et c(l) be the first derivative of l**6/2 + 3*l**5/5 - 3*l**4/2 - 2*l**3 + 3*l**2/2 + 3*l - 5. Factor c(o).
3*(o - 1)**2*(o + 1)**3
Let w be (1 - (-382)/(-192)) + 1. Let i(h) be the third derivative of -w*h**4 - 3*h**2 + 0 + 1/240*h**5 + 0*h**3 + 0*h. Factor i(m).
m*(m - 1)/4
Factor 16 - 9*l - 17*l + 2*l - 6*l**2 - 2*l**3 + 18*l**2.
-2*(l - 2)**3
Let h(i) be the third derivative of i**6/60 - i**5/10 - 4*i**2. Find z such that h(z) = 0.
0, 3
Let o(b) be the first derivative of 4*b**3/3 - 16*b**2 + 64*b + 2. Factor o(q).
4*(q - 4)**2
Let u(l) be the third derivative of -l**8/2688 + l**7/1680 + l**6/320 - l**5/96 + l**4/96 - 19*l**2. Let u(i) = 0. What is i?
-2, 0, 1
Let i(c) be the first derivative of -c**6/90 + c**5/15 - 8*c**3/9 - c**2/2 + 3. Let h(r) be the second derivative of i(r). What is z in h(z) = 0?
-1, 2
Let j(z) be the second derivative of 1/105*z**7 + 3/50*z**5 + 0*z**3 - 1/25*z**6 - 1/30*z**4 + 0*z**2 + 0 - 4*z. Factor j(b).
2*b**2*(b - 1)**3/5
Let i(y) be the first derivative of y**7/630 - y**6/360 - y**5/40 - y**4/36 + y**3 + 1. Let c(q) be the third derivative of i(q). Solve c(u) = 0 for u.
-1, -1/4, 2
Let y be ((-24)/(-32))/(2/8). Let c(m) be the first derivative of -m**2 + 1 + 16*m**y - 8*m**4 + 2*m - 8*m**2 - 1 + 3. Factor c(t).
-2*(t - 1)*(4*t - 1)**2
Suppose 15 = 54*j - 49*j. Let q be (6/(-2))/(6/(-4)). Factor -2/7 + 4/7*l + 0*l**q - 4/7*l**j + 2/7*l**4.
2*(l - 1)**3*(l + 1)/7
Let f be (2/6)/(4/36). Factor -8*s + 11*s + 2*s**3 + 6*s**2 + s**f.
3*s*(s + 1)**2
Let i(x) = 18*x**2 - 18*x - 4. Let o(r) = -18*r**2 + 17*r + 4. Let k(d) = 3*i(d) + 4*o(d). Factor k(w).
-2*(w - 1)*(9*w + 2)
Let z(b) = -b**3 - 9*b**2 - 11*b - 9. Let x be z(-8). Factor -3*j + 6*j**2 - x*j**3 + 3*j + 9*j**4.
3*j**2*(j - 1)*(3*j - 2)
Let c(n) be the third derivative of 1/8*n**4 + 0*n + 0 - 4*n**2 - n**3 + 3/20*n**5. What is w in c(w) = 0?
-1, 2/3
What is m in 331*m**3 - 660*m**3 + 5292*m + 333*m**3 - 252*m**2 - 37044 = 0?
21
Factor 2/3*k + 0 + 2/3*k**2.
2*k*(k + 1)/3
Let j(s) be the third derivative of -s**7/70 + s**6/20 - s**4/4 + s**3/2 - 8*s**2. Factor j(a).
-3*(a - 1)**3*(a + 1)
Factor 6*q**4 + 2*q + q**4 - 6*q**4 + 4*q**3 + 5*q**2.
q*(q + 1)**2*(q + 2)
Let c(z) be the second derivative of -z**5/70 - z**4/42 + z**3/21 + z**2/7 + 8*z. Factor c(l).
-2*(l - 1)*(l + 1)**2/7
Factor 0*g - 2/11*g**3 + 0 - 2/11*g**4 + 0*g**2.
-2*g**3*(g + 1)/11
Suppose -4*r - 37 + 2 = -3*z, 4*r + 30 = 2*z. Let g(b) = -13*b**2 - 19*b + 5. Let h(o) = 32*o**2 + 48*o - 12. Let f(q) = z*h(q) + 12*g(q). Solve f(p) = 0 for p.
-3, 0
Let x(d) be the second derivative of -d**6/150 + d**5/100 + d**4/60 - d**3/30 - 3*d. Factor x(i).
-i*(i - 1)**2*(i + 1)/5
Suppose 126/11*m**3 + 102/11*m**4 + 18/11*m**5 + 0*m - 54/11*m**2 + 0 = 0. What is m?
