 + 8*p - 5. Let n be i(6). Find s such that 2*s - n*s - 3*s**2 - s - 3 + 0*s = 0.
-1
Let f(c) be the first derivative of -c**6/10 + 3*c**5/25 + 9*c**4/20 - c**3/5 - 3*c**2/5 - 4. Solve f(y) = 0.
-1, 0, 1, 2
Find y such that -3/2*y + 3/2*y**3 + 3/2 - 3/2*y**2 = 0.
-1, 1
Let o(a) be the second derivative of a**7/21 + 8*a**6/45 + a**5/5 - a**3/9 - 5*a. Suppose o(z) = 0. What is z?
-1, 0, 1/3
Let o(p) = 4*p**2 - 4*p - 5. Let b(k) = k**2 - k - 1. Let m(c) = -5*b(c) + o(c). Factor m(l).
-l*(l - 1)
Let m(r) = 3*r**2 + 2*r + 1. Let f be m(-1). Factor -l**2 + 2*l - 7*l + f*l + 2*l.
-l*(l + 1)
Suppose -600*q + 2*q**5 - 196*q**3 + 499*q**3 + 1588 - 60*q**4 + 295*q**3 + 412 - 1940*q**2 = 0. What is q?
-1, 1, 10
Let c(b) = -3*b**2 + 0*b + 2*b**2 + b. Let h(v) = -v**4 - 2*v**3 + 6*v**2 - 7*v. Let s(m) = -14*c(m) - 2*h(m). Factor s(g).
2*g**2*(g + 1)**2
Let x be 3/((-48)/401)*-4. Let s = 101 - x. Solve -3/4*i**3 - 9/4*i**2 + 3/2*i**4 + s*i + 3/4 = 0 for i.
-1, -1/2, 1
Factor 16/5 - 64/5*o - 4/5*o**5 - 76/5*o**3 + 20*o**2 + 28/5*o**4.
-4*(o - 2)**2*(o - 1)**3/5
Let r(l) = -12*l**3 + 22*l**2 - 24*l + 2. Let n(a) = 6 + a**3 + 24*a**2 - 5 - 24*a**2. Let h(p) = -6*n(p) - r(p). Factor h(b).
2*(b - 2)*(b - 1)*(3*b - 2)
Let s(l) be the first derivative of 0*l + 0*l**2 - 1/21*l**6 + 1/14*l**4 - 1 - 2/35*l**5 + 2/21*l**3. Find j, given that s(j) = 0.
-1, 0, 1
Let t(b) be the second derivative of b**5/270 - b**4/27 + 4*b**3/27 - 2*b**2 - 6*b. Let j(g) be the first derivative of t(g). Factor j(a).
2*(a - 2)**2/9
Let s(b) be the first derivative of 0*b - 2/5*b**2 + 3 + 1/5*b**4 - 2/15*b**3 + 2/25*b**5. Factor s(c).
2*c*(c - 1)*(c + 1)*(c + 2)/5
Let f(t) = 24*t**2 - 4*t - 6. Let p(u) = -10*u**2 + u + 4. Let r(m) = -m**2 + 1. Let s(o) = p(o) - 2*r(o). Let n(q) = -5*f(q) - 14*s(q). Solve n(k) = 0.
-1/4, 1
Let w(r) be the first derivative of -3*r**6/4 + 3*r**5/5 + 27*r**4/8 - 6*r**3 + 3*r**2 + 10. What is t in w(t) = 0?
-2, 0, 2/3, 1
Let c be (0 + 2)*(-12)/(-8). Let g(m) = 3*m**2 - 4*m + 3. Let r(k) = -k**2 + k - 1. Let p(w) = c*g(w) + 6*r(w). Find j, given that p(j) = 0.
1
Suppose 0 = 3*q - 2*q + 24. Let b = q - -26. Solve -3*u**2 - 1/2*u**4 - 1/2 - b*u**3 - 2*u = 0.
-1
Let v(c) be the first derivative of -c**5/10 - c**4/3 - c**3/3 - 3*c + 1. Let r(s) be the first derivative of v(s). Solve r(m) = 0 for m.
-1, 0
Let o(f) = -6*f + 2. Let c be o(1). Let a be 6/c*(-4)/4. Factor a*s**4 + 0 + 3/2*s**3 + 1/2*s**2 + 0*s + 1/2*s**5.
s**2*(s + 1)**3/2
Let n(h) = -h**3 - h**2 + h - 4. Let g be n(-3). Suppose 0 = q - 5*x - g + 34, 5*q = -5*x + 35. Determine i so that -2/3*i**q - 4/3*i - 2/3 = 0.
-1
Let w = -473 - -473. Factor -5/3*a**2 - 1/3*a**4 - 4/3*a**3 + w - 2/3*a.
