- 1/6*n**3 + x + 1/6*n**2.
-n**2*(n - 1)/6
Let j(x) be the first derivative of -1/12*x**3 + 0*x**2 + 1/16*x**4 + 1 + 0*x. Factor j(d).
d**2*(d - 1)/4
What is o in 0 + 0*o**2 + 0*o - 9/2*o**5 - 3*o**4 + 3/2*o**3 = 0?
-1, 0, 1/3
Let i(t) be the first derivative of t**6/27 + 2*t**5/15 + t**4/18 - 2*t**3/9 - 2*t**2/9 + 9. Solve i(r) = 0 for r.
-2, -1, 0, 1
Let s(p) be the first derivative of 7/4*p**3 - 2 - 3/8*p**2 - 3/2*p**4 + 0*p - 12/5*p**5. Suppose s(k) = 0. Calculate k.
-1, 0, 1/4
Factor 2 + 3/2*v**2 - 3*v - 1/4*v**3.
-(v - 2)**3/4
Let y = 368/595 - 4/85. Let -2/7 + 4/7*o + 2/7*o**4 + 0*o**2 - y*o**3 = 0. What is o?
-1, 1
Let j(k) = -k**2 + 9*k - 5. Let s be j(5). Suppose 3*t - 11 = 5*u + s, 16 = -4*u. Find n such that 2/3*n**t + 0 - 4/3*n = 0.
0, 2
Suppose 0 = -11*n - 0*n. Determine i so that 1/4*i**3 + n - 1/2*i - 1/4*i**2 = 0.
-1, 0, 2
Suppose -4*w + 60 = 3*b - b, 3*w + 4*b - 40 = 0. Let c be 5/6 - 8/w. Determine o, given that 0 - 1/3*o**5 + 1/3*o**2 + c*o**3 - 1/3*o**4 + 0*o = 0.
-1, 0, 1
Let g(b) = b**3 + 8*b**2 - 10*b - 6. Let a be g(-9). Let k = a + -1. Factor 4/3 - 2/3*t**k - 2/3*t.
-2*(t - 1)*(t + 2)/3
Let y(g) be the first derivative of -g**6/156 + 7*g**5/390 - g**4/78 - g**2 - 4. Let o(a) be the second derivative of y(a). Factor o(c).
-2*c*(c - 1)*(5*c - 2)/13
Let g = -90 + 90. Let s(k) be the third derivative of 0*k**3 + g*k + 0*k**4 - 1/315*k**7 + 1/60*k**6 + 0 - 3*k**2 - 1/45*k**5. Suppose s(w) = 0. What is w?
0, 1, 2
Let d(k) be the first derivative of -k**9/1512 + k**8/210 - k**7/105 - 2*k**3/3 + 2. Let g(h) be the third derivative of d(h). Factor g(o).
-2*o**3*(o - 2)**2
Factor -1/3*t**2 + 1/6 + 1/6*t**4 + 0*t + 0*t**3.
(t - 1)**2*(t + 1)**2/6
Let n be -4 + 0 + (-104)/(-22). Factor n*a + 24/11*a**2 + 0 + 18/11*a**3.
2*a*(3*a + 2)**2/11
Let q(h) be the second derivative of -h**6/1080 + h**5/360 + 2*h**3/3 + 5*h. Let x(r) be the second derivative of q(r). Solve x(n) = 0.
0, 1
Suppose 0 = -2*u - 2*u + 16. Find r, given that 5*r**3 - r**3 + 0*r**u - 2*r**2 + 4*r**4 - 6*r**4 = 0.
0, 1
Let b(s) be the second derivative of s**5/240 + s**4/96 + 3*s**2/2 + s. Let t(p) be the first derivative of b(p). Find u such that t(u) = 0.
-1, 0
Let p(n) be the first derivative of -n**4/4 + n**3 - 7*n - 3. Let j(k) be the first derivative of p(k). Solve j(m) = 0 for m.
0, 2
Suppose -4*f + 18 + 2 = 0. Suppose 0*j + 5*j = 25. Let f*x**3 - 2*x**j - 2*x**4 - 5*x**3 = 0. Calculate x.
-1, 0
Suppose i = -2*i + 12. Let q be 1/i - 4/(-112). Let -2/7*n + 0 - q*n**2 = 0. What is n?
-1, 0
Let a(x) be the third derivative of -x**8/672 + x**7/105 - x**6/48 + x**5/60 - 12*x**2. Factor a(p).
-p**2*(p - 2)*(p - 1)**2/2
Let j(f) be the first derivative of -f**4/4 + f**3 - 3*f**2/2 - 5*f + 2. Let k(m) be the first derivative of j(m). Let k(u) = 0. Calculate u.
1
Suppose 0 + 1/5*h + 2/5*h**2 + 1/5*h**3 = 0. Calculate h.