-3, 0, 1/3
Let c(n) be the first derivative of n**3/3 - 2*n**2 + 3*n - 5. Find i such that c(i) = 0.
1, 3
Let s(w) be the first derivative of -2 - 7/9*w**3 - 5/6*w**2 + 2/3*w. Factor s(t).
-(t + 1)*(7*t - 2)/3
Let i(y) be the third derivative of 3*y**5/80 - 11*y**4/32 + 3*y**3/4 - 10*y**2. Suppose i(j) = 0. Calculate j.
2/3, 3
Let f(d) = -d**3 + 5*d**2 + 2. Let g be f(5). Let n be (g - (-9)/(-6))*0. Factor -2*t**4 + 0*t**3 + n*t**4 - 2*t**3.
-2*t**3*(t + 1)
Suppose -8*p + 36 = 4. Let m(y) be the second derivative of -2*y - 3/2*y**3 + 1/4*y**p + 0 + 3*y**2. Factor m(a).
3*(a - 2)*(a - 1)
Let l be 48/9 - (-11)/(-33). Let t = -6 - -10. Find c, given that 0 + 0*c**3 + 2/3*c**2 - 2*c**t + 0*c + 4/3*c**l = 0.
-1/2, 0, 1
Let v be -16 - (4 + -8)/(-1). Let s be ((-27)/(-6))/(v/(-24)). Factor -81/5 - 3/5*n**3 - s*n**2 - 81/5*n.
-3*(n + 3)**3/5
Suppose 6/7*j**3 + 0 - 4/7*j - 2/7*j**2 = 0. Calculate j.
-2/3, 0, 1
Let h(s) be the first derivative of s**4/18 + 10*s**3/27 + 2*s**2/3 + 14. Factor h(b).
2*b*(b + 2)*(b + 3)/9
Let a = -7 + 10. Let k = 17 + -14. Factor -g**5 + k*g**4 - g**a - 3*g**3 + g**3 + g**2.
-g**2*(g - 1)**3
Let g(o) be the second derivative of -147*o**5/20 + 63*o**4/2 - 30*o**3 + 12*o**2 - 12*o. Suppose g(q) = 0. Calculate q.
2/7, 2
Determine t, given that 0 + 8/9*t**2 + 8/9*t + 4/9*t**4 - 14/9*t**3 = 0.
-1/2, 0, 2
Suppose 4*x = j + 6, 10*j + 20 = 5*x + 15*j. Determine h, given that 8/7*h + 6/7*h**x + 2/7 = 0.
-1, -1/3
Let n(c) be the first derivative of c**6/18 - 2*c**5/5 + 13*c**4/12 - 4*c**3/3 + 2*c**2/3 + 11. Factor n(r).
r*(r - 2)**2*(r - 1)**2/3
Let u = 15 + -6. Suppose 2*s + u + 4 = 5*d, -5*d - 3*s + 18 = 0. Factor r**4 + 4 + 12*r + 2*r**d + 0*r**2 + 13*r**2 + 4*r**3.
(r + 1)**2*(r + 2)**2
Let w(o) be the second derivative of -o**4/132 - o**3/66 + 3*o**2/11 + o. Solve w(g) = 0.
-3, 2
Let -6/7*y**4 + 2/7*y**5 + 0*y - 2/7*y**2 + 6/7*y**3 + 0 = 0. Calculate y.
0, 1
Let z(k) be the second derivative of k**5/90 - k**4/54 - 2*k**3/27 + 3*k. Find l such that z(l) = 0.
-1, 0, 2
Let a(v) be the first derivative of -v**6/6 - 4*v**5/5 - v**4 + 2. Factor a(r).
-r**3*(r + 2)**2
Suppose -4*j - 23 = -5*w, -2*w + 4*w - 14 = 4*j. Factor 2/5*c**w + 0 + 0*c**2 - 2/5*c.
2*c*(c - 1)*(c + 1)/5
Let i(j) be the third derivative of -j**7/840 + j**6/240 + j**4/4 - 5*j**2. Let g(m) be the second derivative of i(m). Factor g(o).
-3*o*(o - 1)
Factor -7 + 28*o**2 - 13*o - 3*o + 1 + 3*o.
(4*o - 3)*(7*o + 2)
Let v(i) be the third derivative of i**7/525 - i**5/25 - 2*i**4/15 - i**3/5 + 14*i**2. Factor v(h).
2*(h - 3)*(h + 1)**3/5
Suppose 0 = a + 5*a. Let b(q) be the second derivative of 2*q + 0 - 1/36*q**4 - 1/30*q**6 + a*q**2 + 0*q**3 - 1/20*q**5 - 1/126*q**7. What is f in b(f) = 0?
-1, 0
Let i(j) be the first derivative of -j**7/2240 - j**6/2880 + j**5/480 + 3*j**3 + 3. Let y(x) be the third derivative of i(x). Factor y(g).
