+ 24*i**3 - 9*i**2 - 6*i**2 - i.
-i*(i - 1)**2*(11*i - 2)
Suppose -5*i = -o + 2*o - 19, 3*i - 17 = 5*o. Let f = 5 - i. Let -f - 13*b - b**2 + 11*b - b**2 + b**2 = 0. Calculate b.
-1
Let o(v) be the third derivative of -v**8/112 - v**7/35 + v**5/10 + v**4/8 + 16*v**2. Factor o(u).
-3*u*(u - 1)*(u + 1)**3
Suppose v = 2*k - 3*k + 5, 0 = 4*v + 2*k - 14. Factor a**2 - 6*a - 5*a**2 - 3 + a**v.
-3*(a + 1)**2
Let h(m) = -3*m + 3. Let d be h(0). Factor 1/2*t + d*t**3 + 0 + 1/2*t**5 - 2*t**4 - 2*t**2.
t*(t - 1)**4/2
Let p(b) be the second derivative of -b**5/4 + 5*b**4/2 - 25*b**3/6 + 39*b. Let p(o) = 0. Calculate o.
0, 1, 5
Suppose -92 = -m + 10. Let p = m - 302/3. Find u such that -p*u**2 - 2*u**3 + 0 + 0*u + 0*u**4 + 2/3*u**5 = 0.
-1, 0, 2
Let y(f) be the first derivative of 0*f + 2 - 2/3*f**2 - 2/9*f**3. Find c, given that y(c) = 0.
-2, 0
Let c(f) be the first derivative of -f**6/180 + f**5/90 + f**4/36 - f**3/9 - f**2 - 2. Let p(h) be the second derivative of c(h). Factor p(y).
-2*(y - 1)**2*(y + 1)/3
Let h(c) be the second derivative of 1/20*c**4 + 1/10*c**2 + 1/100*c**5 + 1/10*c**3 + 0 + 3*c. Factor h(i).
(i + 1)**3/5
Determine k so that 23*k + 2*k**3 + 2*k**3 - 3*k**3 + 13*k**2 + 11 = 0.
-11, -1
Let s(u) be the first derivative of 3/8*u**4 + 0*u**2 - 1/6*u**3 + 0*u + 1/12*u**6 - 3/10*u**5 + 1. Factor s(r).
r**2*(r - 1)**3/2
Let v be 15/(-7) - (-4)/28. Let i be v/8 - (-42)/8. Determine g so that 3/4*g**3 + 0 + 0*g + 1/4*g**2 + 3/4*g**4 + 1/4*g**i = 0.
-1, 0
Let c = -6 - -8. Let 0*s - 2/5*s**c + 2/5 = 0. What is s?
-1, 1
Let r(y) = -y**3 + 4*y**2 + 13*y - 4. Let p be r(6). Let d(l) be the second derivative of 2*l - 1/8*l**3 - 1/48*l**4 + 0 - 1/4*l**p. Factor d(u).
-(u + 1)*(u + 2)/4
Let k(f) be the third derivative of -f**7/42 - f**6/24 + f**5/4 + 25*f**4/24 + 5*f**3/3 - 36*f**2 + f. Factor k(s).
-5*(s - 2)*(s + 1)**3
Let n(a) be the third derivative of 11*a**6/120 + 13*a**5/60 + a**4/12 - 31*a**2. Factor n(y).
y*(y + 1)*(11*y + 2)
Let y(j) be the third derivative of j**9/1512 + j**8/420 - j**7/420 - j**6/90 + j**3/6 - 4*j**2. Let i(u) be the first derivative of y(u). Factor i(z).
2*z**2*(z - 1)*(z + 1)*(z + 2)
Let b(i) be the first derivative of -i**6/2 - 3*i**5/5 + 3*i**4/4 + i**3 + 24. Let b(n) = 0. What is n?
-1, 0, 1
Let z = -464/7 + 65. Let g = z + 34/21. Let -g*o**2 - 1/3 + 2/3*o = 0. What is o?
1
Let h(y) be the third derivative of -y**8/840 - y**7/105 - 3*y**6/100 - 7*y**5/150 - y**4/30 + 8*y**2. Suppose h(b) = 0. Calculate b.
-2, -1, 0
Let b(g) be the second derivative of 1/1980*g**6 + 0*g**2 + 0*g**4 + 1/2*g**3 - 1/660*g**5 + 0 + 2*g. Let z(j) be the second derivative of b(j). Factor z(x).
2*x*(x - 1)/11
Let l = -3/53 + 139/3392. Let b = 119/576 - l. Suppose -2/9*w**2 - 2/9*w + 2/9 + b*w**3 = 0. What is w?
