
Let m(l) = l**3 + 3*l + 4. Let h(p) = -p - 1. Let j(d) = -4*h(d) - m(d). Factor j(u).
-u*(u - 1)*(u + 1)
Let r(y) = -15*y - 358. Let t be r(-24). Factor -4/3 + 22/3*d - 6*d**t.
-2*(d - 1)*(9*d - 2)/3
Let f(y) be the first derivative of 3 + 1/2*y**6 + 0*y + y**3 + 0*y**2 - 3/4*y**4 - 3/5*y**5. Solve f(i) = 0 for i.
-1, 0, 1
Let n(a) be the first derivative of 2*a**6/15 + 3*a**5/25 - 9*a**4/20 + 2*a**3/15 - 33. What is b in n(b) = 0?
-2, 0, 1/4, 1
Let c(k) be the first derivative of 108*k**3 + 36*k**2 + 4*k - 38. Let c(f) = 0. Calculate f.
-1/9
Let u(z) be the first derivative of -3/10*z**4 + 1/5*z**3 + 2 + 0*z**2 + 1/5*z**6 + 0*z - 3/25*z**5. Let u(w) = 0. Calculate w.
-1, 0, 1/2, 1
Suppose l - 28 = -5*y, 4*l + l + 16 = y. Factor 14*f**2 - 4*f**3 + y - 6 + 4 - 14*f.
-2*(f - 2)*(f - 1)*(2*f - 1)
Factor -9/5*y**2 + 0 - 3/5*y**3 + 12/5*y.
-3*y*(y - 1)*(y + 4)/5
Let w(x) be the second derivative of -x**6/120 + 3*x**5/80 - x**4/16 + x**3/24 + 11*x. Factor w(h).
-h*(h - 1)**3/4
Let j = 400/1881 - -2/209. Let b(q) be the first derivative of 1/15*q**5 + 4 - j*q**3 + 0*q + 0*q**2 + 1/12*q**4. What is s in b(s) = 0?
-2, 0, 1
Let l(m) = 5*m**3 + 17*m**2 + 8*m. Let v(c) = 25*c**3 + 86*c**2 + 39*c. Let q(y) = 11*l(y) - 2*v(y). Factor q(z).
5*z*(z + 1)*(z + 2)
Let y be 3/((-2)/(-4)*2). Suppose -3*j - 3*s = -j - 3, -j - y*s + 3 = 0. Factor 1/4*c**3 + 0*c + 1/4*c**5 + j*c**2 + 0 + 1/2*c**4.
c**3*(c + 1)**2/4
Let i = -3115/9 + 349. Let s = -164/63 + i. Suppose 0 - s*q**2 + 2/7*q = 0. What is q?
0, 1
Find z, given that 3/4*z**3 + 3/4*z + 3/2*z**2 + 0 = 0.
-1, 0
Factor 2/3*f**5 + 0*f**2 - 2/3*f**3 + 0 + 0*f**4 + 0*f.
2*f**3*(f - 1)*(f + 1)/3
Factor -6*l**2 + l - 8*l**3 + 18*l**2 + 1 - 7*l.
-(2*l - 1)**3
Let s(u) = -u**2 - 6*u + 10. Let q be s(-7). Factor q*t**2 + 3*t - t**2 - t.
2*t*(t + 1)
Let k(c) be the first derivative of -2*c**3/9 + c**2/3 + 4*c/3 - 29. Find v, given that k(v) = 0.
-1, 2
Let l(k) be the second derivative of -1/6*k**5 + 0 + 2/27*k**3 + 3*k - 1/27*k**7 + 0*k**2 + 1/54*k**4 + 19/135*k**6. Factor l(n).
-2*n*(n - 1)**3*(7*n + 2)/9
Let m(q) be the first derivative of 16/5*q**2 - 4/3*q**3 + 16/5*q + 5. Factor m(w).
-4*(w - 2)*(5*w + 2)/5
Let z(v) be the second derivative of -v**6/105 + v**5/14 - v**4/6 + v**3/7 - 5*v. Factor z(j).
-2*j*(j - 3)*(j - 1)**2/7
Let q(s) be the third derivative of s**4/24 + s**3/6 - s**2. Let w be q(1). Factor 4/9*p - 2/9*p**w + 0.
-2*p*(p - 2)/9
Let u = -363 - -2543/7. Determine y, given that -12/7*y + 18/7 + u*y**2 = 0.
3
Let f(t) be the second derivative of -1/120*t**6 + 0*t**2 - 3*t + 1/24*t**3 + 1/48*t**4 + 0 - 1/80*t**5. Determine w, given that f(w) = 0.
-1, 0, 1
Factor 3*j**2 - 9*j + 7*j + j**2 - 2*j**2.
