et r(i) be the first derivative of i**6 - 16*i**5/5 + 3*i**4 - i**2 - 32. Factor r(z).
2*z*(z - 1)**3*(3*z + 1)
Let u(r) be the first derivative of -r**6/225 - r**5/50 - r**4/45 + 2*r + 8. Let q(b) be the first derivative of u(b). Factor q(j).
-2*j**2*(j + 1)*(j + 2)/15
Factor 0 + 2/15*p**4 + 0*p + 4/15*p**3 + 2/15*p**2.
2*p**2*(p + 1)**2/15
Suppose -14*n = 4*n. Factor 0*u - 6/5*u**3 + n - 2/5*u**2 - 4/5*u**4.
-2*u**2*(u + 1)*(2*u + 1)/5
Let q(j) be the first derivative of 1/3*j**6 + 3 + 0*j**2 - 2/5*j**5 + 0*j - 1/2*j**4 + 2/3*j**3. Find k such that q(k) = 0.
-1, 0, 1
Let t(p) be the third derivative of -p**8/16800 + p**6/1800 + p**4/12 + p**2. Let d(i) be the second derivative of t(i). Find y, given that d(y) = 0.
-1, 0, 1
Let i(p) be the third derivative of 1/9*p**3 - p**2 - 7/60*p**5 + 0 + 1/72*p**4 + 0*p. Factor i(g).
-(3*g - 1)*(7*g + 2)/3
Suppose 2*m - 2 = 0, 4*u + 2*m - 20 + 2 = 0. Suppose -u*y = -3*y - 2. Factor 2/7 + 6/7*p**y + 8/7*p.
2*(p + 1)*(3*p + 1)/7
Let i be (82/(-6))/((-14)/(-42)). Let z = -122/3 - i. Let 1/3*s**4 - 2/3*s + 0 - z*s**2 + 2/3*s**3 = 0. What is s?
-2, -1, 0, 1
Let x(m) be the first derivative of -m**8/10080 + m**7/5040 + m**6/2160 - m**5/720 - 4*m**3/3 + 6. Let q(z) be the third derivative of x(z). Factor q(k).
-k*(k - 1)**2*(k + 1)/6
Suppose 2*w + 5*l + 25 = 0, 2*w - 20 = -l + 5*l. Factor -d**2 - 3*d + 0*d - 2*d**2 + w*d**2.
-3*d*(d + 1)
Let b(m) be the second derivative of 0 - 2/9*m**6 - 32/3*m**2 - 1/63*m**7 - 40/9*m**4 - 3*m - 4/3*m**5 - 80/9*m**3. Factor b(o).
-2*(o + 2)**5/3
Let o(n) be the first derivative of 2*n**6/21 + 4*n**5/35 - 3*n**4/7 - 20*n**3/21 - 4*n**2/7 + 25. Suppose o(h) = 0. Calculate h.
-1, 0, 2
Let h(a) be the second derivative of 4*a - 8/3*a**3 + 0 - 39/10*a**4 - 4/5*a**2 - 81/50*a**5. Factor h(b).
-2*(b + 1)*(9*b + 2)**2/5
Let l(u) = -u**2 + 8*u. Suppose 5 = 2*s + 41. Let x(b) = -9*b + 0*b + 8*b. Let k(w) = s*x(w) - 2*l(w). Factor k(y).
2*y*(y + 1)
Let s(c) be the second derivative of -c**7/525 + c**6/150 - c**5/150 - 3*c**2/2 - c. Let o(d) be the first derivative of s(d). Suppose o(k) = 0. Calculate k.
0, 1
Let m(a) be the first derivative of 2*a**6 + 8*a**5 + 4*a**4 - 32*a**3/3 + 9. Factor m(l).
4*l**2*(l + 2)**2*(3*l - 2)
Let y(c) be the third derivative of -c**6/300 - c**5/75 + c**2. Determine d so that y(d) = 0.
-2, 0
Factor -4*n**2 - 1/4 + 2*n.
-(4*n - 1)**2/4
Let x be -3 + 82 - 0/(-2). Let b = -235/3 + x. Determine s, given that -1/3*s**3 + 0 - 1/3*s - b*s**2 = 0.
-1, 0
Let l be 16/3 - (-15)/(-5). What is z in -l*z**2 - 3/2*z**4 - z - 1/6 - 8/3*z**3 - 1/3*z**5 = 0?
-1, -1/2
Let t(n) be the first derivative of -6 + 1/6*n**2 + 0*n + 1/12*n**4 + 2/9*n**3. Suppose t(a) = 0. Calculate a.
-1, 0
Let h(w) be the second derivative of 0 - 1/3*w**3 - 1/6*w**4 + 8*w + 0*w**2. Suppose h(o) = 0. What is o?
