ative of v(s). Determine p, given that m(p) = 0.
3
Let z(f) = f**3 - 3*f**2 + 2*f. Let j be z(3). Let n(y) = -7*y**2 + 2*y - 4. Let h(s) = -20*s**2 + 5*s - 12. Let a(t) = j*h(t) - 17*n(t). Factor a(m).
-(m + 2)**2
Let t(x) be the third derivative of -2*x**2 - 1/504*x**8 + 0 + 0*x**4 + 0*x**3 + 1/360*x**6 + 0*x + 0*x**5 + 1/630*x**7. Solve t(r) = 0.
-1/2, 0, 1
Let g be (-3)/((-7)/((-210)/(-9))). Let q = g + -6. Find i, given that 3/5*i**2 - 1/5*i**3 + 2/5*i + 0 - 1/5*i**5 - 3/5*i**q = 0.
-2, -1, 0, 1
Let k = 338 - 1009/3. Suppose k*s**4 - 2/3*s + 0 + s**5 - 5/3*s**2 - 1/3*s**3 = 0. Calculate s.
-1, -2/3, 0, 1
Let y(s) be the second derivative of s**4/42 + 4*s**3/21 + 3*s**2/7 - s + 6. Let y(c) = 0. Calculate c.
-3, -1
Factor -9 - 1/4*m**2 - 3*m.
-(m + 6)**2/4
Let p be 2 + 56 - 6/2. Let m be p/(-175) + 3/5. Let 0*g**2 - 2/7*g + m*g**3 + 0 = 0. Calculate g.
-1, 0, 1
Let n(s) be the third derivative of -s**5/20 - 4*s**2. Find o such that n(o) = 0.
0
Let r(d) be the third derivative of d**7/10080 + d**6/1440 + d**5/480 - d**4/4 + 4*d**2. Let v(z) be the second derivative of r(z). Suppose v(f) = 0. What is f?
-1
Let w(a) be the first derivative of -a**5/5 + 1. Let q(s) = 2*s**3 - 3*s**2 + 2*s - 2. Let z be q(2). Let d(x) = -x**4. Let m(u) = z*w(u) - 4*d(u). Factor m(n).
-2*n**4
Suppose 45 = 5*d + 10*d. Let i(m) be the second derivative of -d*m - 1/2*m**3 - 2/5*m**6 + 0*m**2 - 9/10*m**5 - 1/14*m**7 - m**4 + 0. Let i(n) = 0. What is n?
-1, 0
Solve -2/5*x**2 + 0*x**3 + 0*x + 1/5*x**4 + 1/5 = 0 for x.
-1, 1
Let q(u) = -81*u**4 + 41*u**3 + 32*u**2 + 4*u. Let b(k) = k**3. Let a(t) = -12*b(t) - 3*q(t). Factor a(o).
3*o*(o - 1)*(9*o + 2)**2
Let u(v) = 2*v + 39. Let q be u(-18). Factor 1/6*w**5 + 1/6*w**q + 0 + 0*w**2 + 0*w + 1/3*w**4.
w**3*(w + 1)**2/6
Factor -10/7*c**2 - 4/7 + 2*c.
-2*(c - 1)*(5*c - 2)/7
Let b(c) = 5*c + 52. Let w be b(-10). Factor -14/5*z**2 + 4/5 - w*z.
-2*(z + 1)*(7*z - 2)/5
Let a be 3 + (1 - (-64)/(-18)). Solve -a*y - 2/9*y**3 + 0 + 2/3*y**2 = 0.
0, 1, 2
Let o = 7 - 0. Let b(z) be the third derivative of -z**2 + 1/3*z**3 + 0*z + 1/3*z**4 + 1/105*z**o + 1/5*z**5 + 1/15*z**6 + 0. Determine g so that b(g) = 0.
-1
Suppose 0 = -2*r - 3*t + 69, -5*t = -3*r - 18 + 131. Suppose 0 = -33*d + r*d - 15. Factor 0 - 2/5*g**3 + 0*g**4 + 1/5*g + 1/5*g**d + 0*g**2.
g*(g - 1)**2*(g + 1)**2/5
Let i(w) be the first derivative of w**6/15 + 2*w**5/25 - w**4/5 - 4*w**3/15 + w**2/5 + 2*w/5 + 10. Solve i(g) = 0.
-1, 1
Factor 1/3*k**2 + 0 + 2/9*k + 1/9*k**3.
k*(k + 1)*(k + 2)/9
Let d = 28 + -10. Factor 41*s**3 - d*s - 7*s**2 - 11*s**3 - 4 - s**2.
2*(s - 1)*(3*s + 1)*(5*s + 2)
Let k(a) be the second derivative of -1/30*a**5 - a**2 + 0 - 3*a + 0*a**3 + 1/12*a**4. Let j(r) be the first derivative of k(r). Factor j(b).