2*j*(j - 1)
Let y = -47968/45 + 1066. Let x(d) be the first derivative of -y*d**5 + 1/18*d**4 + 0*d**3 + 1 + 0*d**2 + 0*d. Solve x(f) = 0.
0, 1
Let l(q) be the first derivative of -q**5/2 + 7*q**4/8 - q**3/3 - 6. Find m, given that l(m) = 0.
0, 2/5, 1
Let s(f) be the second derivative of -5*f**5/2 - 95*f**4/6 - 64*f**3/3 - 12*f**2 + 18*f. Factor s(g).
-2*(g + 3)*(5*g + 2)**2
Let b(y) = 15*y**2 - 15*y - 12. Let v(n) = -n**2 + n + 1. Let o(h) = -b(h) - 18*v(h). Factor o(m).
3*(m - 2)*(m + 1)
Let v(f) be the third derivative of f**5/100 + f**4/40 - 5*f**2. Factor v(b).
3*b*(b + 1)/5
Let c(w) be the first derivative of -w**8/2016 - w**7/315 - w**6/144 - w**5/180 - w**2/2 - 3. Let u(l) be the second derivative of c(l). Factor u(y).
-y**2*(y + 1)**2*(y + 2)/6
Let y(v) = 1. Let l = 10 + -2. Suppose 4*g - l = -0*g. Let m(c) = c**2 + 4*c + 6. Let o(s) = g*y(s) - m(s). Factor o(f).
-(f + 2)**2
Let b(a) be the second derivative of 0*a**2 + 0*a**3 + 1/42*a**7 + 0 - 4*a + 1/30*a**6 + 0*a**4 + 0*a**5. Factor b(t).
t**4*(t + 1)
Let o(u) be the second derivative of 2*u**7/189 + 31*u**6/135 + 88*u**5/45 + 208*u**4/27 + 256*u**3/27 - 256*u**2/9 + 6*u - 1. Let o(l) = 0. What is l?
-4, 1/2
Let o(a) = a - 2. Let k be o(5). Let u be 5 + 1*(-2)/6. Determine f so that -26/3*f**4 - u*f**k + 0 + 2/3*f - 4*f**5 + 2/3*f**2 = 0.
-1, -1/2, 0, 1/3
Suppose 0 = 5*p - 10. Suppose 2*j = 3*j - 2. Factor 3 + 3*x**p - j*x - 2*x**2 + 2 - 4.
(x - 1)**2
Let u(p) = p**2 - 3*p. Let y be u(3). Let o(z) be the second derivative of -1/39*z**3 + y*z**4 + 0 + z + 1/130*z**5 + 0*z**2. Find n, given that o(n) = 0.
-1, 0, 1
Let s(b) be the second derivative of -b**6/6 + b**5/4 + 5*b**4/3 - 10*b**3/3 + 29*b. Factor s(g).
-5*g*(g - 2)*(g - 1)*(g + 2)
Let q(s) be the second derivative of 3*s**5/80 - 5*s**4/16 + s**3/4 + 3*s**2 - 18*s. Find v, given that q(v) = 0.
-1, 2, 4
Let l be (-2 - (-40)/22)/(102/(-374)). Suppose 1/3*d**5 + 0*d**2 + 0 + 1/3*d**3 + 0*d + l*d**4 = 0. Calculate d.
-1, 0
Let r(w) = -3*w**4 + w**3 + w**2 - 29*w - 16. Let v(b) = b**4 + b**3 - b**2 + b. Let x = -5 + 6. Let l(q) = x*r(q) + 5*v(q). Factor l(t).
2*(t - 2)*(t + 1)*(t + 2)**2
Let g(r) = 6*r**2 - 21*r + 11. Let w(a) = 3*a**2 - 4*a**2 + a - 2 + 3*a. Suppose 0 = 5*b - 10. Let i(f) = b*g(f) + 11*w(f). Factor i(x).
x*(x + 2)
Let y(k) be the first derivative of -k**4/12 - 5*k**3/9 - 4*k**2/3 - 4*k/3 - 48. Factor y(g).
-(g + 1)*(g + 2)**2/3
Let v(r) be the third derivative of -r**8/672 + r**7/105 - r**6/48 + r**5/60 - 27*r**2. Factor v(n).
-n**2*(n - 2)*(n - 1)**2/2
Suppose 25 = 3*a + 2*a. Suppose 5*c + x = -3, 3*x + 1 + 8 = a*c. Factor c + 2/7*g**2 + 0*g.
2*g**2/7
Let y(p) be the second derivative of -p**5/160 + p**4/32 + p**3/48 - 3*p**2/16 + 2*p. Solve y(b) = 0 for b.
-1, 1, 3
Let u(d) be the third derivative of -d**6/60 - d**5/10 - d**4/4 - d**3/3 - d**2. Factor u(f).
