Let o(a) = 6*a + 27. Let q be o(-4). Suppose -8/3 + 76/3*r + 48*r**q - 212/3*r**2 = 0. What is r?
2/9, 1/4, 1
Let l = -406/5 + 84. Solve 8/5 + 34/5*n**2 - 32/5*n + 18/5*n**5 + l*n**3 - 42/5*n**4 = 0 for n.
-1, 2/3, 1
Let x(t) = -5*t - 18. Let p be x(-4). Let n(o) be the second derivative of 1/4*o**p + 1/40*o**5 + 1/8*o**4 - 3*o + 0 + 1/4*o**3. Factor n(y).
(y + 1)**3/2
Let f(x) be the third derivative of -x**10/120960 - x**9/20160 - x**8/13440 - x**4/8 - 2*x**2. Let l(z) be the second derivative of f(z). Factor l(h).
-h**3*(h + 1)*(h + 2)/4
Let b(i) be the second derivative of i**6/360 + i**5/90 + i**4/72 + 3*i**2/2 + 2*i. Let j(r) be the first derivative of b(r). Suppose j(t) = 0. Calculate t.
-1, 0
Factor 10*m**3 + 13*m**4 + 12*m**2 - 11*m**4 - 16 - 8*m + 0*m**4.
2*(m - 1)*(m + 2)**3
Factor g**3 - 8*g**2 - 2*g**2 + g**2 + 18 + 7 + 15*g.
(g - 5)**2*(g + 1)
Let v(n) = 5*n**4 + 36*n**3 - 48*n. Let y(c) = -2*c**4 - 12*c**3 + 16*c. Let u(t) = -6*v(t) - 17*y(t). Factor u(r).
4*r*(r - 2)**2*(r + 1)
Let s(z) be the third derivative of -z**5/20 + z**4/8 + z**3 - 3*z**2. Factor s(d).
-3*(d - 2)*(d + 1)
Let j = -47 - -74. Let z(l) = -l - 1. Let k be z(-2). Determine w, given that -9 + 36*w + k + j*w**3 - 55*w**2 + 20*w**2 - 19*w**2 = 0.
2/3
Let z(x) be the first derivative of -3*x**6/2 - 3*x**5 + 3*x**4/4 + 5*x**3 + 3*x**2 - 13. Suppose z(f) = 0. Calculate f.
-1, -2/3, 0, 1
Let v(r) be the third derivative of r**7/105 - 2*r**6/15 + r**5/5 + 10*r**4/3 + 25*r**3/3 - 7*r**2 - 2. Factor v(w).
2*(w - 5)**2*(w + 1)**2
Let l(d) be the first derivative of -4 - 1/12*d**4 - 5/6*d**2 + 2/3*d + 4/9*d**3. Factor l(f).
-(f - 2)*(f - 1)**2/3
Let u(m) = -2*m**4 + 4*m**3 + 18*m**2 + 4*m - 20. Let t(l) = -l**2 - l + 1. Let x(r) = -12*t(r) - u(r). Factor x(w).
2*(w - 2)**2*(w + 1)**2
Let z be 2/17 - (-3)/(-170). Let r(l) be the first derivative of -2/25*l**5 + 0*l**2 - z*l**4 + 0*l + 2/15*l**3 + 1/15*l**6 + 2. Factor r(y).
2*y**2*(y - 1)**2*(y + 1)/5
Let m(q) be the third derivative of q**7/945 - q**6/270 + q**5/270 + 25*q**2. Factor m(n).
2*n**2*(n - 1)**2/9
Let f(m) be the third derivative of m**8/112 - m**7/70 - m**6/40 + m**5/20 + 6*m**2. Factor f(q).
3*q**2*(q - 1)**2*(q + 1)
Let m(w) = w**3 - w**2 - w + 2. Let g be m(2). Let h = g + 2. Let n**2 + h*n**4 + 6*n**3 + 2*n**2 + 2*n**5 - n**2 = 0. What is n?
-1, 0
Let g(n) be the first derivative of -n**4/20 + n**3/15 + 4*n**2/5 - 12*n/5 - 3. Factor g(d).
-(d - 2)**2*(d + 3)/5
Let y be (12/(-384))/(30/(-8)). Let v(u) be the third derivative of -u**2 + 0*u + 0*u**4 - 1/60*u**5 + y*u**6 + 0 + 0*u**3. Determine p, given that v(p) = 0.
0, 1
Let g(i) be the second derivative of -i**8/504 - i**2 + 2*i. Let c(w) be the first derivative of g(w). Factor c(s).
-2*s**5/3
Let a(x) = 6*x**2 - 4*x. Let n(l) be the first derivative of 7*l**3/3 - 5*l**2/2 - 3. Let h(w) = -6*a(w) + 5*n(w). Factor h(q).
-q*(q + 1)
Solve -4/9*c**2 - 8/3 + 20/9*c = 0 for c.
2, 3
Let k be ((896/6)/7)/(2*1). Let u(c) be the second derivative of -16*c**2 + c - 4*c**4 + 4/5*c**5 + 0 - 1/15*c**6 + k*c**3. Find t such that u(t) = 0.