-1, 0
Let 1/4*h**3 - h - 1 + 1/4*h**2 = 0. Calculate h.
-2, -1, 2
Determine x so that 8/9*x**5 - 2/9*x**3 - 2/3*x + 14/9*x**4 - 14/9*x**2 + 0 = 0.
-1, -3/4, 0, 1
Let m be (5/30)/((-3)/(-30)). Let q(p) be the first derivative of -3 + 0*p + 7/6*p**6 - p**5 + m*p**3 - 9/4*p**4 + p**2. Factor q(w).
w*(w - 1)**2*(w + 1)*(7*w + 2)
Suppose 0 = 3*m - 7 + 1. Factor 5*d**3 + 4*d**2 - 2*d**3 + 2*d**2 - 3*d**m.
3*d**2*(d + 1)
Let a(n) = n**3 + 9*n**2 + 6*n - 9. Let w be a(-8). Determine q so that -6*q**3 + 6*q**2 + 3*q**4 - w*q**2 + 4*q**2 = 0.
0, 1
Suppose 3/2*p**2 + 0 + 3/2*p**4 - 3*p**3 + 0*p = 0. What is p?
0, 1
Let g(b) be the first derivative of -2*b**3/3 + 2*b**2 - 5. Factor g(j).
-2*j*(j - 2)
Suppose t + 6 - 23 = -4*q, 0 = -q - 2*t + 6. Determine m, given that 2*m + 15*m**q + m - 3*m**3 - 15*m**2 - 12*m**5 + 12*m**3 = 0.
-1, 0, 1/4, 1
Let p(l) = -l**4 + 6*l**3 - l**2 - 2*l + 2. Let b(q) = q**3 + q**2 - q + 1. Let h(n) = 6*b(n) - 3*p(n). Factor h(y).
3*y**2*(y - 3)*(y - 1)
Let z be -6 - 0*(-2)/(-6). Let x = -4 - z. What is m in m**x - 3*m**2 + 0*m**2 = 0?
0
Let j(i) be the first derivative of -2*i**6/15 + i**4/5 + 2. Determine f so that j(f) = 0.
-1, 0, 1
Let j(r) be the second derivative of r**7/98 + 11*r**6/210 + r**5/10 + r**4/14 - r**3/42 - r**2/14 - 2*r. Factor j(y).
(y + 1)**4*(3*y - 1)/7
Let p(j) be the first derivative of -18/5*j**5 - 5/6*j**6 + 2*j - 8/3*j**3 + 3/2*j**2 - 11/2*j**4 - 3. Suppose p(u) = 0. Calculate u.
-1, 2/5
Determine n so that -20*n - 2*n**2 + 4*n + 0*n**2 - 2*n**2 = 0.
-4, 0
Let 2/13*i**3 + 6/13*i**2 + 0 + 4/13*i = 0. What is i?
-2, -1, 0
Let f(a) = -35*a**4 - 25*a**3 - 15*a**2 + 25*a - 40. Let t(b) = b**4 + b**3 + b**2 - b + 1. Let d(g) = -f(g) - 30*t(g). Suppose d(r) = 0. What is r?
-1, 1, 2
Let d(w) be the third derivative of w**7/1470 - w**6/168 + w**5/70 - 7*w**2. Let d(m) = 0. Calculate m.
0, 2, 3
Suppose -3*p + 3 = -9. Suppose -2*d + p*d - 10 = 0. Let 3 - 5 - i - 4*i**2 + 3*i**3 + d - 1 = 0. What is i?
-2/3, 1
Factor 2*x + 12/5 - 2/5*x**3 - 4/5*x**2.
-2*(x - 2)*(x + 1)*(x + 3)/5
Let s(o) be the third derivative of o**7/6720 + o**6/1920 - o**5/160 - o**4/3 - 4*o**2. Let v(k) be the second derivative of s(k). Factor v(p).
3*(p - 1)*(p + 2)/8
Let p(m) be the third derivative of 1/90*m**5 + 0 - 1/72*m**4 + 0*m**3 + 3*m**2 - 1/360*m**6 + 0*m. Suppose p(n) = 0. What is n?
0, 1
Determine n so that -9/2 - 1/2*n**2 + 3*n = 0.
3
Let z = 317/206 + -4/103. Factor -z*f - 3/2*f**2 + 0.
-3*f*(f + 1)/2
Solve -3/7*x**2 + 2/7 - 1/7*x + 1/7*x**4 + 1/7*x**3 = 0 for x.
-2, -1, 1
Let j(b) be the second derivative of b**6/30 - b**5/10 + 27*b. Determine q, given that j(q) = 0.
0, 2
Let l(g) be the first derivative of -g**7/315 + g**6/90 - g**4/18 + g**3/9 - g**2 + 3. Let w(j) be the second derivative of l(j). Solve w(y) = 0 for y.
