 + 1. Let o be n(-1). Let s = 109 + -106. Factor 1/2*h**s - 2*h**o + 5/2*h - 1.
(h - 2)*(h - 1)**2/2
Let t = -12 - -37/3. Factor -3 - 2*k - t*k**2.
-(k + 3)**2/3
Solve 7/3*r**5 + 2/3*r**4 + 0*r**3 + 0*r + 0*r**2 + 0 = 0 for r.
-2/7, 0
Let i(s) be the second derivative of -s**6/180 + s**4/72 - 44*s. Solve i(z) = 0 for z.
-1, 0, 1
Suppose 0*g - 8 = -4*g. Let a(k) be the third derivative of 0 + 0*k**3 - 2*k**g + 0*k + 0*k**4 + 1/180*k**5. Factor a(h).
h**2/3
Let b(z) = 5*z**3 + 23*z**2 + 33*z + 15. Let h(q) = -q**2 - q. Let u(x) = b(x) - 2*h(x). Factor u(f).
5*(f + 1)**2*(f + 3)
Factor 1/6*k + 1/3*k**2 - 1/6*k**5 + 0*k**3 + 0 - 1/3*k**4.
-k*(k - 1)*(k + 1)**3/6
Let c = -13 - -20. Suppose 0 = 2*a - 3*q - c, -3*q = q + 4. Factor -1/3*f**4 + 0*f**a + 0*f + 0 + 1/3*f**3.
-f**3*(f - 1)/3
Suppose -3*s + 20 = s. Let x(o) be the third derivative of 0 + 0*o - o**2 - 1/240*o**s + 0*o**3 - 1/48*o**4. Factor x(a).
-a*(a + 2)/4
Let t(z) = 2*z + 2. Let w be t(2). Suppose 0 = 2*x + 5*s - 11, 14 = 3*x - s + w. Factor -4*f**3 + 3*f**3 - f**x + f**2 - 4*f + 5*f**2.
-2*f*(f - 2)*(f - 1)
Let i = -232 - -234. Factor 0*d**i - 2/5*d**3 + 0 + 0*d + 2/5*d**4.
2*d**3*(d - 1)/5
Factor 2/9*s**2 + 2/9 + 4/9*s.
2*(s + 1)**2/9
Suppose 89*a - 86*a - 12 = 0. Let x(q) be the first derivative of -1/16*q**a + 0*q + 1/12*q**3 - 1 + 1/4*q**2. Suppose x(l) = 0. What is l?
-1, 0, 2
Let u = -1 + 1. Suppose u*q = 4*q. Factor q*j + 2*j**2 - 6*j**3 + 0*j.
-2*j**2*(3*j - 1)
Let o(p) be the third derivative of 0 - 2/21*p**3 - 3*p**2 + 1/105*p**5 - 1/12*p**4 + 1/60*p**6 + 0*p. Factor o(d).
2*(d - 1)*(d + 1)*(7*d + 2)/7
Let t = -9 + 10. What is i in -1 + 33*i**2 - t - 9*i - 5*i**3 - 45*i**2 = 0?
-1, -2/5
Let t(s) be the third derivative of s**8/336 + s**7/120 - s**6/240 - s**5/30 - s**4/48 + s**3/24 - 5*s**2. Let t(q) = 0. Calculate q.
-1, 1/4, 1
Suppose -4*m = 5*o - 20, 4*m + 0*m + 4*o - 16 = 0. Suppose 4*l - 13 = -7*h + 2*h, m = 2*l + 5*h - 9. Factor 24*s - s**2 + 8*s**2 + s**2 + 16 + 2*s**3 + 4*s**l.
2*(s + 2)**3
Let a(t) = 8*t**2 - 10*t + 10. Suppose -4*f + h + 4 = 0, 0*f - 2*f - 3*h = -2. Let z(d) = -44 + 84 - 39. Let l(g) = f*a(g) - 8*z(g). Find w such that l(w) = 0.
1/4, 1
Let z(i) = -17*i**4 - 18*i**3 + 8*i**2 + 18*i + 17. Let l(m) = 11*m**4 + 12*m**3 - 5*m**2 - 12*m - 11. Let r(u) = 8*l(u) + 5*z(u). Let r(o) = 0. What is o?
-1, 1
Let x be ((-6)/(-5))/(5/25). Suppose -2*d + 2 = n, 2*d - 2 = n - 4. Factor -5 - 12*o + d*o**3 - 3 - x*o**2 - o**3.
