3
Let n be (-2 - -2*1)*(-43 - -42). Determine o, given that n - 8/7*o - 12/7*o**2 + 4/7*o**4 + 0*o**3 = 0.
-1, 0, 2
Determine x so that 8*x**2 - 30*x + 10 + 69*x - 3*x**2 - 54*x = 0.
1, 2
Let g(o) be the third derivative of -2/15*o**5 + 1/35*o**7 + 0 - 1/6*o**4 + 1/30*o**6 - 3*o**2 + 1/3*o**3 + 0*o. Solve g(x) = 0 for x.
-1, 1/3, 1
Let j(h) = 5*h**2 - 8*h - 1. Suppose o + 14 = 3*o. Let p(d) = -2*d**2 + 4*d + 1. Let l(w) = o*p(w) + 3*j(w). Solve l(v) = 0.
-2
Let u be (8/(-3))/(2/(-3)). Suppose -u*d = -a + 5*a + 12, 0 = -2*d - 4*a - 14. Determine t so that 2*t - d + 3 - 3*t**2 - t = 0.
-2/3, 1
Let a = -45 + 47. Let z(l) be the second derivative of 0 + 1/15*l**7 + 3/10*l**5 + 0*l**2 + 19/75*l**6 - 2/15*l**3 + 1/30*l**4 + a*l. Factor z(s).
2*s*(s + 1)**3*(7*s - 2)/5
Let f(y) = y + 1. Let i(r) = r**2 - 2. Suppose 3*v - 4*t + 0*t + 19 = 0, -3*t = 3*v - 9. Let q(h) = v*i(h) - 2*f(h). Find j such that q(j) = 0.
-2, 0
Let x(v) = v**5 + 9*v**4 + 48*v**3 + 64*v**2 + 3. Let m(t) = 2*t**5 + 17*t**4 + 96*t**3 + 128*t**2 + 7. Let u(y) = -3*m(y) + 7*x(y). Let u(b) = 0. What is b?
-4, 0
Let s(p) = -p**5 + 3*p**3 - p**2 + 3*p. Suppose -t = 2*t - 9. Let h(u) = u**5 - 3*u**3 + 2*u**2 - 4*u. Let y(m) = t*h(m) + 4*s(m). Solve y(v) = 0.
-1, 0, 2
Let o(i) be the second derivative of -i**6/180 + i**5/24 - i**4/12 - i**3/9 + 2*i**2/3 - 15*i. Factor o(u).
-(u - 2)**3*(u + 1)/6
Let f(c) be the third derivative of -c**5/60 + c**3/6 - 14*c**2. Determine k so that f(k) = 0.
-1, 1
Let p = 11/24 + -29/168. Factor -p*z - 2/7*z**2 + 2/7 + 2/7*z**3.
2*(z - 1)**2*(z + 1)/7
Let m be 1 - 3/(5 + 1). Factor 0 - m*j**2 + 1/2*j.
-j*(j - 1)/2
Let k be 21/(-28)*(0 - 4). Suppose -6 = -0*o - k*o. Find c, given that -1/2*c**o + 0 + 1/2*c = 0.
0, 1
Find m, given that -2 - m**3 + 10*m - 7*m - 4 + 4 = 0.
-2, 1
Let t(g) be the second derivative of g**4/3 + 4*g**3/3 - 6*g**2 + 21*g. Factor t(o).
4*(o - 1)*(o + 3)
Let f(x) = -9*x + 3. Let h(o) = 4*o - 1. Let s(y) = -3*f(y) - 7*h(y). Let b be s(-4). Find z, given that -2*z + 10*z**2 + 6*z**3 + b*z - 2 + 2*z = 0.
-1, 1/3
Let k(h) = 363*h**2 - 134*h + 14. Let t(v) = -2541*v**2 + 939*v - 99. Suppose 28 + 32 = 4*a. Let w(m) = a*k(m) + 2*t(m). Factor w(z).
3*(11*z - 2)**2
Let o(v) be the first derivative of -5*v**3/3 - 15*v**2/2 - 10*v - 18. Factor o(t).
-5*(t + 1)*(t + 2)
Suppose -5*r + 19 = -4*j, 5*r - 1 = -2*j + 12. Suppose -r*u = -6 - 0. Factor g**3 - 11 + 11 + g**u.
g**2*(g + 1)
Let x(t) be the first derivative of -5/4*t**4 - 1/5*t**5 - 8/3*t**3 - 2*t**2 + 3 + 0*t. Determine f so that x(f) = 0.
-2, -1, 0
Determine g, given that 2/7*g**3 + 0 - 2/7*g + 2/7*g**2 - 2/7*g**4 = 0.
-1, 0, 1
What is k in 4/9 + 0*k**2 - 2/9*k**3 + 2/3*k = 0?