-a*(a + 1)**2*(a + 2)/3
Let l = 51 + -47. Let s(k) be the third derivative of 0*k + 1/30*k**5 + 1/6*k**l + 1/3*k**3 + 0 + 2*k**2. Factor s(b).
2*(b + 1)**2
Let m = 10 - 10. Factor 3*f + m*f**2 + f**2 - 2*f.
f*(f + 1)
Let o(k) be the second derivative of 1/100*k**5 + 1/6*k**3 + 1/5*k**2 + 0 + 2*k + 1/15*k**4. Determine c, given that o(c) = 0.
-2, -1
Let u(r) = -r**2 + 13*r - 8. Let o be u(12). Let b(z) = z**2 - 5*z + 4. Let g be b(o). Factor 3/7*v + 0*v**2 + 3/7*v**5 + 0 + g*v**4 - 6/7*v**3.
3*v*(v - 1)**2*(v + 1)**2/7
Let s be 4/(-6)*-3*(-3)/(-21). Determine y so that -s*y - 2/7 + 2/7*y**2 + 2/7*y**3 = 0.
-1, 1
Factor 3/2*t - 3/2*t**3 + 1/2*t**4 - 1 + 1/2*t**2.
(t - 2)*(t - 1)**2*(t + 1)/2
Let 1/2 - o**3 + 7/2*o**2 + 11/4*o - 7/4*o**5 - 4*o**4 = 0. Calculate o.
-1, -2/7, 1
Let k = -1/83 + 175/747. Let o(g) be the second derivative of 1/18*g**4 - k*g**3 + 1/3*g**2 + g + 0. What is s in o(s) = 0?
1
Let a(b) be the first derivative of -b**6/18 + b**5/5 - b**4/6 + 12. Factor a(q).
-q**3*(q - 2)*(q - 1)/3
Factor 3/5*k**5 + 0*k + 9/5*k**3 + 3/5*k**2 + 0 + 9/5*k**4.
3*k**2*(k + 1)**3/5
Let r(v) be the third derivative of v**7/3780 + v**6/540 + v**5/270 + v**3/2 - 3*v**2. Let y(f) be the first derivative of r(f). Factor y(p).
2*p*(p + 1)*(p + 2)/9
Solve -8*l**3 + 3*l**4 - 23*l**4 + 25*l**5 + 3*l**5 = 0.
-2/7, 0, 1
Let k(d) = d**2 - 13*d + 12. Let z be k(12). Let b be 2/(-10) - (-5)/25. Let 2/3*x**2 + b*x + 2/3*x**3 + z = 0. What is x?
-1, 0
Let x(n) = -2 - n + 0*n**2 - 1 + n**2. Let t be x(3). Factor 2*q**5 + 0*q**2 - 6*q**4 + q**5 + 6*q**2 - 3*q**t.
3*q**2*(q - 2)*(q - 1)*(q + 1)
Suppose -5*p + 3*q + 24 = 0, p + p - 4*q - 18 = 0. Suppose 3*d - d - 15 = -p*i, 0 = -i - d + 6. Suppose i - 1 - k - 3*k + 2*k**2 = 0. What is k?
1
Suppose 22 + 5 = -3*t. Let s be (-3)/t + 8/3. Factor -s*a**2 + 6*a**3 - 5*a**2 + 9 - 3 - 9*a - a**2.
3*(a - 2)*(a + 1)*(2*a - 1)
Let l(s) be the second derivative of s**4/6 + 4*s**3/3 + 4*s**2 - 2*s. Solve l(d) = 0.
-2
Let v(l) be the first derivative of 9/4*l**2 - 1/3*l**3 - 9/8*l**4 - 3 + l. Factor v(k).
-(k - 1)*(k + 1)*(9*k + 2)/2
Let r(u) = -u**2 - 7*u. Let c be r(-6). Let k(v) = 2*v - 9. Let o be k(c). Factor 0 - l**2 + 1/2*l + 1/2*l**o.
l*(l - 1)**2/2
Let l(p) = -p**3 - 4*p**2 + 5*p + 4. Let h be l(-5). Factor -3*c**2 + 3*c**h + 2*c**2 - c**2 - 4*c**3 - 5*c**4.
-2*c**2*(c + 1)**2
Let z(m) be the second derivative of -2*m**6 - 7*m**5/20 + m**4/6 - 8*m. Factor z(y).
-y**2*(4*y + 1)*(15*y - 2)
Let c = 41/132 + -5/22. Let h(g) be the second derivative of -1/6*g**3 + 0 + 0*g**2 - 1/30*g**6 + c*g**4 - 2*g + 1/20*g**5. Factor h(y).
-y*(y - 1)**2*(y + 1)
Suppose a - 67 = -4*v, 3*a + 2 = -13. Let w be (7/(-21))/((-2)/v). Factor -4*k**4 - 2/3*k**2 - w*k**3 + 0*k + 0 - 5/3*k**5.