-1, 0
Let k = -135 + 138. Factor -3 + 3/2*l**2 - 9/2*l + 9/2*l**k + 3/2*l**4.
3*(l - 1)*(l + 1)**2*(l + 2)/2
Let i(c) be the first derivative of -c**4/8 - c**3/2 - 3*c**2/4 - c/2 + 15. What is u in i(u) = 0?
-1
Let x(y) be the third derivative of y**6/180 - y**5/90 - y**4/36 + y**3/9 - 10*y**2. Let x(h) = 0. Calculate h.
-1, 1
Let l(c) be the third derivative of -c**8/840 - 2*c**7/525 + 3*c**6/100 + c**5/75 - 2*c**4/15 - 63*c**2. Solve l(n) = 0.
-4, -1, 0, 1, 2
Suppose 0 = 2*k + 33 - 41. Suppose 5 = -3*l + 2*l, 20 = -c - 4*l. Factor 2/3*i**5 + 0 + 2/3*i + 0*i**2 - 4/3*i**3 + c*i**k.
2*i*(i - 1)**2*(i + 1)**2/3
Let q(v) = 16*v - 29. Let k be q(2). Factor k*i - 9/2*i**2 + 0 + 3/2*i**4 + 0*i**3.
3*i*(i - 1)**2*(i + 2)/2
Suppose -15*s**3 + 9*s**2 + 24*s - 17 + 12*s + 29 = 0. Calculate s.
-1, -2/5, 2
Suppose 3*l + 2*l + 10 = 0. Let q be (l - 0)*(-2)/12. Let -1/3*u - q*u**2 + 0 = 0. What is u?
-1, 0
Let t = -45 - -30. Let s = -13 - t. Factor -2/3*c + 2/3*c**s - 4/3.
2*(c - 2)*(c + 1)/3
Let r(d) be the second derivative of 0*d**2 + 0*d**4 + 1/6*d**3 + 0 + 5*d - 1/20*d**5. Factor r(j).
-j*(j - 1)*(j + 1)
Let j(i) = -i**2. Let w(m) = m**2 + 2*m. Suppose 5*x - 18 = u, -5*x + 5*u + 30 = -0*u. Let y(l) = x*j(l) + w(l). Factor y(a).
-2*a*(a - 1)
Let h(b) be the first derivative of -b**6/9 - 8*b**5/45 - b**4/18 + 1. Factor h(c).
-2*c**3*(c + 1)*(3*c + 1)/9
What is o in 1/3*o**2 + 1/3*o**3 + 0 + 0*o = 0?
-1, 0
Factor 3*f - f**2 + 3*f + 0*f - 6*f**3 + 2*f**4 + 3*f**2 - 4.
2*(f - 2)*(f - 1)**2*(f + 1)
Factor 539*q + 2916 - 12*q**2 + 126*q**2 + 4*q**3 - 6*q**2 + 433*q.
4*(q + 9)**3
Let p(q) be the first derivative of 49/30*q**4 + 1 + 4/5*q**2 + q + 28/15*q**3. Let c(n) be the first derivative of p(n). Suppose c(o) = 0. What is o?
-2/7
Determine g so that -23/5*g**2 + 0*g + 3/5*g**5 + 4/5 + 33/5*g**3 - 17/5*g**4 = 0.
-1/3, 1, 2
Let p = 11 - 11. Suppose 0 = 2*t - p*t. Factor t*r**2 + 2*r - 4/3 - 2/3*r**3.
-2*(r - 1)**2*(r + 2)/3
Let c(s) be the first derivative of s**8/2352 + s**7/1470 - s**6/840 - s**5/420 - 7*s**2/2 - 3. Let l(t) be the second derivative of c(t). Factor l(f).
f**2*(f - 1)*(f + 1)**2/7
Let k(i) be the second derivative of -7*i**5/90 - 5*i**4/54 + 2*i**3/27 - i. Determine o so that k(o) = 0.
-1, 0, 2/7
Factor -10*x**3 + 0 + 8*x + 2*x**4 - 16 + 5*x**2 - 8*x**2 + 15*x**2.
2*(x - 2)**3*(x + 1)
Let o(u) be the second derivative of 0*u**2 + 0 + 4*u - 1/20*u**5 - 1/12*u**4 + 1/30*u**6 + 1/6*u**3. Find x such that o(x) = 0.
-1, 0, 1
Suppose 5*t + 4*l = 10 + 1, 3*t - 10 = l. Let j(x) be the second derivative of x + 0*x**2 - 1/120*x**6 + 0 - 3/80*x**5 - 1/16*x**4 - 1/24*x**t. Factor j(u).
-u*(u + 1)**3/4
Let h be 2 + 0 + -3 - 9. Let t be 6/4 - h/(-12). Factor -2*r + 2*r**2 + t - 2/3*r**3.
