 1. Let h be r(-1). Suppose 0*n**2 - h + 1 + n**2 = 0. Calculate n.
-1, 1
Let d(f) = f - 6. Let v be d(8). Determine s so that -v*s**4 + s**3 - s**4 - 4*s**3 - s**2 - s**5 = 0.
-1, 0
Suppose -x = 4*z + 1, 4*z + 4*x + 8 - 4 = 0. Let y(a) be the second derivative of -1/12*a**4 - a + z - 1/30*a**6 - 1/10*a**5 + 0*a**3 + 0*a**2. Factor y(j).
-j**2*(j + 1)**2
Suppose -2*a - 5 = -13. Let x(p) be the third derivative of 0*p - 1/36*p**a - 2/27*p**3 + 3*p**2 - 1/270*p**5 + 0. Suppose x(k) = 0. Calculate k.
-2, -1
Suppose -42 = -q - 3*t, -3*t = 5*q + 2*t - 210. Suppose -5*d = -7*d + q. Suppose -d*l**3 + l**2 - 7*l**2 + 6*l**4 - 16*l**5 + 37*l**5 = 0. What is l?
-1, -2/7, 0, 1
Factor -2*g**2 - 1 + g**2 + 1 + g.
-g*(g - 1)
Suppose -61 = -5*y + 29. Factor -y*z + 1 + 12*z**2 + 6*z**3 - 6*z**2 + 2*z**3 + 3.
2*(z - 1)*(z + 2)*(4*z - 1)
Let o(v) be the second derivative of v**6/195 - v**4/39 + v**2/13 - 2*v. Factor o(d).
2*(d - 1)**2*(d + 1)**2/13
Let m(v) = v**3 - 4*v**2 - 3*v. Let g be m(5). Suppose -4*l + 11 = u, -3*l - u + 2*u = -g. Factor -4 + 0*h**l - 2*h + 2*h**3 + 4*h**2 + 0*h**3.
2*(h - 1)*(h + 1)*(h + 2)
Let d(b) = b**3 + 12*b**2 + b + 15. Let a be d(-12). Solve -3 + s**5 - s + 16*s**4 - 6*s**a - 7*s**5 + 13*s - 12*s**2 - s**4 = 0.
-1, 1/2, 1
Let c(p) = 19*p**3 - 9*p**2 - 10*p - 4. Let z(q) = -18*q**3 + 9*q**2 + 9*q + 3. Let o(f) = 3*c(f) + 4*z(f). Factor o(r).
-3*r*(r - 1)*(5*r + 2)
Let p(o) = 5*o**2 - 5*o - 2. Let y(w) = 11*w**2 - 11*w - 4. Let c(i) = -9*p(i) + 4*y(i). Factor c(z).
-(z - 2)*(z + 1)
Let s = 1114/1405 - -2/281. Solve -s - 4/5*w**3 + 4/5*w + 4/5*w**2 = 0.
-1, 1
Let f(o) be the second derivative of o**6/200 - 2*o**5/75 + 7*o**4/120 - o**3/15 + o**2 + o. Let i(k) be the first derivative of f(k). Factor i(s).
(s - 1)**2*(3*s - 2)/5
Let k(s) be the third derivative of s**8/6720 + s**7/1800 + s**6/1800 - s**4/24 - s**2. Let w(z) be the second derivative of k(z). Factor w(o).
o*(o + 1)*(5*o + 2)/5
Let b(a) be the first derivative of -a**4/14 + 3*a**2/7 - 4*a/7 + 3. What is g in b(g) = 0?
-2, 1
Let c(a) be the first derivative of 1/6*a**3 - 3/4*a**2 - 2 + a. Factor c(g).
(g - 2)*(g - 1)/2
Let k = 9/490 + 4/49. Let s(w) be the first derivative of -3/5*w**2 - k*w**4 + 2/5*w + 2/5*w**3 + 2. Factor s(h).
-2*(h - 1)**3/5
Let z(d) be the first derivative of 0*d + 0*d**5 + 1/9*d**4 - 1/27*d**6 - 1/9*d**2 + 0*d**3 + 4. Determine q so that z(q) = 0.
-1, 0, 1
Let d(c) be the second derivative of -5*c - 3*c**2 + 0 - 1/8*c**4 - c**3. Determine m so that d(m) = 0.
-2
Let r(w) = w**2 - 13*w + 14. Let f = 15 - 3. Let m be r(f). Factor -6/7*j**m - 2/7*j**4 + 0 + 2/7*j + 6/7*j**3.
-2*j*(j - 1)**3/7
Let y = -5 + 5. Let x be (0 - (2 + -1))*y. Factor 7*u**2 + 4 + x*u**2 - 12*u + 28*u.