-(o + 2)**3
Factor 9/7*k**2 + 3/7*k**4 - 9/7*k**3 - 3/7*k + 0.
3*k*(k - 1)**3/7
Let f(q) = 4*q**2 + 2*q + 3. Let s(w) = 7*w**2 + 4*w + 5. Let o(a) = -10*f(a) + 6*s(a). Find t such that o(t) = 0.
-2, 0
Let s(w) = 3*w + 15*w**2 + 3*w - 16*w**2. Let n be s(6). Factor 2/3*d**2 - 2/3*d**3 - 2/9*d + 2/9*d**4 + n.
2*d*(d - 1)**3/9
Let i(j) be the third derivative of -j**8/1680 - j**7/1050 + j**6/150 + j**5/75 + 16*j**2. Solve i(g) = 0 for g.
-2, -1, 0, 2
Let y(n) be the first derivative of n**7/840 - n**5/40 + n**4/12 + n**3 + 3. Let m(i) be the third derivative of y(i). Let m(c) = 0. Calculate c.
-2, 1
Let b = 5 - 2. Suppose 0 = -b*o + 3 + 15. Let 13*t**2 - o*t - 6*t**2 + 4*t**3 - t + 5*t = 0. Calculate t.
-2, 0, 1/4
Let w be -1*(-3 + 30/9)*-15. Let k(f) be the first derivative of -f**2 - 5/3*f**3 - 7/6*f**6 + 9/4*f**4 + 0*f - 2 + f**w. Determine c so that k(c) = 0.
-1, -2/7, 0, 1
Let g(o) = 3*o**3 + o**2 - 1. Let y be g(1). Factor -y*s**4 + 3*s**5 + 4*s**2 - 4*s**2.
3*s**4*(s - 1)
Let w(y) be the first derivative of 4*y**3/3 - 8*y**2 - 20*y - 7. Factor w(b).
4*(b - 5)*(b + 1)
Let k = -70795152700/3003 + 23574810. Let w = -2/429 + k. Find u, given that w*u**2 + 2/7*u + 2/7*u**3 + 0 = 0.
-1, 0
Suppose -5*i = -16 + 1. Factor -2*f**i - 2*f**2 - 5*f**4 + 4*f**2 - f**3.
-f**2*(f + 1)*(5*f - 2)
Let n(i) = -9*i**2 - 11*i - 1. Let x = 9 - 17. Let t(z) = -26*z**2 - 34*z - 4. Let d(u) = x*n(u) + 3*t(u). Factor d(s).
-2*(s + 2)*(3*s + 1)
Let a(z) be the third derivative of -z**5/105 - 8*z**4/21 - 128*z**3/21 - z**2 + 15*z. Find o, given that a(o) = 0.
-8
Let d be (3 - 3) + 2/9. Let c = 1334/9 - 148. Factor -c*q + d*q**3 - 2/9 + 2/9*q**2.
2*(q - 1)*(q + 1)**2/9
Let t be (8/(-60))/((-3)/15). Find a such that 4/3 + t*a - 2/3*a**2 = 0.
-1, 2
Let i be (34/(-51))/(-1 - 0). Suppose -4/9 + i*d - 2/9*d**2 = 0. What is d?
1, 2
Let p(h) be the third derivative of h**8/168 - 2*h**7/105 + h**5/15 - h**4/12 + 8*h**2. Factor p(x).
2*x*(x - 1)**3*(x + 1)
Let w(h) be the first derivative of -h**3/2 + 9*h**2/2 - 27*h/2 + 23. Solve w(l) = 0.
3
Let n(k) be the second derivative of k**5/130 - k**3/39 - 3*k. What is d in n(d) = 0?
-1, 0, 1
Let v(g) = g**2. Let i(l) = -3*l**3 + 3*l**2 - l. Let h(a) = i(a) - v(a). Let k(s) = 4*s**3 - 3*s**2 + 2*s. Let b(q) = 3*h(q) + 2*k(q). Factor b(j).
-j*(j - 1)*(j + 1)
Let m(a) be the second derivative of a**4/12 + a**3/3 + a**2/2 - 23*a. Factor m(b).
(b + 1)**2
Factor -6*t + t**4 - 21*t**2 + 2*t**4 + 12*t**2.
3*t*(t - 2)*(t + 1)**2
Let d = 13 - 13. Determine s so that -8*s**5 + d*s**5 - 2*s**4 + 2*s**2 + 13*s**3 - 5*s**3 = 0.
