t - 1. Let j(m) = 4*l(m) + 3*z(m). Let j(k) = 0. What is k?
-1
Let f(u) be the first derivative of -u**6/60 + u**5/30 + u**2/2 - 1. Let h(c) be the second derivative of f(c). Suppose h(r) = 0. Calculate r.
0, 1
Let s(m) be the second derivative of -m**5/90 - m**4/108 + m**3/54 + 46*m. Let s(g) = 0. Calculate g.
-1, 0, 1/2
Factor -1/2*f - 1/2 - 1/8*f**2.
-(f + 2)**2/8
Let i(k) be the first derivative of 2/3*k - 1 - 2/9*k**3 + 0*k**2. Factor i(t).
-2*(t - 1)*(t + 1)/3
Let i(h) be the first derivative of -h**6/9 - 2*h**5/3 - 7*h**4/6 + 2*h**3/9 + 8*h**2/3 + 8*h/3 - 24. Determine c, given that i(c) = 0.
-2, -1, 1
Let -4/5 - 16/5*l**5 - 8/5*l**3 + 24/5*l + 36/5*l**4 - 32/5*l**2 = 0. Calculate l.
-1, 1/4, 1
Suppose -2*w = -0 - 14. Factor -4 + 3 + w + 3*t**2 - 9*t + 0*t**2.
3*(t - 2)*(t - 1)
Let f = -5/897 - -3929/383019. Let t = f + 2981/1708. Factor 0*i + 3*i**5 + 0 + 1/4*i**3 - t*i**4 + 0*i**2.
i**3*(3*i - 1)*(4*i - 1)/4
Let v(z) be the third derivative of -z**8/84 + z**6/30 + 15*z**2. Let v(p) = 0. What is p?
-1, 0, 1
Suppose 2*r + 16 = 5*c, -r + 7 = 4*c - 11. Let s(b) be the second derivative of 2*b + 0*b**3 - 1/6*b**c + 0*b**2 + 0. Factor s(y).
-2*y**2
Let t be (-12)/(-42) + (-166)/(-7). Suppose 0*n - t = -2*n. Factor 5*u**4 + 3*u + 10*u**2 - 2*u**3 + 4 - 3 + 2*u + n*u**3 + u**5.
(u + 1)**5
Factor 2 - 40*p**3 + 7 + 7 - 4*p**2 - 16*p + 44*p**3.
4*(p - 2)*(p - 1)*(p + 2)
Let v(u) = -u**2 - u - 1. Let g be v(-1). Let b(n) = -n**3 - n**2 - 1. Let t(s) = -2*s**3 + 2*s**2 + 8*s + 1. Let l(j) = g*t(j) + 3*b(j). Solve l(p) = 0.
-2, -1
Let y = -335 - -1343/4. Find s, given that 0 - 1/2*s - y*s**4 + 1/4*s**2 + s**3 = 0.
-2/3, 0, 1
Factor 0*s - 2*s - 6*s + 2*s**2 + 6.
2*(s - 3)*(s - 1)
Let s = 13 - 9. Solve -l**s + 3*l**4 - 3*l - 6*l**2 - l = 0 for l.
-1, 0, 2
Factor m**3 + 1 + 2*m - 3*m**3 + 10*m**4 + 0*m**3 - 11*m**4.
-(m - 1)*(m + 1)**3
Let w(y) be the third derivative of -y**7/195 + 3*y**6/260 + y**5/78 - 3*y**4/52 + 2*y**3/39 - 12*y**2. Let w(i) = 0. Calculate i.
-1, 2/7, 1
Let u(y) be the second derivative of y**7/14 - 7*y**6/30 - 7*y**5/20 + 9*y**4/4 - 10*y**3/3 + 2*y**2 + 4*y. Suppose u(r) = 0. What is r?
-2, 1/3, 1, 2
Let v(j) = j**3 - j**2 - 8 + j**3 - 14*j + 3*j**2. Let a(d) = -3*d**3 - 2*d**2 + 13*d + 7. Let q(x) = -6*a(x) - 5*v(x). Factor q(c).
2*(c - 1)*(c + 1)*(4*c + 1)
Let x(o) = 12*o**2 - 2*o - 2. Let u(p) = -p**3 + 48*p**2 - 9*p - 9. Let q(c) = -4*u(c) + 18*x(c). Factor q(s).
4*s**2*(s + 6)
Let y(n) be the first derivative of 3*n - 1/3*n**3 - n**2 - 7. Factor y(i).
-(i - 1)*(i + 3)
Let z be (1/5)/(80/200). Factor 0 + n**2 - 1/2*n**3 - z*n.
-n*(n - 1)**2/2
Let c be 4/(-38) - 4794/(-2584). Let -3/2*u**3 - 1/2*u**2 - 3/4 + c*u - 1/4*u**5 + 5/4*u**4 = 0. What is u?