2
Let h(p) = -p + 15. Let j be h(11). Let q(b) = -b**4 + 6*b**3 - b**2 + 4. Let t(g) = -6*g**4 + 30*g**3 - 6*g**2 + 21. Let s(v) = j*t(v) - 21*q(v). Factor s(n).
-3*n**2*(n + 1)**2
Find y such that 9/7*y**4 - 12/7*y**2 + 6/7*y**3 + 3/7 - 6/7*y = 0.
-1, 1/3, 1
Let w be 320/70 + (-12)/21. Suppose 2*r - w*i - 10 = -r, i = -1. What is g in 4/3 + 6*g + 14/3*g**r = 0?
-1, -2/7
What is u in 429 - 429 + 2*u**2 = 0?
0
Let u = 607/4 - 151. Let 1/4*t - 1/4*t**4 + 0 - u*t**2 + 3/4*t**3 = 0. What is t?
0, 1
Let b(r) be the third derivative of r**5/300 + r**4/20 + 3*r**3/10 + 6*r**2. Determine m, given that b(m) = 0.
-3
Find b such that -10*b**2 - 12*b**2 - 68*b**3 + 8*b - 4*b - 6*b - 48*b**4 = 0.
-1, -1/4, -1/6, 0
Let l be (2 + 69/(-30))/((-51)/136). Factor l + 2/5*t - 2/5*t**2.
-2*(t - 2)*(t + 1)/5
Suppose 7*q - 4*q = 9. Let n(p) be the second derivative of 0*p**2 - 1/30*p**5 + 0 - 1/9*p**q + p + 1/9*p**4. Factor n(s).
-2*s*(s - 1)**2/3
Let r(z) = -2*z - 37. Let p be r(-19). Solve -1/4*q**2 - 1/4*q**5 + 5/4*q**3 - p + 1/4*q**4 - 2*q = 0 for q.
-1, 2
Let i be 46/414 + 11/63. Factor -2/7*x**2 + 0*x + i.
-2*(x - 1)*(x + 1)/7
Let n(r) be the third derivative of -r**6/180 + r**5/60 - 5*r**3/3 + r**2. Let d(a) be the first derivative of n(a). Factor d(x).
-2*x*(x - 1)
Suppose 8*a = -8 + 24. Factor 0 + a*c**4 + c**5 + 5/4*c**3 + 0*c + 1/4*c**2.
c**2*(c + 1)*(2*c + 1)**2/4
Factor 2/17*y**3 + 4/17*y**2 + 0*y + 0 - 2/17*y**4.
-2*y**2*(y - 2)*(y + 1)/17
Let f be (-1)/6 - (-561)/1530. Determine r, given that 2/5 - f*r - 1/5*r**2 = 0.
-2, 1
Let d(a) be the second derivative of -a**4/4 + 3*a**3/10 + 3*a**2/5 + 8*a. Determine p, given that d(p) = 0.
-2/5, 1
Suppose 4*d + 0*d = 0. Determine y, given that 9*y + 5 + d*y**2 - y**2 + 4*y**2 + 1 = 0.
-2, -1
Factor 144/5*i + 96/5*i**3 - 48/5 - 27/5*i**4 - 168/5*i**2 + 3/5*i**5.
3*(i - 2)**4*(i - 1)/5
Let z be 2212/(-66) - 8/(-44). Let a = z - -34. Factor -a*q**4 + 1/3*q - 1/3*q**5 + 2/3*q**2 + 0*q**3 + 0.
-q*(q - 1)*(q + 1)**3/3
Let p be 4 + -6 + 5 + 0. Let i(g) be the first derivative of -g + 1/3*g**p + 0*g**2 + 1. Solve i(j) = 0 for j.
-1, 1
Factor 4*s + 0 + 14*s**2 - s**3 - 14*s**4 - 3*s**3 + 0.
-2*s*(s - 1)*(s + 1)*(7*s + 2)
Let s(n) be the second derivative of -n**6/432 - n**5/240 + n**4/72 - n**3/6 + n. Let o(w) be the second derivative of s(w). Factor o(t).
-(t + 1)*(5*t - 2)/6
Suppose -3*v - 14 = -35. Let m(a) be the third derivative of 0*a**3 + 0*a + 16/525*a**v + 11/300*a**6 + 1/75*a**5 + 0*a**4 + 0 + 1/120*a**8 + a**2. Factor m(k).
2*k**2*(k + 1)**2*(7*k + 2)/5
What is k in 0 - 14/11*k + 2/11*k**3 - 12/11*k**2 = 0?
-1, 0, 7
Factor 0*k**2 - 2/7*k**5 - 8/7*k**4 + 0*k - 8/7*k**3 + 0.
-2*k**3*(k + 2)**2/7
Let u(w) be the second derivative of w**7/700 + w**6/900 - w**5/25 - w**4/15 - w**3/6 - 8*w. Let d(g) be the second derivative of u(g). Solve d(s) = 0.
-2, -1/3, 2
Find d such th