-2*(r - 1)**3/3
Let 3/5*t - 1/5*t**3 + 0*t**2 + 2/5 = 0. What is t?
-1, 2
Find y such that 2/11*y**2 + 6/11 + 8/11*y = 0.
-3, -1
Suppose -2 = 2*l - 12. Let a be 0 - 3 - (-30)/l. Let 4*z**2 - 2*z**3 - 3*z**2 + 2*z**3 + z**a = 0. What is z?
-1, 0
Let w be -33*5/(-30) + -5. Let d(k) be the second derivative of -4*k + 0 - 1/4*k**4 + 1/10*k**6 + 3/20*k**5 - w*k**3 + 0*k**2. Factor d(s).
3*s*(s - 1)*(s + 1)**2
Let r be (4/10)/((-15)/(-225)). Suppose 0 = 2*b - r*b. Factor b*i + 0 + i**3 + 1/3*i**5 - 1/3*i**2 - i**4.
i**2*(i - 1)**3/3
Let i(v) = v**2 - 8*v + 16. Let u be i(4). Solve 3/7*h**2 + 0 + u*h + 3/7*h**3 = 0 for h.
-1, 0
Suppose -5*d + 3 = -s, -5*s + 4 = -3*d - 3. Factor 63/2*a**3 + d + 49/4*a**4 + 109/4*a**2 + 9*a.
(a + 1)**2*(7*a + 2)**2/4
Let w be 16/(-65) - (192/(-60))/8. Solve 0*g + w - 2/13*g**2 = 0.
-1, 1
What is r in -18*r**2 + 274*r**3 - 270*r**3 + 24*r + 0 - 8 = 0?
1/2, 2
Let c(b) = 2*b**2 + 3*b - 4. Let s be c(-3). Suppose 0 = s*w - w + 4*i - 20, -3*w - 5*i + 17 = 0. Solve 0*a + 0 + 0*a**2 - 2/5*a**5 - 2/5*a**3 - 4/5*a**w = 0.
-1, 0
Suppose 4*a - 15 = a. Determine o, given that -5*o**3 + o**3 - 11*o**2 + 2 + 2*o**3 - 2*o**3 - a*o = 0.
-2, -1, 1/4
Let z be (-65)/(-75) + (1 - (-18)/(-15)). Suppose 1/3*i**2 + 0 - z*i**3 + 2/3*i - 1/3*i**4 = 0. Calculate i.
-2, -1, 0, 1
Let h be (63/(-84))/(3/(-2)). Find w such that w**2 + 0 - h*w**3 - 1/2*w = 0.
0, 1
Factor 8/3*c + 0 - 2/3*c**4 + 4/3*c**3 + 14/3*c**2.
-2*c*(c - 4)*(c + 1)**2/3
Let o(w) = -6*w**3 - 14*w**2 - 8*w - 2. Let a(b) = -b**4 + 5*b**3 + 15*b**2 + 8*b + 2. Let y(t) = 2*a(t) + 3*o(t). Factor y(f).
-2*(f + 1)**4
Let h(n) be the second derivative of -n**7/147 - 2*n**6/35 - 13*n**5/70 - 2*n**4/7 - 4*n**3/21 + 10*n. Factor h(a).
-2*a*(a + 1)**2*(a + 2)**2/7
Let p(d) be the second derivative of 3*d**4/16 - d**3/2 - 3*d**2/2 - 11*d. Factor p(l).
3*(l - 2)*(3*l + 2)/4
Let v(y) = -3*y - 9. Let i be v(-3). Suppose -2/3*p**4 + 0*p**2 - 2/3*p**3 + i*p + 0 = 0. Calculate p.
-1, 0
Factor 16*r**3 - 8*r**3 - 6*r - 9*r**2 + 9*r**4 + 2*r**5 - 5*r**3 + r**5.
3*r*(r - 1)*(r + 1)**2*(r + 2)
Let a(r) be the second derivative of -r**5/4 + 5*r**4/4 - 5*r**3/2 + 5*r**2/2 + 31*r. Factor a(o).
-5*(o - 1)**3
Let l(f) be the first derivative of f**5/20 + 3*f**4/16 - f**2/2 + 33. Factor l(z).
z*(z - 1)*(z + 2)**2/4
Suppose 5*p - 2*p = -l, 0 = 3*p - 2*l. Let c(i) be the third derivative of p*i**5 - 2*i**2 + 1/210*i**7 + 1/120*i**6 + 0*i + 0 + 0*i**3 + 0*i**4. Factor c(z).
z**3*(z + 1)
Factor -8/5 + 8/5*z - 2/5*z**2.
-2*(z - 2)**2/5
Let p(x) be the third derivative of x**5/390 - x**4/156 - 2*x**3/13 - 16*x**2. Determine l, given that p(l) = 