(u + 2)*(7*u + 2)
Let q(t) be the second derivative of 5*t**5/14 + 35*t**4/6 + 184*t**3/21 + 36*t**2/7 - 20*t. Factor q(n).
2*(n + 9)*(5*n + 2)**2/7
Let x(q) be the second derivative of q**7/420 + q**6/120 + q**5/120 + 5*q**2/2 + 2*q. Let g(s) be the first derivative of x(s). Suppose g(p) = 0. What is p?
-1, 0
Solve -2/5*w + 0 + 0*w**2 - 2/5*w**5 + 4/5*w**3 + 0*w**4 = 0.
-1, 0, 1
Let b(i) be the second derivative of 0 + 0*i**3 + 0*i**2 + 1/12*i**4 + 3*i. Determine g so that b(g) = 0.
0
Let k(m) be the first derivative of -8*m**6/3 - 48*m**5/5 - m**4 + 16*m**3 - 8*m**2 + 4. Factor k(v).
-4*v*(v + 2)**2*(2*v - 1)**2
Let h(a) be the second derivative of -a**4/12 + a**3/2 + 5*a**2/2 - 2*a. Let n be h(3). Factor 0 + 0*o - 5/3*o**4 - o**n + 0*o**2 - 2/3*o**3.
-o**3*(o + 1)*(3*o + 2)/3
Let q(u) be the first derivative of -u**4/12 + 2*u**3/9 - u**2/6 + 29. Suppose q(c) = 0. Calculate c.
0, 1
Let p be (4 - 0) + (-2)/(-4). Determine v, given that -1/2 + 5/4*v + p*v**2 = 0.
-1/2, 2/9
Let l = 5 - 3. Suppose -t = l*w + 6, -t + 6 = -3*w + 2*w. Determine x so that 0 + 1/3*x**t - 1/3*x = 0.
0, 1
Let t(j) be the first derivative of -5*j**5 - 10*j**4 - 5*j**3/3 + 5*j**2 + 11. Determine g so that t(g) = 0.
-1, 0, 2/5
Let q(k) be the third derivative of -k**7/840 - k**6/240 - k**4/8 - 5*k**2. Let g(f) be the second derivative of q(f). Determine u, given that g(u) = 0.
-1, 0
Let y(w) be the third derivative of -w**10/196560 + w**9/49140 - w**8/43680 + w**4/3 - w**2. Let v(u) be the second derivative of y(u). Factor v(o).
-2*o**3*(o - 1)**2/13
Factor 5/3 - 4/3*x - 1/3*x**2.
-(x - 1)*(x + 5)/3
Let b(m) = -m**2 + 16*m - 4. Let n(u) = -u**2 - 9*u - 6. Let r be n(-8). Let j(o) = -o. Let a(y) = r*b(y) + 22*j(y). Factor a(l).
-2*(l - 4)*(l - 1)
Solve -8/7 - 8/7*w - 2/7*w**2 = 0.
-2
Let l = 10 - 6. Factor -4*v**3 + 4*v**3 - 3*v**5 - 3*v**l.
-3*v**4*(v + 1)
Let n(v) = -12*v**3 + 6*v**2 + 15*v. Let o(q) = q**2 + q + 1. Suppose 0*w = -4*w - 12. Let i(j) = w*o(j) + n(j). Solve i(a) = 0 for a.
-1, 1/4, 1
Solve 8/7*k**3 - 16/7 - 20/7*k**4 + 16/7*k + 60/7*k**2 = 0 for k.
-1, 2/5, 2
Let q = 8 - 4. Let w be (-1)/2 + 10/q. Factor -4*f + w*f**5 + f - f**3 - 3*f**3 + 5*f.
2*f*(f - 1)**2*(f + 1)**2
Let v(c) = 2*c**3 - c**2 + c - 2. Let x be v(-2). Let d be 1/3*x/(-28). Suppose 6/7*h**2 - d*h**3 + 2/7 - 6/7*h = 0. Calculate h.
1
Let k be 4/672*(-2)/(-10). Let a(w) be the third derivative of 1/240*w**5 - 2*w**2 + 0*w**3 + 0*w + 0 + 1/1344*w**8 - 1/480*w**6 + 0*w**4 - k*w**7. Factor a(x).
x**2*(x - 1)**2*(x + 1)/4
Let r(n) = -n**2 - 2*n. Let h be r(-2). Suppose 6*d - 11*d = h. What is x in -4/9*x + 2/9*x**2 - 2/9*x**4 + 4/9*x**3 + d = 0?
-1, 0, 1, 2
Let u = -190 - -1712/9. Factor 0*s + u*s**2 - 8/9*s**3 + 0.