-1, 1
Let p(n) = -6 - 9 - 1 + 0 - 2*n. Let h be p(-8). Factor 0*m + 0*m**2 + h + 2/3*m**3 - 2/3*m**4 - 4/3*m**5.
-2*m**3*(m + 1)*(2*m - 1)/3
Let d = 3/38 - -23/190. Let p(y) be the first derivative of -1 - d*y**5 - 1/24*y**6 - 3/8*y**4 - 1/8*y**2 - 1/3*y**3 + 0*y. Factor p(o).
-o*(o + 1)**4/4
Let o be 1/(-6)*2/((-2)/39). Solve -o*c**4 + 0 - 15/2*c**3 - 7/2*c**2 - 1/2*c - 2*c**5 = 0 for c.
-1, -1/4, 0
Let c(w) = 5*w - 2*w + 3 - 1 - w**2. Let s be c(3). What is r in -2*r**s + 3*r**5 - 3*r**5 + 2*r**5 + 2*r**4 - 2*r**3 = 0?
-1, 0, 1
Suppose 52 = 94*g - 68*g. Determine b, given that 0 - 2/9*b**g - 4/9*b = 0.
-2, 0
Let a(h) be the first derivative of -6 - 6/7*h**2 - 1/7*h**3 - 9/7*h. Factor a(b).
-3*(b + 1)*(b + 3)/7
Let w(o) be the third derivative of -o**7/70 - o**6/10 - o**5/4 - o**4/4 - 21*o**2. Find c such that w(c) = 0.
-2, -1, 0
Let 11*s - 15*s - 2*s**2 + 1 - 1 = 0. What is s?
-2, 0
Let c be -6 + (14 - 19)/(10/(-12)). Factor -2/15*n**2 - 2/3*n**4 - 4/15*n + 16/15*n**3 + c.
-2*n*(n - 1)**2*(5*n + 2)/15
Let d(w) be the second derivative of 3*w**5/4 - 3*w**4/4 - 17*w. Solve d(g) = 0 for g.
0, 3/5
Let m = 27 + -25. What is j in 3*j**m + 373*j - 373*j = 0?
0
Let f(o) = 4*o + o**3 - o**2 + 6 - 4 - 5*o + 0*o - o**4. Let v(x) = -2*x**4 + 2*x**3 - 3*x**2 - 2*x + 5. Let n(g) = 5*f(g) - 2*v(g). What is s in n(s) = 0?
-1, 0, 1
Suppose -4*s = 2*g + 66, 0 = 4*g - s + 4*s + 137. Let q = g + 38. Factor 1/5*t**q + 0 + 4/5*t - 4/5*t**2.
t*(t - 2)**2/5
Let 0 - 3*j**5 - 27/7*j**4 + 6/7*j + 15/7*j**3 + 27/7*j**2 = 0. Calculate j.
-1, -2/7, 0, 1
Suppose -4*j = -0*j - 16, 9 = -3*y + 3*j. Let s(v) = 3*v**2 - 1. Let h be s(y). Factor 4*i**3 - 6*i + 2 - 4*i**3 + 6*i**3 - h*i**2.
2*(i - 1)*(i + 1)*(3*i - 1)
Let r(q) be the third derivative of -q**6/200 + q**5/50 + q**4/40 - q**3/5 + 7*q**2. Factor r(o).
-3*(o - 2)*(o - 1)*(o + 1)/5
Let x(r) be the first derivative of r**6/60 - 3*r**5/25 + 13*r**4/40 - 2*r**3/5 + r**2/5 + 9. Find f such that x(f) = 0.
0, 1, 2
Let i = -2/7 - -11/14. Let w(n) be the first derivative of -i*n**4 + 0*n**2 + 4/3*n**3 + 0*n + 1. Let w(b) = 0. What is b?
0, 2
Let s(l) be the third derivative of l**7/105 - 6*l**2. Determine b, given that s(b) = 0.
0
Let a = -139/6 - -1009/42. Solve 0*o**2 + a - 3/7*o**3 + 9/7*o = 0.
-1, 2
Let 0 - 1/8*s**4 + 3/8*s**2 + 0*s**3 - 1/4*s = 0. Calculate s.
-2, 0, 1
Let t(i) be the third derivative of 0*i - 1/2*i**3 - 4*i**2 + 1/40*i**6 + 1/20*i**5 - 1/8*i**4 + 0. Factor t(f).
3*(f - 1)*(f + 1)**2
Let l(q) = -q**3 + 5*q**2 + q. Let m be l(5). Let a(y) be the first derivative of 0*y**2 + 0*y**4 + 4 + 0*y**3 + 0*y + 1/5*y**m. Facto