-1, 1
Factor -4*u + 16*u**2 + 3*u**3 + 2*u**2 + 31*u.
3*u*(u + 3)**2
Let d(p) be the third derivative of p**4/24 + 2*p**3 - 2*p**2. Let z be d(-10). Determine m so that 4*m**z + 3*m**3 + 8*m**5 - 2*m**5 - 4*m**4 - 9*m**3 = 0.
-1, 0, 2/3, 1
Let c = -766 - -770. Factor 0 + 2*s**3 - c*s - 6*s**4 + 8*s**2 - 9/4*s**5.
-s*(s + 2)**2*(3*s - 2)**2/4
Let f(h) = h**4 - h + 1. Let j(c) = -11*c**4 + 4*c**3 + 9*c - 9. Let q(g) = -18*f(g) - 2*j(g). Solve q(a) = 0 for a.
0, 2
Suppose 4*j - 66*j**4 + 3*j**2 + 65*j**4 - 1 - 9*j**2 - 4*j**3 + 8*j**3 = 0. Calculate j.
1
Factor -12*x - 12*x**2 + 15*x**2 - 6*x**2.
-3*x*(x + 4)
Let l(m) be the second derivative of -3*m**5/80 + 3*m**4/16 - 3*m**2/2 - 48*m. Factor l(t).
-3*(t - 2)**2*(t + 1)/4
Let t(f) be the third derivative of 0*f - 7/12*f**4 + 3/10*f**5 + 1/105*f**7 + 0 - 1/12*f**6 + 2/3*f**3 - 2*f**2. Find d, given that t(d) = 0.
1, 2
Let u(i) be the second derivative of -i**6/900 - i**5/300 + i**3/6 + 4*i. Let a(w) be the second derivative of u(w). Factor a(n).
-2*n*(n + 1)/5
Suppose -4*t = -0*k - 2*k - 10, -23 = -k - 5*t. Let v be (-12)/(-2) - (3 + 1). Factor -1/2*w**k - v*w - 2*w**2 + 0.
-w*(w + 2)**2/2
Let 1/4*f**2 + 0 + 0*f = 0. Calculate f.
0
Let 0 + 0*o - 5/4*o**2 = 0. What is o?
0
Let n(r) = -r**2 + 11*r - 4. Let u be n(10). Let o(p) = p - 3. Let i be o(u). Determine x so that -1/2 - x + 1/2*x**4 + x**i + 0*x**2 = 0.
-1, 1
Find l, given that -6/7*l**2 + 0 - 3/7*l**5 + 3/7*l**3 + 6/7*l**4 + 0*l = 0.
-1, 0, 1, 2
Let q(j) be the first derivative of j**6/30 + 3*j**5/20 + j**4/12 - j**3/2 - j**2 - j + 2. Let s(h) be the first derivative of q(h). Factor s(a).
(a - 1)*(a + 1)**2*(a + 2)
Let c(w) be the third derivative of -w**6/40 + 11*w**5/60 - w**4/2 + 2*w**3/3 - 16*w**2. Let c(t) = 0. Calculate t.
2/3, 1, 2
Factor -15*p**3 + p + 13 - 12*p**2 - 1 + 8*p + 6*p.
-3*(p - 1)*(p + 1)*(5*p + 4)
Suppose -p = 3*t - 8*t + 17, 0 = 5*t + p - 13. Let g(m) be the second derivative of -1/6*m**2 + 0*m**3 + 1/36*m**4 - t*m + 0. Suppose g(d) = 0. Calculate d.
-1, 1
Let -4 + 111*k**3 + 4*k**2 - 221*k**3 - 14*k + 124*k**3 = 0. What is k?
-1, -2/7, 1
Let d(h) be the second derivative of h**7/147 - h**6/105 - h**5/35 + h**4/21 + h**3/21 - h**2/7 - 10*h. Let d(j) = 0. What is j?
-1, 1
Let a(q) be the third derivative of -q**6/360 + q**5/180 + q**4/72 - q**3/18 + 12*q**2. Let a(s) = 0. Calculate s.
-1, 1
Let h(b) be the third derivative of b**8/2016 + b**7/420 + b**6/720 - b**5/120 - b**4/72 + 8*b**2. Factor h(m).
m*(m - 1)*(m + 1)**2*(m + 2)/6
Let a(r) be the second derivative of r**5/270 + r**4/18 + r**3/3 + 5*r**2/2 - 4*r. Let m(j) be the first derivative of a(j). Suppose m(d) = 0. What is d?
-3
Let c be 4 + (4 - -2)/(-3). Let q(x) be the first derivative of -2/15*x**3 - 1/10*x**4 + 1/5*x**c - 1 + 2/5*x. Let q(w) = 0. Calculate w.