-2*b*(b - 1)
Let v(i) be the first derivative of 0*i**2 - 1/5*i**5 + 1/3*i**3 + 0*i + 1 + 0*i**4. Determine t so that v(t) = 0.
-1, 0, 1
Factor -4/5*d**4 - 6/5*d**2 + 0 + 0*d + 2*d**3.
-2*d**2*(d - 1)*(2*d - 3)/5
Let n be (8/(-4))/(4/(-2)). Let p = 2 + n. Solve 7*j**2 - 5*j + p - 6 + 1 = 0 for j.
-2/7, 1
Suppose -37 - 6*a**2 + 2*a**2 + 37 + 4*a = 0. Calculate a.
0, 1
Let b be ((-2)/(-12)*-13)/(-3). Let s = b - 1/18. Factor 2/3*o**3 + 2/3 - 2/3*o - s*o**2.
2*(o - 1)**2*(o + 1)/3
Suppose g + 0 = 3. Solve -w**3 - w**3 + 3*w**2 - g*w**3 + 2*w**3 - 3*w**4 + 3*w = 0.
-1, 0, 1
Factor 3/4*h - 1/4*h**2 + 0.
-h*(h - 3)/4
Let j(g) be the second derivative of -g**6/15 - 6*g**5/5 - 9*g**4 - 36*g**3 - 81*g**2 - 18*g. Determine z so that j(z) = 0.
-3
Let n be ((-1)/(-7))/((-10)/(-35)). Let y(k) be the first derivative of -1/6*k**3 + n*k - 1 - 1/4*k**2 + 1/8*k**4. Solve y(u) = 0.
-1, 1
Let d(b) be the third derivative of b**10/176400 + b**9/52920 + b**8/70560 + b**5/30 + 2*b**2. Let l(m) be the third derivative of d(m). Factor l(q).
2*q**2*(q + 1)*(3*q + 1)/7
Let x = 146/3 - 48. Factor 2/3*h**2 - x + 0*h.
2*(h - 1)*(h + 1)/3
Let f(o) = -9*o**4 + o**3 - o**2 - o - 5. Let y(i) = -10*i**4 + 2*i**3 - 2*i**2 - 2*i - 6. Let n(q) = -6*f(q) + 5*y(q). Solve n(v) = 0 for v.
-1, 0, 1
Let f be -2 + 195/36 - 2. Let l = f + -1/12. What is m in 0 - 4/3*m**2 + 0*m**3 + 2/3*m**5 + l*m**4 - 2/3*m = 0?
-1, 0, 1
Let a(l) be the first derivative of 125*l**6/48 + 135*l**5/4 + 345*l**4/4 - 586*l**3/3 + 129*l**2 - 36*l - 8. Factor a(t).
(t + 6)**2*(5*t - 2)**3/8
Suppose 0 = 15*h - 10*h. Let 5*x + h - 1 + 3 - 9*x**3 - 6*x**2 = 0. Calculate x.
-1, -1/3, 2/3
Let v be -1 + (0 - -3) + (-4)/3. Suppose 4 = 2*h - 4*s + 5*s, -2*s = 0. Find x such that -1/3*x**h + v*x - 1/3 = 0.
1
Solve -2*c**4 - 6 + 0*c**3 - 20*c + 13*c**2 - 37*c**2 - 12*c**3 = 0.
-3, -1
Let i(o) be the third derivative of 1/60*o**4 - 2/525*o**7 + 0 + 0*o**6 + 2*o**2 + 0*o**3 - 1/840*o**8 + 1/75*o**5 + 0*o. Find x such that i(x) = 0.
-1, 0, 1
Let k(o) be the second derivative of o**4/6 + 2*o**3 - 11*o. Factor k(w).
2*w*(w + 6)
Let h(m) = m**3 - m**2 + m. Let o(i) = -2*i**3 - i. Suppose -4*g + 3*g = 2. Let v(l) = g*h(l) - 2*o(l). Factor v(q).
2*q**2*(q + 1)
Let s(p) = p**3 + p**2 + p + 2. Let g be s(0). Let 11 + b - 4*b**g - 3*b - 9 = 0. Calculate b.
-1, 1/2
Let g(w) be the second derivative of 2*w**6/45 + w**5/15 - 2*w**4/9 + 12*w. Factor g(i).
4*i**2*(i - 1)*(i + 2)/3
Let a(h) be the second derivative of h**6/90 - h**5/60 - h**4/36 + h**3/18 + h. Factor a(o).
o*(o - 1)**2*(o + 1)/3
Let o(b) = -b**3 + 12*b**2 - b + 14. Let w be o(12). Let 2*x - 6*x**3 + 2*x**3 + 10*x**4 - 2*x**3 + x**w - 3*x**2 - 4*x**5 = 0. What is x?
