
-5*(i + 8)*(3*i - 2)**2
Suppose 3*j + 12 = 3*o, 4*o + 4*j - 8 = -0*o. Determine n so that 2/9*n**2 + 0*n + 2/9*n**4 + 0 - 4/9*n**o = 0.
0, 1
Factor 0 - 12/7*w + 3/7*w**2.
3*w*(w - 4)/7
Let a = 670/1661 - 6/151. Let n = -14/15 - -184/165. Factor -n*t**2 - 6/11*t - a.
-2*(t + 1)*(t + 2)/11
Solve -8/3*t**2 + 0 - 4/3*t - 1/3*t**4 - 5/3*t**3 = 0 for t.
-2, -1, 0
Let z(x) = x**4 + x**3 - x**2 - x. Let o(p) = 10*p**4 + 25*p**3 + 20*p**2 + 5*p. Suppose 4*t - 5 = -t. Let f(j) = t*o(j) + 2*z(j). Factor f(d).
3*d*(d + 1)**2*(4*d + 1)
Let b be 23/(-161) + (-11)/(-28). Factor 0*a + 1/4 - b*a**2.
-(a - 1)*(a + 1)/4
Let w = 53 - 51. Find a, given that -6/7*a + 2/7*a**w + 4/7 = 0.
1, 2
Let p(z) be the first derivative of 0*z**2 + 0*z - 2 + 2/3*z**3. Factor p(o).
2*o**2
Factor 0*v**2 + 0 + 0*v**3 + 0*v - 2/15*v**4 - 2/15*v**5.
-2*v**4*(v + 1)/15
Let o(a) = -24*a**3 - 24*a**2 + 14. Let w(m) = 5*m**3 + 5*m**2 - 3. Let p(z) = 3*o(z) + 14*w(z). Determine x, given that p(x) = 0.
-1, 0
Let m = -40 - -44. Let i(b) be the second derivative of 1/3*b**3 + 0*b**2 + 1/6*b**m + 0 + 3*b. Factor i(r).
2*r*(r + 1)
Let t(z) be the first derivative of -z**9/3024 - z**8/840 + z**6/180 + z**5/120 + z**3/3 - 1. Let a(i) be the third derivative of t(i). Factor a(v).
-v*(v - 1)*(v + 1)**3
Let s(u) be the third derivative of 0 - 1/30*u**6 + 1/5*u**5 - 8/3*u**3 + 0*u - 4*u**2 + 0*u**4. Let s(y) = 0. What is y?
-1, 2
Let p(d) be the third derivative of -d**9/68040 + d**8/7560 - d**7/2268 + d**6/1620 - d**4/3 + 2*d**2. Let m(w) be the second derivative of p(w). Factor m(n).
-2*n*(n - 2)*(n - 1)**2/9
Let y(u) be the second derivative of -u**7/189 - 2*u**6/135 - u**5/90 - 10*u. Factor y(r).
-2*r**3*(r + 1)**2/9
Let f = -12 + 12. Let v(s) be the third derivative of f + 1/3*s**3 + 0*s**4 + 2*s**2 + 0*s - 1/30*s**5. Factor v(y).
-2*(y - 1)*(y + 1)
Suppose n + 11 - 47 = -3*r, r - 7 = -2*n. Let j(h) = -3*h**3 - 3*h**2 + 3*h - 3. Let f(k) = 7*k**3 + 5*k**2 - 5*k + 6. Let y(x) = r*j(x) + 6*f(x). Factor y(v).
3*(v - 1)**3
Let v = 1 - -1. Factor -2/7*u**4 + 6/7*u**v + 8/7*u - 4/7*u**3 - 8/7.
-2*(u - 1)**2*(u + 2)**2/7
Let r(o) = o + 8. Let v be r(-4). Suppose 2*b = 3*b - v. Solve 2*p**4 - p**b + 9*p**2 + 2 - 4*p - 5*p**3 - 3*p = 0.
1, 2
Let m(s) be the first derivative of -s**4/6 - 2*s**3 - 8*s**2 - 32*s/3 - 37. Let m(x) = 0. Calculate x.
-4, -1
Let v be (-75)/5*(1 + -2). Let m = v + -15. Let m + 0*r + 1/4*r**2 = 0. What is r?
0
Suppose -4*k + 8 + 8 = 0. Suppose 4*v = 6*v - k. Factor 1/2*x**3 - 1/2 + 1/2*x**v - 1/2*x.
(x - 1)*(x + 1)**2/2
Let b = -1/21 + 8/21. Let t(f) be the first derivative of b*f**3 - 3 + f + f**2. Solve t(h) = 0 for h.
-1
Suppose -2*i + 39 = -3*c, 9*i - 107 = 4*i - 2*c. Let t be 1/(-2) - i/(-6). Suppose 2*b**2 - b**3 - b**2 + t*b**2 + 3*b**3 = 0. Calculate b.