-1, 2
Let j(q) be the first derivative of -q**4/2 - 8*q**3/3 - 3*q**2 + 6. Factor j(l).
-2*l*(l + 1)*(l + 3)
Suppose -2*f = 4*j - 24, -3*f - j + 36 = 3*j. Factor -2 - 7*g**2 + f*g + 3*g**2 - g - 5*g**2.
-(g - 1)*(9*g - 2)
Suppose 0*v + v = -15. Let n = 15 + v. Factor -1/5*k**4 + 1/5*k**2 + 0*k + n*k**3 + 0.
-k**2*(k - 1)*(k + 1)/5
Let s(p) be the first derivative of 0*p - 2*p**2 + p**4 - 4/3*p**3 - 10 + 4/5*p**5. Factor s(x).
4*x*(x - 1)*(x + 1)**2
Suppose 0 = 2*d - 3 - 3. Let h(y) be the first derivative of -1/7*y**2 + 0*y + 2/35*y**5 - 2/21*y**d + 1/14*y**4 - 2. Factor h(o).
2*o*(o - 1)*(o + 1)**2/7
Let r = -6 - -10. Factor -1 + r*i**4 - i**5 - 2*i**3 + 1 - i**5.
-2*i**3*(i - 1)**2
Let d(j) = -j + 6. Let n be d(4). Let 20*b**3 - 2*b**5 + 8*b - 20*b**2 - 10*b**4 + 4*b**5 + 2*b - n = 0. Calculate b.
1
Let g(o) be the second derivative of o**10/10080 + o**9/1680 - o**7/210 - o**4/2 + 2*o. Let v(b) be the third derivative of g(b). Factor v(u).
3*u**2*(u - 1)*(u + 2)**2
Let p(l) be the third derivative of -l**5/90 - l**4/18 - l**3/9 + 9*l**2. Solve p(a) = 0 for a.
-1
Suppose -4*c**4 + 5 + 0*c - 16*c**2 + 5*c - 25*c**3 + c**2 - 6*c**4 = 0. Calculate c.
-1, 1/2
Factor 12/13*k - 14/13 + 2/13*k**2.
2*(k - 1)*(k + 7)/13
Let h = -195 - -198. Let 0*k + 0*k**h + 0 - 26*k**4 + 8/3*k**2 + 70/3*k**5 = 0. What is k?
-2/7, 0, 2/5, 1
Let r = -56 + 56. Factor 4/5*a**4 + 0*a - 2/5*a**3 + 0*a**2 + r - 2/5*a**5.
-2*a**3*(a - 1)**2/5
Factor -3/5*d - 1/5*d**2 + 4/5.
-(d - 1)*(d + 4)/5
Suppose 115 = 22*p + 27. Let 0*r + 4/7*r**2 + 2/7*r**3 - 2/7*r**p + 0 = 0. Calculate r.
-1, 0, 2
Let -2/3*w**2 + 0 + 1/3*w**3 - 4/3*w + 1/6*w**4 = 0. What is w?
-2, 0, 2
Let r = 0 + 16. Suppose -t - 3*t = -r. Let -i - 4*i + i**2 + t*i = 0. Calculate i.
0, 1
Let n(c) be the second derivative of -c**7/1680 + c**6/360 - c**5/240 + 2*c**3/3 - 2*c. Let d(t) be the second derivative of n(t). Factor d(k).
-k*(k - 1)**2/2
Let f(n) be the third derivative of n**8/672 + n**7/420 - n**6/120 - 7*n**2. Determine d, given that f(d) = 0.
-2, 0, 1
Let b = 1992/17 + -42971/357. Let p = -20/7 - b. Find q such that 0*q + p*q**3 - 1/3*q**2 + 0 = 0.
0, 1
Let i = -5 + 6. Determine y, given that 4*y**2 + 8*y**3 + i - 6*y**4 - 3*y + 1 - 5*y = 0.
-1, 1/3, 1
Suppose 15*d - 8 - 11*d**2 + 4*d**2 - 2 + 2*d**2 = 0. Calculate d.
1, 2
Let b(a) be the second derivative of a**7/14 + a**6/5 - a**4/2 - a**3/2 - 7*a. Suppose b(f) = 0. Calculate f.
-1, 0, 1
Let t = 21/82 - -10/41. Let k(h) be the first derivative of 1/3*h + 2/9*h**3 + t*h**2 + 2. Factor k(l).
(l + 1)*(2*l + 1)/3
Let m(q) = q**2 - q - 3. Let w be m(-3). Let y be (1 - 0)/(w - 5). Determine b so that -1/2 + 7/4*b - y*b**4 + 5/4*b**3 - 9/4*b**2 = 0.
1, 2
Suppose -r - 2*r + 6 = 3*f, r - 14 = -5*f. Find c, given that -2/5*c**f + 2/5*c + 0*c**2 - 1/5 + 1/5*c**4 = 0.