-1/2, 0, 1
Let b = 5 - 1. Factor 4*r**2 + 2*r + 0*r - r**b - r**2.
-r*(r - 2)*(r + 1)**2
Suppose -5*o - 20 = 0, -5*o + 28 = 2*i + i. Let k = i - 13. What is b in 1/5 - 1/5*b**4 + 0*b**2 - 2/5*b + 2/5*b**k = 0?
-1, 1
Suppose -2*k + k = -2. Let z(t) = -2*t - 6. Let j be z(-5). Factor -j*o**4 - k*o**5 + 0*o**5 + 6*o**4.
-2*o**4*(o - 1)
Suppose i = 5*d + 10, d + 4 - 2 = 2*i. Suppose 1/3*c**4 + 0 + 0*c**2 - 1/3*c**3 + i*c = 0. Calculate c.
0, 1
Let q(c) be the first derivative of 5/3*c**5 - 2*c**2 + 4/3*c + 5/2*c**4 + 1 - 11/9*c**3. Factor q(b).
(b + 1)**2*(5*b - 2)**2/3
Suppose 0 = 3*z + 20 - 11. Let v(y) = -3*y**3 - 3*y**2 + 4*y + 4. Let s(p) = -p**3 - p**2. Let g(c) = z*v(c) + 6*s(c). Determine k so that g(k) = 0.
-2, -1, 2
Find j, given that 0*j + 0*j**3 + 4/19*j**2 - 2/19*j**4 - 2/19 = 0.
-1, 1
Let y(b) be the first derivative of -b**5/120 + b**3/12 + 3*b**2/2 - 3. Let w(d) be the second derivative of y(d). Suppose w(q) = 0. Calculate q.
-1, 1
Let n(z) be the second derivative of z**4 - 2*z**3/3 - 4*z**2 - 3*z. Let n(g) = 0. What is g?
-2/3, 1
Let q(x) be the second derivative of x**6/60 + x**5/15 + x**4/12 + x**2/2 + 4*x. Let g(l) be the first derivative of q(l). Factor g(f).
2*f*(f + 1)**2
Let u(h) = -h**3 - 3*h**2 - 2*h - 4. Let d be u(-3). Let b = 0 - -2. Factor -4 + 0*k**d + 2 + b*k**2.
2*(k - 1)*(k + 1)
Suppose 4*w - 43 = -11. Suppose -3*o - 2*x = -w*o + 4, -5*x - 10 = -4*o. Find c such that 2/3*c**4 + 4/3*c**3 - 2/3 - 4/3*c + o*c**2 = 0.
-1, 1
Suppose -5*d = -3*d. Solve b**3 + 6*b**2 + d*b + 2 + b**3 + 6*b = 0.
-1
Let w be 5/(-60) + 3/4. Let d = 353 - 3173/9. Solve -d*j + 2/9 - w*j**2 = 0.
-1, 1/3
Let b(i) be the first derivative of i**4/8 - i**3/3 + 12. Factor b(w).
w**2*(w - 2)/2
Let x = 26 + -11. Suppose x = 4*j - 9. Find t, given that 0*t + 4*t - j*t**3 - 2*t**2 + 4*t**2 = 0.
-2/3, 0, 1
Let y(d) = d + 1. Let f(v) = -v**2 - 5*v - 4. Let z(j) = -f(j) - 3*y(j). Find m, given that z(m) = 0.
-1
Suppose 13 = -3*l - 5*w, -24 = -l - w + 5*w. Factor -2/5*h**2 + 0*h**3 + 1/5 + 1/5*h**l + 0*h.
(h - 1)**2*(h + 1)**2/5
Let g(t) be the first derivative of 3*t**3/4 + 29*t**2/8 + 3*t/2 + 20. Determine f, given that g(f) = 0.
-3, -2/9
Let k(g) be the first derivative of 2*g**5/35 + g**4/7 - 2*g**3/21 - 2*g**2/7 + 9. Determine z so that k(z) = 0.
-2, -1, 0, 1
Suppose 18*i - 7*i - 22 = 0. Let n(t) be the second derivative of 1/4*t**i + 0 + t - 3/8*t**3 + 7/48*t**4. Factor n(f).
(f - 1)*(7*f - 2)/4
Let o(g) be the first derivative of -14*g**3/15 - 26*g**2/5 + 16*g/5 + 3. Factor o(u).
-2*(u + 4)*(7*u - 2)/5
Solve 2/13*z - 2/13*z**2 + 0 = 0.
0, 1
Suppose -n + 2*n - 2 = 0. Find f such that -3*f**2 + 2*f**2 - 6*f - 2*f**2 + n*f**3 + f**3 = 0.
-1, 0, 2
Let s be (-2)/6 + (-394)/(-30). Suppose 0 = -n + 5 - 2. Solve -4/5*h**2 + 