-2, 0
Let a = -257/7 - -37. Find b, given that 6/7*b**4 + 0*b + a*b**5 + 0 + 6/7*b**3 + 2/7*b**2 = 0.
-1, 0
Let i(k) = k**4 - 6*k**3 + 13*k**2 - 17*k - 1. Let n(u) = u**4 - 6*u**3 + 13*u**2 - 18*u - 2. Let r(v) = 6*i(v) - 5*n(v). Factor r(s).
(s - 2)**2*(s - 1)**2
Let i(u) be the third derivative of -7*u**6/360 + u**5/6 - u**4/2 + 4*u**3/9 + u**2. Find z such that i(z) = 0.
2/7, 2
Let k be 375/6*(-4)/(-5). Let g be (60/k)/(9/10). Suppose 2/3 + g*d + 2/3*d**2 = 0. What is d?
-1
Suppose 3*v + 7 + 23 = 0. Let p be 4/v - (-9)/10. Solve -3/2*b**3 - p + 1/2*b**2 + 3/2*b = 0 for b.
-1, 1/3, 1
Suppose -2*r = 3*o - 6, 2 - 12 = -3*r - 5*o. Suppose -2/3*l**3 + r*l**2 + 1/3 - 1/3*l**4 + 2/3*l = 0. What is l?
-1, 1
Let t(m) be the second derivative of -3*m**5/80 + 3*m**4/8 - 3*m**3/2 + 3*m**2 - m. Suppose t(u) = 0. Calculate u.
2
Let j be 2 + 6 - 1 - -3. Let b be (1/(-5))/(j/(-25)). Factor -1/2 - 2*d**2 + b*d**4 + 1/4*d**5 - 1/2*d**3 - 7/4*d.
(d - 2)*(d + 1)**4/4
Let c(n) be the third derivative of 3*n**2 - 1/168*n**8 + 0*n**5 + 0 + 0*n + 1/105*n**7 + 0*n**3 + 0*n**4 + 0*n**6. Factor c(t).
-2*t**4*(t - 1)
Let u(c) be the first derivative of c**6/42 + 3*c**5/35 - c**4/7 - 16*c**3/21 + 16*c/7 + 37. Determine w, given that u(w) = 0.
-2, 1, 2
Let x(a) = 3*a - 2. Let q be x(2). Let o = -193 + 195. Factor 0*f**o + 0 + 0*f + f**3 + 7/2*f**q.
f**3*(7*f + 2)/2
Let f(t) = -2*t - 14. Let d be f(-7). Factor 2/5*s**3 + 0 - 1/5*s + d*s**2 + 0*s**4 - 1/5*s**5.
-s*(s - 1)**2*(s + 1)**2/5
Let m(c) be the first derivative of -c**6/27 + 2*c**5/45 + c**4/9 - 4*c**3/27 - c**2/9 + 2*c/9 + 3. Factor m(h).
-2*(h - 1)**3*(h + 1)**2/9
Let x(z) = z. Let c(s) = s**2 - s. Let q(t) = c(t) - x(t). Let q(o) = 0. What is o?
0, 2
Let c(x) = x + 8. Let m be c(-6). Let l(g) be the second derivative of 1/2*g**2 + m*g + 1/3*g**3 + 0 + 0*g**4 - 1/30*g**6 - 1/10*g**5. Factor l(k).
-(k - 1)*(k + 1)**3
Let m(s) be the second derivative of -s**9/1512 - s**8/420 - s**7/420 + s**3/3 + 5*s. Let t(w) be the second derivative of m(w). Determine x so that t(x) = 0.
-1, 0
Suppose -48 + 18 = -10*u. Let o(q) be the first derivative of -3 - 6*q - q**u - 9/2*q**2. Find l, given that o(l) = 0.
-2, -1
Let v(c) be the second derivative of -2/3*c**3 + 5/6*c**4 + 1/15*c**6 + 0 - 2/5*c**5 - 2*c + 0*c**2. Determine x so that v(x) = 0.
0, 1, 2
Let g(l) = 6*l**4 - 46*l**3 - 46*l**2 + 6*l - 16. Let j(o) = -o**4 + 9*o**3 + 9*o**2 - o + 3. Let m(q) = -3*g(q) - 16*j(q). Factor m(k).
-2*k*(k + 1)**3
Factor 0*i - 3/4*i**4 + 3/4*i**3 + 0 + 3/2*i**2.
-3*i**2*(i - 2)*(i + 1)/4
Let i(t) = -14*t**2 + 32*t - 12. Let f(z) = -28*z**2 + 64*z - 25. Let r = -1 - -5. Let n(v) = r*f(v) - 9*i(v). Factor n(k).