-1, 1
Factor -61*n + n**2 + 24*n + 33*n.
n*(n - 4)
Solve 14/5*z**5 + 4/5*z + 54/5*z**3 - 26/5*z**2 + 0 - 46/5*z**4 = 0 for z.
0, 2/7, 1
Let l(i) be the third derivative of i**7/210 + i**6/60 - i**5/60 - i**4/12 + 70*i**2. Factor l(n).
n*(n - 1)*(n + 1)*(n + 2)
Suppose 0 = -2*j - 2*w + 4, -4*j + 5*j - 5*w + 10 = 0. Suppose j*g - 4*g = -8. Solve 2*y**3 + y + 5*y - y**2 + 7*y**2 + g = 0 for y.
-1
Let m(u) be the third derivative of -u**6/40 + u**5/10 + u**4/8 - u**3 - 14*u**2. Suppose m(o) = 0. Calculate o.
-1, 1, 2
Solve 4 - 8*u**3 - 4 - 2*u**2 - 6*u**4 = 0 for u.
-1, -1/3, 0
Let b(s) = s**2 - 2*s - 2. Let l(w) = w**2 - 3*w - 3. Let a(k) = 3*b(k) - 2*l(k). Factor a(x).
x**2
Let k(h) be the second derivative of 3*h**5/100 - 3*h**4/20 + 9*h. Factor k(u).
3*u**2*(u - 3)/5
Let h(c) be the first derivative of 4 - 4*c + 0*c**2 + c**3 + 1/4*c**4. Factor h(g).
(g - 1)*(g + 2)**2
Let b(f) be the second derivative of -f**8/11760 - f**7/5880 + f**6/504 - f**5/280 - f**3/6 + f. Let d(i) be the second derivative of b(i). Factor d(t).
-t*(t - 1)**2*(t + 3)/7
Let j(a) be the first derivative of 2/7*a**3 + 6 - 1/14*a**4 + 2/7*a - 3/7*a**2. Solve j(i) = 0.
1
Let c be 3 - 7/((-49)/782). Let j = 115 - c. Solve -j + 2/7*u**2 + 0*u = 0.
-1, 1
Let d(k) be the third derivative of -k**6/300 - k**5/50 + 4*k**3/15 + 15*k**2. Factor d(y).
-2*(y - 1)*(y + 2)**2/5
Let m(f) be the third derivative of -f**7/56 + f**6/60 + f**5/8 - f**4/4 - f**3/2 + 2*f**2. Let x(l) be the first derivative of m(l). Factor x(k).
-3*(k - 1)*(k + 1)*(5*k - 2)
Let z(f) be the second derivative of f**5/80 - f**4/16 + f**3/12 - 15*f. Factor z(o).
o*(o - 2)*(o - 1)/4
Let a(i) be the second derivative of 0 - 2*i + 1/30*i**4 + 2/15*i**3 - 1/50*i**5 + 0*i**2. Let a(w) = 0. Calculate w.
-1, 0, 2
Let v be ((-6)/10*-5)/(3 - 2). Factor 0 + 1/2*p**5 + 5/2*p**2 - 3/2*p**v - 1/2*p**4 - p.
p*(p - 1)**3*(p + 2)/2
Suppose 2*j - 1 = -g + j, 4*g - 2*j + 2 = 0. Factor -1/5*c**5 + 0*c**4 + 2/5*c**3 + g*c**2 - 1/5*c + 0.
-c*(c - 1)**2*(c + 1)**2/5
Let c = 131/2 + -65. Solve 0*s**2 + 3/2*s - c*s**3 + 1 = 0.
-1, 2
Let o(w) be the second derivative of 0*w**2 - 1/50*w**6 - 1/10*w**3 + 3/100*w**5 + 1/20*w**4 + 3*w + 0. Factor o(n).
-3*n*(n - 1)**2*(n + 1)/5
Let i(d) = -12*d - 6. Let j(m) = -m**2 - 1. Let k(r) = -i(r) - 3*j(r). Determine p so that k(p) = 0.
-3, -1
Let y(x) be the first derivative of 2/25*x**5 + 3/10*x**4 - 1 + 2/5*x**3 + 0*x + 1/5*x**2. Suppose y(n) = 0. What is n?
-1, 0
Let z be (-50)/(-24) + (-30)/15. Let b(x) be the second derivative of 0 + 0*x**2 - z*x**4 - 1/20*x**5 - 2*x + 0*x**3. Find r, given that b(r) = 0.
-1, 0
Let y(m) = 2*m + 0*m - m. Let b be y(3). Find r such that -r**4 + b*r**3 - 4*r**2 + 0*r + r**2 + r = 0.
0, 1
Let c(l