-1, 1, 3
Suppose 4/3*h**2 + 4/3*h - 8/3 = 0. Calculate h.
-2, 1
Let n(o) be the second derivative of 2*o**6/15 + o**5/20 - o**4/3 - o**3/6 + 10*o. Suppose n(d) = 0. Calculate d.
-1, -1/4, 0, 1
Let y be (-16 - -1)/(-3) - 2. Let i(q) be the first derivative of 0*q + 2/5*q**y + 1 + 1/5*q**2. Let i(c) = 0. What is c?
-1/3, 0
Let m(h) = -73*h**2 + 159 - 24*h**2 - 14*h**2 + 81*h**3. Let p(t) = -5*t**3 + 7*t**2 - 10. Let g(o) = 2*m(o) + 33*p(o). Factor g(v).
-3*(v - 2)**2*(v + 1)
Let p(o) be the second derivative of -o**6/210 + 3*o**5/140 - o**4/84 - o**3/14 + o**2/7 + 12*o. Factor p(u).
-(u - 2)*(u - 1)**2*(u + 1)/7
Let j = -92/777 + -8/111. Let t = 1/7 - j. Factor -t*r**2 + 2/3 - 1/3*r.
-(r - 1)*(r + 2)/3
Suppose 5 = 4*f - 11. Suppose -5 = -o, 2*w + f*o + 6 = 28. What is d in -3*d**2 + 0 + 5*d**2 - d**2 - w = 0?
-1, 1
Factor -1/3*m**3 + 0 + 2/3*m**2 - 1/3*m.
-m*(m - 1)**2/3
Let h(i) = 22*i**3 + 4*i**2 - 2*i - 2. Let n(m) = 43*m**3 + 9*m**2 - 4*m - 5. Let f = -23 + 21. Let q(c) = f*n(c) + 5*h(c). Factor q(g).
2*g*(3*g + 1)*(4*g - 1)
Suppose -11/5*t**2 - 4/5 - 13/5*t - 2/5*t**3 = 0. Calculate t.
-4, -1, -1/2
Let t(q) be the first derivative of -1 + 0*q**2 + 0*q**3 + q - 1/48*q**4. Let w(v) be the first derivative of t(v). Factor w(p).
-p**2/4
Let g(s) be the first derivative of -s**4/18 - 4*s**3/27 + s**2/9 + 4*s/9 - 12. Determine n so that g(n) = 0.
-2, -1, 1
Let b(t) be the third derivative of -t**5/30 - t**4/2 - 3*t**3 - 7*t**2. Let b(s) = 0. What is s?
-3
Let h(m) be the first derivative of -m**3/6 + m**2/4 - 17. Find c such that h(c) = 0.
0, 1
Suppose z - 3*y + 6 = -z, -z + 4*y - 8 = 0. Let b be (2 - 4) + (2 - z). Factor 2/3 - 2/3*c**2 + b*c.
-2*(c - 1)*(c + 1)/3
Let p(c) be the first derivative of -c**6/60 - c**5/30 + 2*c**2 - 3. Let f(b) be the second derivative of p(b). Factor f(m).
-2*m**2*(m + 1)
Factor 6/5*t - 2/5 + 8/5*t**2.
2*(t + 1)*(4*t - 1)/5
Let i**3 + 2*i - 4*i**3 + 0*i**3 + 3*i**4 - 3*i**2 + i = 0. Calculate i.
-1, 0, 1
Let t(d) be the first derivative of -5*d**4/2 - 25*d**3/3 + 10*d**2 + 15*d - 6. Factor t(j).
-5*(j - 1)*(j + 3)*(2*j + 1)
Factor 0*y**5 + 5*y**5 - 3*y**5 - 3*y**5.
-y**5
Let c(o) be the third derivative of -o**6/60 - o**5/15 + o**4/4 + 12*o**2. Determine k so that c(k) = 0.
-3, 0, 1
Factor -3*d - 9/2*d**4 - 9*d**2 - 39/4*d**3 - 3/4*d**5 + 0.
-3*d*(d + 1)**2*(d + 2)**2/4
Let i(x) = x - 3. Let o be i(3). Let s be (2 - o)/(-2)*-2. Find j such that -2/3*j**s - 2/3 + 4/3*j = 0.
1
Let o(c) = -c**3 + 8*c**2 - c + 5. Let a be o(8). Let s = 6 + a. Factor -j**2 + 0 + 1/2*j**s + 1/2*j.
j*(j - 1)**2/2
Factor -16/5 + 2/5*v**3 + 2*v**2 + 4/5*v.
2*(v - 1)*(v + 2)*(v + 4)/5
Let v = -24 - -27. Let d(u) be the first derivative of 0*u - 2 - 1/3*u**v + 1/2*u**2. Solve d(a) = 0 for a.