2*(k - 2)*(7*k - 2)
Factor -r**3 + 1 - 6*r**2 + 5*r**2 - 5*r + 6*r.
-(r - 1)*(r + 1)**2
Suppose 4*m + 11 = 27. Let n(w) be the second derivative of 0*w**m + 0*w**2 + 0*w**3 + 0 - 1/20*w**5 - 2*w. Solve n(f) = 0.
0
Let l(f) be the first derivative of 6 + 6*f**2 - 4/3*f**3 + 0*f. Factor l(a).
-4*a*(a - 3)
Let c be 24/(-9) + 2 - -1. Factor 1/3*x**2 + c*x - 2/3.
(x - 1)*(x + 2)/3
Let d(x) be the first derivative of 10 - 4*x - 5/2*x**2 - 1/3*x**3. Find r, given that d(r) = 0.
-4, -1
Suppose 5*r - z - 20 = z, -r - 13 = 3*z. Factor 2/3*h**r - 1/3*h**5 + 0*h + 0 + 4/3*h**4 - 5/3*h**3.
-h**2*(h - 2)*(h - 1)**2/3
Let s(f) be the second derivative of -f**5/300 + f**3/30 - 2*f**2 - 4*f. Let r(o) be the first derivative of s(o). Factor r(w).
-(w - 1)*(w + 1)/5
Let u be (-2)/(-31) - 840/(-7161). Let 2/11 - 2/11*l**2 - u*l**3 + 2/11*l = 0. Calculate l.
-1, 1
Let f(g) be the first derivative of 0*g**2 + 3 - 1/12*g**4 - 1/18*g**3 + 1/60*g**5 - 3*g + 1/30*g**6. Let j(a) be the first derivative of f(a). Factor j(z).
z*(z - 1)*(z + 1)*(3*z + 1)/3
Factor 1/2*p - 1/2*p**2 + 1.
-(p - 2)*(p + 1)/2
Let q(z) be the third derivative of z**7/630 - z**6/180 + z**4/36 - z**3/18 - 12*z**2. Factor q(b).
(b - 1)**3*(b + 1)/3
Let j(n) be the third derivative of n**6/600 - n**4/120 + 4*n**2. Let j(z) = 0. What is z?
-1, 0, 1
Let o = 17 + -13. Let k(s) be the second derivative of 1/10*s**5 + 0*s**2 + 1/6*s**o - s + 0 + 0*s**3. Factor k(p).
2*p**2*(p + 1)
Suppose 19*o = 18*o + 2. Factor -2/9*u**o - 2/3*u - 4/9.
-2*(u + 1)*(u + 2)/9
Let b be (-6 - -3) + (7 - 2). Suppose 1 - b + 2*i - 1 + 0 - 2*i**3 + 2*i**2 = 0. Calculate i.
-1, 1
Let c(j) be the third derivative of -j**7/735 + j**5/70 + j**4/42 - 4*j**2. Solve c(l) = 0.
-1, 0, 2
Suppose 0 = 5*f + 2*y - 10, -f + 2*y - 4*y + 10 = 0. Let s(c) be the first derivative of f*c**2 + 0*c - 1 + 2/3*c**3. Suppose s(p) = 0. What is p?
0
Let t(v) = -v**2 + 4*v + 3. Let f be t(4). Factor b**f + 4*b**2 - 3*b**2 - 2*b**2.
b**2*(b - 1)
Let t = 59 + -56. What is v in -1/4*v**2 + v + 1/4 - v**t = 0?
-1, -1/4, 1
Let x = 26 - 24. Solve -o**x - 19*o + 19*o - 2*o**2 = 0.
0
Factor -13*s**3 - 3*s**4 + 4*s**3 + 635*s**2 - 641*s**2.
-3*s**2*(s + 1)*(s + 2)
Let n = -1643/5 - -330. Let v be (-16 - 2)*(-9)/30. Find o such that -2/5*o - v*o**3 - n*o**5 + 0 - 13/5*o**2 - 23/5*o**4 = 0.
-1, -2/7, 0
Suppose 2*f + 0 + 2 = -y, -5*f - 4*y - 8 = 0. Let t(h) be the second derivative of 0*h**2 - 2*h - 1/66*h**4 - 2/33*h**3 + f. Factor t(o).
-2*o*(o + 2)/11
What is p in 0 - 1/4*p**2 - 1/4*p = 0?
-1, 0
Determine g, given that 4/11*g**4 + 0*g**3 + 2/11*g**5 - 2/11*g + 0 - 4/11*g**2 = 0.
-1, 0, 1
Let x(f) be the second derivative of -2/5*f**5 + 0 - 2/3*f**3 - 4*f + 3/2*f**4 + 0*f**2. Let x(d) = 0. Calculate d.
0, 1/4, 2
Let h(p) be th