-k**2*(k + 1)**2*(5*k + 2)/3
Suppose 5*h - 20 = 5*r, -r + 4 = 4*h - 2*r. Suppose -y - 2*y = 3*g - 24, -4*y + 3*g + 4 = h. Factor -1/2 - 1/2*k**y + 2*k + 2*k**3 - 3*k**2.
-(k - 1)**4/2
Let b(j) be the second derivative of -7*j**5/180 - 2*j**4/9 - 2*j**3/9 + 2*j**2 + 3*j. Let g(z) be the first derivative of b(z). Factor g(c).
-(c + 2)*(7*c + 2)/3
Let n(v) be the third derivative of -5*v**8/504 + 2*v**7/315 + v**6/36 - v**5/45 + 9*v**2. Let n(k) = 0. What is k?
-1, 0, 2/5, 1
Let v(z) be the third derivative of -z**5/160 + 5*z**4/8 - 25*z**3 - z**2 - 2. What is s in v(s) = 0?
20
Let c = 0 - -4. Let k be ((-8)/10 - -1)*2. Factor 0 + 2/5*x**2 - 2/5*x**c + k*x**3 - 2/5*x.
-2*x*(x - 1)**2*(x + 1)/5
Let p be (12/(-4) - -4)*0. Suppose c + p*c = 0. Let 2/3*a + c*a**2 + 4/9 - 2/9*a**3 = 0. Calculate a.
-1, 2
Let x = 13 + -13. Let i(o) be the second derivative of -1/48*o**4 + 0 + 0*o**5 + o + x*o**3 + 1/120*o**6 + 0*o**2. Find r such that i(r) = 0.
-1, 0, 1
Suppose 3*m = 5 + 4. Factor -4*k**2 + 12*k**4 - k + 2 + 6*k**m - 2*k**3 + 4*k - 7*k**5 - 10*k**2.
-(k - 1)**3*(k + 1)*(7*k + 2)
Let l = 5/36 + 43/36. Factor 8/3*p**2 + 6*p**5 + 2/3*p - 8*p**4 + 0 - l*p**3.
2*p*(p - 1)**2*(3*p + 1)**2/3
Suppose 12 = 8*g - 5*g. Let h(j) be the second derivative of 3/4*j**2 + g*j + 1/2*j**3 + 0 + 1/8*j**4. Factor h(r).
3*(r + 1)**2/2
Let t(w) be the third derivative of -w**6/10 - 3*w**5/20 + w**4/8 - 7*w**2. Suppose t(i) = 0. What is i?
-1, 0, 1/4
Suppose 0 = 3*f + 14 - 20. Solve -1/4*x**3 - 1/2 + 0*x**f + 3/4*x = 0 for x.
-2, 1
Suppose -m + 4 = 0, -5*m = -n + 2*n - 23. Factor 3 - 6*a**2 + 3*a**2 + 3*a - n*a.
-3*(a - 1)*(a + 1)
Let n = 10/37 + -16/333. Solve -n*p**4 - 8/9*p**3 - 8/9*p - 2/9 - 4/3*p**2 = 0.
-1
Let o(b) be the second derivative of 0*b**3 + 0*b**4 + 0 + 1/50*b**5 + 0*b**2 - 1/105*b**7 + 0*b**6 + 3*b. Factor o(l).
-2*l**3*(l - 1)*(l + 1)/5
Let p = 6 - -7. Let v = -11 + p. Factor 0 + 0*u**v + 2/7*u - 2/7*u**3.
-2*u*(u - 1)*(u + 1)/7
Let w(f) be the third derivative of -f**6/180 + f**5/10 - 2*f**4/9 + 13*f**2. Suppose w(b) = 0. What is b?
0, 1, 8
Let n = 26 - 101/4. Let j = 3/43 + 375/172. Factor -n*m**2 + j*m - 3/2.
-3*(m - 2)*(m - 1)/4
Suppose 432/11 - 216/11*r + 36/11*r**2 - 2/11*r**3 = 0. What is r?
6
Suppose 3*g + 77 = -28. Let w = g - -115. Factor -w*d**3 + 8 - 5 + 24*d**2 + 64*d + 13 + 25*d**4.
(d - 2)**2*(5*d + 2)**2
Let m(w) = -w**2 + 13*w + 4. Let k be m(13). Let f(h) be the first derivative of 4/45*h**5 + 1/27*h**6 + 0*h**3 - 2 + 1/18*h**k + 0*h + 0*h**2. Factor f(v).
2*v**3*(v + 1)**2/9
Let i(s) = -s**2 + 4*s - 5. Let u = -5 + 10. Let d(l) = -2*l**2 + 6*l - 8. Let r(p) = u*d(p) - 8*i(p). Suppose r(j) = 0. What is j?
-1, 0
Let k(a) be the third derivative of a**5/480 - a**4/64 + a**3/24 - 6*a**2. Solve k(u) = 0 for u.
1, 2
Let o(f) be the 