-1, 1
Let w(y) be the third derivative of y**10/75600 - y**8/5040 + y**6/360 + y**5/20 - y**2. Let b(c) be the third derivative of w(c). Factor b(u).
2*(u - 1)**2*(u + 1)**2
Let k(b) be the first derivative of b**2 - 1 - 1/84*b**4 - 1/420*b**6 - 1/105*b**5 + 0*b**3 + 0*b. Let m(y) be the second derivative of k(y). Factor m(h).
-2*h*(h + 1)**2/7
Let p(z) = -z**2 - 5*z + 5. Let x be p(-5). Let t be 20/25*x/6. Suppose -2/3*l**3 + 1/3*l**4 - 1/3 + 0*l**2 + t*l = 0. What is l?
-1, 1
Let j(y) = y**3 + 5*y**2 + 5*y + 6. Let g be j(-4). Suppose 0 = 4*a - 10 + g. Factor f**3 + 3/4*f**4 + 1/4*f**a + 0 + 0*f.
f**2*(f + 1)*(3*f + 1)/4
Let j(w) = -4*w**5 + 11*w**3 - 7*w**2 + 7*w + 7. Let y(x) = 2*x**5 - 6*x**3 + 4*x**2 - 4*x - 4. Let v(q) = 4*j(q) + 7*y(q). Factor v(l).
-2*l**3*(l - 1)*(l + 1)
What is y in 5*y**2 - 27 - 31 - 5*y + 28 = 0?
-2, 3
Let h(r) be the second derivative of 1/5*r**5 + 0 - 16*r**2 - 8/15*r**6 + 10/3*r**4 - 4*r + 2/21*r**7 - 8/3*r**3. Factor h(a).
4*(a - 2)**3*(a + 1)**2
Let -1/4*x**4 - 1/4*x**3 + 0 + 1/4*x**2 + 1/4*x**5 + 0*x = 0. What is x?
-1, 0, 1
Suppose 8 = -0*u + 4*u + 3*a, 2*a - 11 = 3*u. Let t be 1/5*-1*u. Let t + 0*n - 1/5*n**2 = 0. What is n?
-1, 1
Let m = -21 - -21. Suppose 2*w + 10 = -4*b, 4*b - 10 = -m*w + 2*w. Let 1/2*g**4 + 2*g**3 + b + 2*g**2 + 0*g = 0. What is g?
-2, 0
Let x(k) be the third derivative of -1/480*k**6 + 0*k**3 + 0*k**4 + 0 - 2*k**2 - 1/240*k**5 + 0*k. Find w such that x(w) = 0.
-1, 0
Let g(j) be the third derivative of 0*j**3 + 0*j + 1/75*j**5 - 4*j**2 + 1/60*j**4 + 1/300*j**6 + 0. Suppose g(z) = 0. What is z?
-1, 0
Let x(h) be the third derivative of -4/105*h**7 + h**2 + 1/15*h**6 - 1/30*h**5 + 0*h + 0*h**4 + 0 + 0*h**3. Solve x(g) = 0 for g.
0, 1/2
Let p = -4 + 8. Let n(g) be the third derivative of 0 + 1/180*g**6 - 1/36*g**p - 1/180*g**5 - g**2 + 1/18*g**3 + 0*g. Determine a, given that n(a) = 0.
-1, 1/2, 1
Let s(c) be the third derivative of -c**8/3360 - c**7/1680 + c**5/20 + 3*c**2. Let b(x) be the third derivative of s(x). Find t such that b(t) = 0.
-1/2, 0
Suppose 441 = -4*x + 1357. Let u = -2517/11 + x. Let -2/11 + 4/11*d - u*d**2 = 0. What is d?
1
Let g = 5 - 6. Let h be ((-4 - -3) + 1)/g. What is j in -3/4*j**3 - 1/2*j**2 + 1/4*j**5 + 0*j + h*j**4 + 0 = 0?
-1, 0, 2
Let q(k) be the second derivative of k**7/21 - 2*k**6/15 - k**5/5 + 2*k**4/3 + k**3/3 - 2*k**2 - 14*k. Let q(f) = 0. What is f?
-1, 1, 2
Factor 1/2*r + 0 + 1/2*r**2.
r*(r + 1)/2
Suppose 2*u = 13*u - 22. Factor 3/4*s + 3/4*s**3 + 0 + 3/2*s**u.
3*s*(s + 1)**2/4
Let j(t) be the first derivative of 7/2*t**2 + 1 + 5/3*t**3 + 2*t. Factor j(c).
(c + 1)*(5*c + 2)
Let x(p) = -p**3 + 4*p*