-g*(g + 1)*(3*g - 2)/8
Let y = -91/3 + 30. Let i = y + 2/3. Factor -i*k**2 - 1/3*k + 0.
-k*(k + 1)/3
What is q in 3*q**4 - 5*q**3 - 2*q**5 - 4*q**4 + 9*q**4 + 11*q**3 - 36*q**2 = 0?
-2, 0, 3
Let l(q) be the second derivative of q**5/110 + 5*q**4/66 + 8*q**3/33 + 4*q**2/11 + 18*q. Let l(m) = 0. What is m?
-2, -1
Find c, given that -1/4*c**2 + 3/2*c - 5/4 = 0.
1, 5
Suppose 3*u = 3*g - 2*u - 10, -4*u = g + 8. Factor 2/5*s**3 + 0*s**4 + g*s**2 - 2/5*s**5 + 0 + 0*s.
-2*s**3*(s - 1)*(s + 1)/5
Suppose 143 = -8*y + 167. Factor 0 + 3/4*n**y + 1/4*n - 1/4*n**4 - 3/4*n**2.
-n*(n - 1)**3/4
Let g = 40066/5565 - -2/5565. Let h be ((-2)/2)/(-1)*2. Factor 4/5 - g*r**2 - h*r.
-2*(2*r + 1)*(9*r - 2)/5
Let c(u) = u**3 + u**2 - 1. Let y(k) = 4*k**4 - 13*k**3 + 3*k**2 + 12*k - 7. Let i(g) = -c(g) - y(g). Solve i(s) = 0 for s.
-1, 1, 2
Let q(p) be the second derivative of -p**6/20 + p**5/40 + p**4/12 + 11*p. Find x, given that q(x) = 0.
-2/3, 0, 1
Let k be (-8)/(-6)*(-9)/(-6). Solve 1 + 2*s**2 + 1 + 0*s**k + 4*s + 0 = 0 for s.
-1
Let f(u) = -u**3 + 12*u**2 - 12*u + 14. Let s be f(11). Suppose 3*t - 2*y + s = 3*y, 5*y = 5*t - 5. Factor 0*d**2 - 2/5*d + 4/5*d**3 - 2/5*d**5 + 0 + 0*d**t.
-2*d*(d - 1)**2*(d + 1)**2/5
Let m = -4 - -8. Let n be 1*m - (4 - 3). Solve d**4 - 4*d**2 - 2*d + 5*d**4 + 4*d**n - 2 + 2*d**5 - 3*d - d = 0.
-1, 1
Let n(f) be the first derivative of 2*f**3/21 + 4*f**2/7 - 10*f/7 - 22. Factor n(m).
2*(m - 1)*(m + 5)/7
Let r(k) = -11*k**2 + 27*k**3 - 2*k - 19*k**4 - 4*k - 5*k. Let h(f) = -5*f**4 + 7*f**3 - 3*f**2 - 3*f. Let m(p) = -22*h(p) + 6*r(p). Factor m(o).
-4*o**3*(o - 2)
Let k(g) be the second derivative of -g**6/6 + 7*g**5 - 245*g**4/2 + 3430*g**3/3 - 12005*g**2/2 + 16*g. Let k(r) = 0. What is r?
7
Let n be -1 + 2 - (-33)/(-33). Factor -2/3*w**2 + 0 - 4/3*w**3 + n*w - 2/3*w**4.
-2*w**2*(w + 1)**2/3
Suppose -o = 2*o. Let b be o + 3 + -6 + 5. Suppose a**2 + b*a**2 + 17*a - 18*a - 2 = 0. What is a?
-2/3, 1
Let s(z) be the second derivative of z**5/120 - z**3/12 + 3*z**2/2 + 3*z. Let k(q) be the first derivative of s(q). Let k(a) = 0. Calculate a.
-1, 1
Let n(a) = 3*a**4 - a**3 - 2*a**2 + 5. Let i(l) = l**4 - l**3 + 1. Let d(h) = 10*i(h) - 2*n(h). Solve d(z) = 0 for z.
0, 1
Determine n so that -79*n**3 - 48*n**5 - 168*n**4 - 3*n - 57*n**2 - 13*n**3 - 3*n - 79*n**3 = 0.
-2, -1, -1/4, 0
Let o(f) be the third derivative of 1/60*f**6 + 0*f**3 + 1/210*f**7 + 0*f - 4*f**2 + 0 + 1/2016*f**8 + 1/45*f**5 + 0*f**4. Factor o(j).
j**2*(j + 2)**3/6
Factor -2/3*q**2 - 2/3 - 4/3*q.
-2*(q + 1)**2/3
Let g be (-687)/(-494) - (-8)/(-52). Let y = g - -24/19. Let 9/2*p*