 + 0 + 1/30*n**6 - 1/126*n**7 + 3*n + 1/6*n**3 - 1/6*n**2. Factor x(v).
-(v - 1)**4*(v + 1)/3
Let n(k) = 9 + 5*k**3 + k**3 - 6*k**2 - 8*k - 5*k**3. Let g be n(7). Determine p so that -1/3*p - 1/3 + 1/3*p**g + 1/3*p**3 = 0.
-1, 1
Let q(o) be the second derivative of -o**5/20 + o**4/12 - 16*o. Find s such that q(s) = 0.
0, 1
Let w(f) be the first derivative of f**7/105 + f**6/60 + f**2 + 3. Let a(j) be the second derivative of w(j). Determine v so that a(v) = 0.
-1, 0
Let s(n) be the third derivative of 3*n**8/112 + n**7/14 + 7*n**6/120 + n**5/60 - 4*n**2. Factor s(h).
h**2*(h + 1)*(3*h + 1)**2
Let t(d) be the third derivative of -d**8/1176 - 2*d**7/735 + d**6/420 + d**5/105 - d**2. Let t(y) = 0. Calculate y.
-2, -1, 0, 1
Factor 0 + 1/6*k**3 + 0*k - 1/6*k**4 + 0*k**2.
-k**3*(k - 1)/6
Suppose -m = 2*m - 9. Suppose 0*v + 0 + 4/7*v**m - 2/7*v**2 - 2/7*v**4 = 0. Calculate v.
0, 1
Let h be (1 - (-140)/5) + -3. Suppose -5*y - 11 = -h. Suppose -4/5*q**y - 2/5*q + q**2 + 0 + 1/5*q**4 = 0. What is q?
0, 1, 2
Let h(v) be the first derivative of 0*v + 0*v**3 + 0*v**2 - 1/2*v**4 + 4/5*v**5 + 1 - 1/3*v**6. Factor h(f).
-2*f**3*(f - 1)**2
Let q(i) be the second derivative of 0 - 3/2*i**6 - 3/4*i**5 + 0*i**3 - 6*i**2 + 3*i + 9/14*i**7 + 15/4*i**4. Find u such that q(u) = 0.
-2/3, 1
Let q be ((-3)/(-90))/((-1)/(-3)). Let x(b) be the second derivative of 2*b + 0*b**2 + 0 - q*b**5 - 1/3*b**4 + 0*b**3. Factor x(z).
-2*z**2*(z + 2)
Let z(o) be the first derivative of -o**6/120 + 3*o**5/40 + 5*o**3/3 - 5. Let p(v) be the third derivative of z(v). Factor p(x).
-3*x*(x - 3)
Let k(x) = -x**2 + 5*x. Let n(r) = -4*r**2 + 24*r. Let h(d) = -16*k(d) + 3*n(d). Factor h(i).
4*i*(i - 2)
Suppose 1169*t = 1172*t - 15. Factor 0*l - 3/4*l**4 + 0*l**3 + 3/4*l**t + 0*l**2 + 0.
3*l**4*(l - 1)/4
Let c(p) = p + 2. Let n be c(-3). Let q(t) = -136*t - t**2 - 1 + 136*t + t**3. Let y(l) = l**4 + 2*l**3 + 6*l**2 + 2. Let k(o) = n*y(o) - 2*q(o). Factor k(a).
-a**2*(a + 2)**2
Factor b**4 - 1/3 - 2/3*b**3 - 1/3*b**5 + b - 2/3*b**2.
-(b - 1)**4*(b + 1)/3
Let d(y) be the first derivative of y**3/15 - 2*y**2/5 - 20. Factor d(u).
u*(u - 4)/5
Let q(s) be the first derivative of s**4/48 - 7*s**3/36 + 5*s**2/8 - 3*s/4 + 6. Suppose q(c) = 0. What is c?
1, 3
Let o(i) = 22*i**3 - 10*i**2 - 76*i + 48. Let a(p) = 7*p**3 - 3*p**2 - 25*p + 16. Let n(s) = -16*a(s) + 5*o(s). Factor n(y).
-2*(y - 2)*(y - 1)*(y + 4)
Factor 0 - 1/2*s**4 + 1/2*s**2 + 0*s**3 + 1/4*s**5 - 1/4*s.
s*(s - 1)**3*(s + 1)/4
Let w be (6/(-10))/(3 - 64/20). Let n(d) be the third derivative of 0*d**w - 1/60*d**5 + 0 - 3*d**2 + 0*d + 1/24*d**4. Factor n(a).
-a*(a - 1)
Let x(b) be the third derivative of 0 + 1/75*b**5 + 0*b + 0*b**3 - 1/30*b**4 - 2*b**2. Factor x(g).