0, 1
Let p(f) be the first derivative of -4 - 1/5*f + 0*f**2 + 1/15*f**3. Solve p(h) = 0 for h.
-1, 1
Let o(l) = 6*l**2 - 4*l + 2. Let b be o(1). Let f be 8*b/(-18) - -2. Determine i, given that 22/9*i + f + 146/9*i**3 + 112/9*i**4 + 86/9*i**2 + 32/9*i**5 = 0.
-1, -1/4
Let h(o) = -3*o**3 + 0*o**3 + 3*o**3 + 1 + 3*o**3 - o**2. Let f be h(1). Factor d**2 + 0 - 1/4*d**f - d.
-d*(d - 2)**2/4
Let d be 1*(-3 - 1 - -9). Let v(j) be the second derivative of 2*j + 2*j**4 + 1/5*j**6 + 0 - 2*j**3 + j**2 - j**d. Find b such that v(b) = 0.
1/3, 1
Let r(c) = -8*c**3 + 64*c**2 - 64*c + 28. Let s be (-18)/117 - 74/26. Let h(m) = -m**3 + 9*m**2 - 9*m + 4. Let v(z) = s*r(z) + 20*h(z). Factor v(x).
4*(x - 1)**3
Let 0 - 3/5*r**4 + 6/5*r + 12/5*r**3 - 3*r**2 = 0. Calculate r.
0, 1, 2
Let w(v) be the first derivative of -11*v**5/10 + 7*v**4/8 + v**3 - 3*v**2 + 4. Let x(n) be the second derivative of w(n). Find k, given that x(k) = 0.
-2/11, 1/2
Let h be (17 + -8)*(0 + 2/3). Let c(g) be the third derivative of -3*g**2 + 0*g + 1/420*g**h + 0*g**3 + 1/210*g**5 + 0*g**4 + 0. Factor c(d).
2*d**2*(d + 1)/7
Let j(m) be the second derivative of 3*m**5/20 - m**3/2 - 5*m. Let j(z) = 0. What is z?
-1, 0, 1
Let d be -6 + 85/15 - (-4)/6. Solve -j**3 + 0 + 0*j - j**4 - 1/3*j**5 - d*j**2 = 0 for j.
-1, 0
Let b be 49/14*2*1. Let m(q) = 5*q**2 + 7*q + 7. Let z(v) = -4*v + 2. Let h be z(2). Let t(k) = 4*k**2 + 6*k + 6. Let n(p) = b*t(p) + h*m(p). Factor n(c).
-2*c**2
Let r(p) be the second derivative of -p**7/105 + p**5/25 - p**3/15 + 5*p. Factor r(c).
-2*c*(c - 1)**2*(c + 1)**2/5
Let 1/6*k**3 - 4/3 + 2*k - k**2 = 0. Calculate k.
2
Let g be (-226)/(-154) + 2/(-11). Factor -12/7*l**2 + 12/7*l - g*l**3 + 0.
-3*l*(l + 2)*(3*l - 2)/7
Factor 0 + m + 3/2*m**2 + 1/2*m**3.
m*(m + 1)*(m + 2)/2
Suppose 4*c - 3*c = 3. Factor k**4 - k**2 - k**3 - 2*k + c*k + 0*k**3.
k*(k - 1)**2*(k + 1)
Let 4/7 - 4/7*b**2 - 2/7*b**3 + 2/7*b = 0. What is b?
-2, -1, 1
Let o = 29 - 10. Let h = o + -19. Factor h + 0*d + 0*d**2 + 2/7*d**4 + 2/7*d**3.
2*d**3*(d + 1)/7
Determine r so that r - 4*r + 8*r - 5*r**2 - 20 - 25*r = 0.
-2
Let t(n) be the second derivative of 169*n**4/36 - 26*n**3/9 + 2*n**2/3 - 6*n. Solve t(a) = 0.
2/13
Find m such that 4*m**4 - 11/4*m**3 + 0 - 7/4*m**5 + 0*m + 1/2*m**2 = 0.
0, 2/7, 1
Let r(q) be the first derivative of q**5/35 - q**4/28 - 8*q**3/21 + 6*q**2/7 + 11. Factor r(a).
a*(a - 2)**2*(a + 3)/7
Suppose 2*p - 12 = -p. Suppose 0*d = -p*d + 24. What is u in -d*u + 4*u - u**3 - 2*u**5 + 5*u**3 = 0?
-1, 0, 1
Let m(o) be the first derivative of o**4 + 8*o**3/15 - 2*o**2 - 8*o/5 - 21. Solve m(y) = 0 for y.
-1, -2/5, 1
Let d(v) be the second derivative of v**5/4 - 35*v**4/12 + 20*v**3/3 + 40*v**2 - 22*v. Solve d(p) = 0.
-1, 4
Let u(d) be 