-2*s**2*(4*s - 1)/9
Let w = -14 + 14. Let r(t) be the third derivative of 1/60*t**6 + 2*t**2 + 0 + 0*t**5 - 1/168*t**8 + 0*t**3 + w*t**7 + 0*t**4 + 0*t. Factor r(o).
-2*o**3*(o - 1)*(o + 1)
Let 0*h**2 - 2/5*h + 0 + 2/5*h**3 = 0. Calculate h.
-1, 0, 1
Factor -51 + 51 + 6*w**2 + 3*w + 3*w**3.
3*w*(w + 1)**2
Let j(s) be the first derivative of -s**4/34 - 2*s**3/51 + s**2/17 + 2*s/17 + 6. Factor j(x).
-2*(x - 1)*(x + 1)**2/17
Let l(y) be the third derivative of y**8/672 + y**7/420 - y**6/120 - y**5/60 + y**4/48 + y**3/12 + 9*y**2. Find i, given that l(i) = 0.
-1, 1
Let w(k) be the first derivative of -k**4/6 + k**3/3 + 2*k**2 + 6*k - 2. Let j(d) be the first derivative of w(d). Let j(r) = 0. Calculate r.
-1, 2
Let i(w) = -2*w**4 + 5*w**3 - 5*w**2 - 1. Let b(s) = s**4 - s**3 + s**2 + 1. Let f(o) = -5*b(o) - 5*i(o). Factor f(t).
5*t**2*(t - 2)**2
Let f(i) be the third derivative of -i**9/60480 - i**8/20160 + i**7/5040 + i**6/720 + i**5/30 - 4*i**2. Let n(s) be the third derivative of f(s). Factor n(o).
-(o - 1)*(o + 1)**2
Suppose u = -4*s - 18, -s = -5*u - 4*s - 5. Let x be (4/(-70))/(u/(-10)). Let 2/7*r**5 + 0 + x*r - 8/7*r**2 - 8/7*r**4 + 12/7*r**3 = 0. Calculate r.
0, 1
Factor -1/4 + 1/2*v - 1/4*v**2.
-(v - 1)**2/4
Suppose 4*r + 4 = 3*u - 13, -3*u = 4*r + 47. Let m(z) = z + 9. Let p be m(r). Factor p + 2 - 1 + 4*n**3 + 10*n**2 + 8*n.
2*(n + 1)**2*(2*n + 1)
Let s(w) = -5*w**2 - 5*w. Let h(i) = -11*i**2 - 9*i + 1. Let m(y) = 4*h(y) - 10*s(y). Factor m(c).
2*(c + 2)*(3*c + 1)
Let n(o) be the second derivative of -o**7/126 + 2*o**6/45 - o**5/15 + 2*o. Suppose n(l) = 0. Calculate l.
0, 2
Let i = -3 + 7. Suppose 3 = i*z - 5. Solve 1/4*v**z - 1/4*v + 0 = 0 for v.
0, 1
Factor -3/4*f**2 + 0 + 21/4*f.
-3*f*(f - 7)/4
Let -325 - 58*p**2 - p**4 + 12*p**3 + 50*p + 13*p**2 + 325 = 0. Calculate p.
0, 2, 5
Let b(p) be the second derivative of p**4/6 + p**3 - 18*p. Factor b(z).
2*z*(z + 3)
Let p(r) be the second derivative of r**9/19656 - r**7/5460 - r**3 - 3*r. Let i(a) be the second derivative of p(a). Determine j so that i(j) = 0.
-1, 0, 1
Let i be (-1*(-2 + 8/4))/2. Factor 0*v + i - 2/5*v**2 - 2/5*v**3.
-2*v**2*(v + 1)/5
Let r(m) be the third derivative of -m**5/360 + m**4/144 + m**3/18 + 7*m**2. Let r(c) = 0. Calculate c.
-1, 2
Suppose -2*y + 2*c + 14 = 0, -3*y - 3*y + 4*c = -34. Determine z so that 1/3*z**2 - 1/3*z - 20/3*z**5 + 7*z**y + 0 - 1/3*z**4 = 0.
-1, -1/4, 0, 1/5, 1
Factor 35*y**3 - 135 + 270*y - 13*y**3 - 5*y**4 - 180*y**2 + 28*y**3.
-5*(y - 3)**3*(y - 1)
Let j(o) be the third derivative of 0 + 0*o**3 + 0*o - 1/84*o**4 + 1/420*o**6 + 0*o**5 - 10*o**2. Factor j(q).
2*q*(q - 1)*(q + 1)/7
Factor 0 - 12/5*r**2 + 0*r + 3/5*r**3.
3*r**2*(r - 4)/5
Let a(j) be the first derivative of 2*j**5/5 - j**4/2 - 2*j**3/3 + j**2 - 2. Fact