4*g*(g - 1)/5
Let i(f) = f**2 + 2*f. Let w(t) = t**2 + 2*t. Let b(g) = -2*i(g) + 3*w(g). Solve b(r) = 0 for r.
-2, 0
Let r(a) = -10*a**3 - 3*a**2 + 7*a. Suppose 61 = -5*v - 0*n - 2*n, 4*n = 2*v + 34. Let f(j) = 21*j**3 + 7*j**2 - 15*j. Let h(z) = v*r(z) - 6*f(z). Factor h(c).
c*(c - 1)*(4*c + 1)
Suppose 0*o + 364 = -4*o. Let p be 1/(-3) - o/39. Solve 1/4 + 3/4*u - 1/4*u**p - 3/4*u**3 = 0.
-1, -1/3, 1
Let k(j) = 2*j - 5. Let v = -13 + 18. Let c be k(v). Factor -u**5 + 10*u**4 - 7*u**4 - 2*u**c.
-3*u**4*(u - 1)
Let o = 159/2 + -78. Let b(c) = 3*c**2 + 4*c + 1. Let t be b(-2). Factor -o - 3/2*f**2 + t*f.
-(f - 3)*(3*f - 1)/2
Let n be (8/6)/((-2)/6). Let h(c) = -5*c + 2*c + 3*c + 2*c - 2*c**2 + 1. Let u(j) = 2*j**2 - 2*j. Let w(q) = n*h(q) - 3*u(q). What is g in w(g) = 0?
-1, 2
Let l(r) be the third derivative of -1/240*r**6 - 5*r**2 + 0 + 1/672*r**8 + 0*r**3 + 0*r**4 + 0*r - 1/420*r**7 + 1/120*r**5. Factor l(f).
f**2*(f - 1)**2*(f + 1)/2
Let o = -185/78 - -33/13. Factor -k - o*k**2 - 3/2.
-(k + 3)**2/6
Let g(u) be the first derivative of 2 + 0*u**2 - 1/12*u**4 + 0*u - 1/9*u**3. Factor g(o).
-o**2*(o + 1)/3
Let h(g) be the first derivative of g - 1 + 0*g**2 - 1/135*g**6 - 1/27*g**3 + 1/90*g**5 + 1/54*g**4. Let k(v) be the first derivative of h(v). Factor k(r).
-2*r*(r - 1)**2*(r + 1)/9
Let g = -13 - -25. Let s = -12 + g. Factor 0 + s*n**3 + 1/2*n**2 - 1/2*n**4 + 1/4*n**5 - 1/4*n.
n*(n - 1)**3*(n + 1)/4
Let b(m) be the first derivative of -m**6/15 - 2*m**5/25 + m**4/10 + 2*m**3/15 + 9. Find f such that b(f) = 0.
-1, 0, 1
Let y be 1/(2/4) - 0. Let g(m) = m - 4. Let r be g(6). Factor 2*a**3 - y*a**r + 0*a**3 - a**3 + a**2.
a**2*(a - 1)
Let d(g) be the second derivative of 1/70*g**6 + 0*g**2 + 0 + 0*g**3 + 1/98*g**7 + 0*g**4 - 8*g + 0*g**5. Factor d(u).
3*u**4*(u + 1)/7
Let v(k) be the second derivative of k**5/150 + k**4/45 + k**3/45 - 5*k. Let v(t) = 0. What is t?
-1, 0
Let a(f) be the first derivative of -f**4/4 + f**2/2 - 10. Suppose a(q) = 0. Calculate q.
-1, 0, 1
Let t(x) = -6*x**3 + 12*x**2 - 18*x + 9. Let m(y) = 13*y**3 - 24*y**2 + 37*y - 19. Let i(w) = 3*m(w) + 7*t(w). Solve i(q) = 0 for q.
1, 2
Let k(w) be the third derivative of -w**6/200 + 3*w**5/20 - 15*w**4/8 + 25*w**3/2 - 7*w**2. Determine l, given that k(l) = 0.
5
Let d(a) = a**3 + 4*a**2 - 3. Let h be d(-3). Let c(z) be the first derivative of 8/5*z**5 - 3*z**4 - z**2 - 1/3*z**h + 8/3*z**3 + 0*z - 2. Factor c(j).
-2*j*(j - 1)**4
Let y(v) be the second derivative of -v**6/15 + 3*v**5/10 - v**4/6 - v**3 + 2*v**2 - 23*v. Factor y(l).
-2*(l - 2)*(l - 1)**2*(l + 1)
Suppose -4*a + 15 + 1 = 0. Suppose 0*s = -2*s + a. Factor 1/3*v**3 + 0*v**s - 1/3*v + 0.
v*(v - 1)*(v + 1)/3
Let o(z) be the third derivative of -5*z**2 - 1/540*z**6 + 0*z - 2/135*z**5 + 0 - 2/27*z**3 - 5/108*z**4. What is w in o(w) = 0?