-2*(f + 1)**3
Let i = 492 - 7378/15. Factor -2/5*j - 4/15 - i*j**2.
-2*(j + 1)*(j + 2)/15
Let 18*a**3 - 9*a**4 + a**4 + a**4 + 8*a + a**2 + a**5 - 21*a**2 = 0. Calculate a.
0, 1, 2
Let t be -5 + 6 + 3 + -4. Determine j, given that t*j**4 + 0*j + 0 - 3/2*j**5 + 0*j**2 + 3/2*j**3 = 0.
-1, 0, 1
Let o(m) be the second derivative of -1/2*m**2 + 2*m - 1/3*m**3 - 1/12*m**4 + 0. Factor o(h).
-(h + 1)**2
Let c = -40 - -43. Let i(b) be the first derivative of 3 + 3*b**2 + 2/3*b**c + 4*b. What is r in i(r) = 0?
-2, -1
Suppose 0*h - 9 = d - 4*h, -h + 6 = d. Suppose 2*q - 4*a - 16 = -0*a, -2*q - 11 = 5*a. Factor 2*p**2 - q*p**2 - d*p**2 + 3*p.
-3*p*(p - 1)
Let d(h) be the first derivative of -h**8/2240 - h**7/280 - h**6/96 - h**5/80 - 2*h**3/3 + 3. Let j(q) be the third derivative of d(q). Solve j(c) = 0 for c.
-2, -1, 0
Factor 3/2*f**3 + 0 + 1/4*f**4 + 9/4*f**2 + 0*f.
f**2*(f + 3)**2/4
Suppose -f = -4*f - 24. Let o = -7 - f. Solve -29*j**2 + 30*j**2 - o + j + 1 = 0.
-1, 0
Let -6*v - v**4 + 6*v**3 + 0*v**4 + 3 + 0 - 2*v**4 = 0. Calculate v.
-1, 1
Let 0*r - 2*r - 6*r**2 - 2*r**3 - 2*r = 0. What is r?
-2, -1, 0
Suppose -t + 2*m - 6 = 0, 15 = 6*m - 3*m. Suppose t - 5*k + k**2 + k**2 + 0 + 11*k = 0. What is k?
-2, -1
Let c(t) be the first derivative of 0*t**2 + 1 + 1/50*t**5 + 0*t**3 - t + 0*t**4. Let w(k) be the first derivative of c(k). Let w(i) = 0. What is i?
0
Let d(c) be the second derivative of -c**5/15 + 4*c**4/9 - 10*c**3/9 + 4*c**2/3 - 10*c. Solve d(l) = 0 for l.
1, 2
Let n(w) be the second derivative of w**4/66 - 4*w. Find g, given that n(g) = 0.
0
Factor 3*j**3 + 2*j**4 - 3*j + 2*j**2 + 5*j**4 - 3*j**2 - 6*j**4.
j*(j - 1)*(j + 1)*(j + 3)
Let i(u) = -u**3 + 8*u**2 - 7*u + 5. Let s be i(7). Let x be (1 - 2)*3 + s. Let r**x - 1/3*r**3 - 2/3*r + 0 = 0. Calculate r.
0, 1, 2
Let g(j) = 4*j**5 - 8*j**4 + j**3 + 3*j**2 + 5*j. Let f(k) = 6*k**5 - 12*k**4 + 2*k**3 + 4*k**2 + 8*k. Let z(a) = 5*f(a) - 8*g(a). Solve z(v) = 0 for v.
-1, 0, 1, 2
Suppose 20 = 5*k + 2*o + 7, -5*k + 17 = -2*o. Factor 0*n**k + 3/4 + 3/2*n**2 + 2*n - 1/4*n**4.
-(n - 3)*(n + 1)**3/4
Let x(c) be the first derivative of c**7/420 + c**6/90 - c**5/60 - c**4/6 + 2*c**3/3 - 3. Let i(v) be the third derivative of x(v). Factor i(s).
2*(s - 1)*(s + 1)*(s + 2)
Let i(a) = -a**3 + 7*a**2 - 6*a - 5. Let p(n) = -n**3 + 8*n**2 - 7*n - 6. Let l be (-3)/(-9)*1*15. Let r(k) = l*p(k) - 6*i(k). Factor r(u).
u*(u - 1)**2
Let k be (-56)/(-5) + (-5 - 3). Factor 32/5 + k*f + 2/5*f**2.
2*(f + 4)**2/5
Let s(p) be the first derivative of -p**6/12 + p**5/5 + p**4/8 - p**3/3 - 5. Determine m so that s(m) = 0.
-1, 0, 1, 2
Let w(d) be the second derivative of d**4/21 - 32*d**3/21 + 128*d**2/7 - 1