-2, -1
Factor -36 - 7*k - 3*k**3 + 2*k**2 - 23*k**2 - 22*k - 19*k.
-3*(k + 2)**2*(k + 3)
Let w be (-1)/((-3)/(-18))*(-5)/25. Let a(r) be the first derivative of -21/10*r**2 - r**3 - w*r + 2. Let a(b) = 0. What is b?
-1, -2/5
Let j(t) be the second derivative of t**6/6 - 2*t**5 + 10*t**4 - 80*t**3/3 + 40*t**2 + 22*t. Factor j(i).
5*(i - 2)**4
Let o(d) be the second derivative of d**7/105 - d**6/15 + 9*d**5/50 - 7*d**4/30 + 2*d**3/15 - 14*d. Factor o(b).
2*b*(b - 2)*(b - 1)**3/5
Let i(r) be the third derivative of -r**5/40 - r**4/4 - 3*r**3/4 + 31*r**2. Factor i(p).
-3*(p + 1)*(p + 3)/2
Let f = -4 + -3. Let w be 0 - 1/f*6. Factor w*c + 2/7*c**2 + 4/7.
2*(c + 1)*(c + 2)/7
Let w be -1*7/(-70)*4/1. Let x = 354 + -1758/5. Suppose 0 - 8/5*r**2 - 2/5*r**5 - x*r**3 - w*r - 8/5*r**4 = 0. Calculate r.
-1, 0
Let p be ((-2)/(-1))/((-5)/(-20)). Let k = -5 + p. Factor -3*c**2 + 2*c + k*c**3 + 6*c**2 + 3*c**2 + c.
3*c*(c + 1)**2
Suppose h = -3*h. Let o(r) = -r**3 - r**2 - r. Let u be o(h). Factor 2 + 0*g + g**2 + 3*g + u*g.
(g + 1)*(g + 2)
Let i(t) be the second derivative of 5*t + 0 + 5/3*t**4 - 18*t**2 + 1/5*t**5 + 2*t**3. Factor i(v).
4*(v - 1)*(v + 3)**2
Factor 0 + 1/3*v**2 - 2/3*v.
v*(v - 2)/3
Let u(b) be the first derivative of -4/5*b**2 - 4/5*b**3 - 2/25*b**5 - 2/5*b**4 - 2 - 2/5*b. Suppose u(v) = 0. Calculate v.
-1
Let j be -6 + 12 + 9/(-4). Factor -3/4*o**3 - j*o + 3*o**2 + 3/2.
-3*(o - 2)*(o - 1)**2/4
Let a(g) be the first derivative of 2*g**5/35 - 10. Factor a(h).
2*h**4/7
Factor -1/7*q**3 - 1/7*q**2 + 2/7*q + 0.
-q*(q - 1)*(q + 2)/7
Suppose -5*c = 7 - 17. Suppose 0*h = -c*h. Factor h + 4/7*b**2 - 2/7*b**3 - 2/7*b.
-2*b*(b - 1)**2/7
Let s(x) be the second derivative of 2/3*x**3 + 1/15*x**6 + 0*x**4 - 1/5*x**5 + 0 + 2*x - x**2. Find l, given that s(l) = 0.
-1, 1
Let r(u) be the first derivative of -u**2 - 1/2*u**3 - 1/12*u**4 + 2 - 4*u. Let d(p) be the first derivative of r(p). Suppose d(a) = 0. Calculate a.
-2, -1
Factor -2/5*u**2 - 6/5*u**3 + 2/5 + 6/5*u.
-2*(u - 1)*(u + 1)*(3*u + 1)/5
Let m = -14 + 16. Let r be (-16)/(-12)*1/2. Factor r + 2/3*q**3 + 2*q + 2*q**m.
2*(q + 1)**3/3
Solve 1/3*m**4 + m**3 + 1/3*m + m**2 + 0 = 0 for m.
-1, 0
Suppose 0 = k - 13 - 0. Factor -k*r**2 - r**3 + 16*r**2 - 3*r + r.
-r*(r - 2)*(r - 1)
Factor -24/7*p**3 - 48/7*p**2 - 32/7*p + 0 - 4/7*p**4.
-4*p*(p + 2)**3/7
What is h in 4*h - 2*h**4 - h**3 + 162 - 160 - 3*h**3 = 0?
-1, 1
Let g(d) = 2*d**3 + 3*d**2 + d + 3. Let n(v) = v**2 + v - 1. Let m(i) = g(i) + 3*n(i). Factor m(l).
2*l*(l + 1)*(l + 2)
Let v(c) = -c - 4. Let q be v(-7). Let t be (-1 + q)*(-10)/(-90). Determine a so that -4/9*a**3 - t*a**2 + 4/9*a + 2/9*a**4 + 0 = 0.
-1, 0, 1, 2
Let i be 0 - 0 