-1, -1/4, 0, 1
Suppose 3*n + 2*n = 45. Suppose 2*c + c = n. Solve -l**3 + 0*l**c + l - 3*l + 3*l**3 = 0.
-1, 0, 1
Let j = 263 + -183. Let d be (6/5)/(8/j). Factor -13/2*u - 1 - 9/2*u**3 - d*u**2.
-(u + 2)*(3*u + 1)**2/2
Let y(f) be the first derivative of -f**6/8 + 9*f**4/8 - 2*f**3 + 9*f**2/8 + 1. Suppose y(m) = 0. Calculate m.
-3, 0, 1
Let q(y) be the first derivative of -1/6*y**6 - 2/5*y**5 + 2/3*y**3 + 0*y**4 + 1/2*y**2 - 4 + 0*y. Factor q(f).
-f*(f - 1)*(f + 1)**3
Let k = 1 - 3. Let f be 1*(3 + k - -1). Factor -l**3 + 3*l**3 - l**2 - l**f.
2*l**2*(l - 1)
Factor 16/11 - 6/11*v**3 - 8/11*v - 20/11*v**2.
-2*(v + 2)**2*(3*v - 2)/11
Let u(b) be the third derivative of 0*b**4 + 0 + 0*b**5 + 1/1260*b**7 - 2*b**2 - 1/720*b**6 + 0*b**3 + 0*b. Factor u(i).
i**3*(i - 1)/6
Let x = 5 + 2. Let 3*q**4 + 2*q**3 - x*q**3 - 2*q**5 - 3*q**3 - 11*q**4 = 0. What is q?
-2, 0
Let k(i) be the first derivative of i**7/630 - i**6/90 + i**5/30 - i**4/18 + i**3/18 - i**2 + 4. Let v(c) be the second derivative of k(c). Solve v(f) = 0.
1
Let v(b) be the third derivative of b**7/420 + b**6/240 - b**5/40 + b**4/6 + 3*b**2. Let r(q) be the second derivative of v(q). Factor r(y).
3*(y + 1)*(2*y - 1)
Let l(c) = c - 7. Let d be l(9). Factor 3*s**2 - 2*s + s - 4*s**d.
-s*(s + 1)
Let z(b) be the third derivative of 0*b**3 + 0*b - 6*b**2 - 1/540*b**6 + 1/135*b**5 - 1/108*b**4 + 0. Find y, given that z(y) = 0.
0, 1
Let s be 15/50*(-4 + 9). Let 0 + 3/2*k**2 + 0*k - s*k**3 = 0. What is k?
0, 1
Let y(n) be the third derivative of 0*n + 3*n**2 + 0 - 1/36*n**4 - 1/27*n**3 + 1/180*n**6 + 1/270*n**5. Determine c so that y(c) = 0.
-1, -1/3, 1
Let t(g) be the first derivative of -g**4/2 + 2*g**3/3 + 37. Factor t(a).
-2*a**2*(a - 1)
Let w(k) be the third derivative of 1/270*k**6 + 0 + 0*k - k**2 + 1/270*k**5 + 0*k**3 - 1/108*k**4. Find y, given that w(y) = 0.
-1, 0, 1/2
Suppose 10*z + 8 - 28 = 0. Factor 0 + 0*k**3 + 0*k - 1/4*k**4 + 1/4*k**z.
-k**2*(k - 1)*(k + 1)/4
Let w = -273 + 495. Let i be 1/(-4) + w/120. Factor -8/5*n - i*n**3 + 12/5*n**2 + 2/5*n**4 + 2/5.
2*(n - 1)**4/5
Suppose 0 = -5*y + 17 - 2. Factor -q**4 + 0*q**2 + 3*q**5 + q**2 + 0*q**y - 2*q**5 - q**3.
q**2*(q - 1)**2*(q + 1)
Determine v so that -2/3*v**4 - 1/3*v**2 - 1/6*v**5 - 5/6*v**3 + 0*v + 0 = 0.
-2, -1, 0
Suppose -18*y + 17*y = -3. Let i(o) be the second derivative of 0 - 1/6*o**4 - 4*o**2 - 4/3*o**3 - y*o. Factor i(p).
-2*(p + 2)**2
Factor -4/7*q**2 - 2*q - 8/7 + 2/7*q**3.
2*(q - 4)*(q + 1)**2/7
Let x = -83/3 + 28. Factor -1/3*m**3 + x*m + 0*m**2 - 1/6*m**4 + 1/6.
-(m - 1)*(m + 1)**3/6
Let c be ((-4)/5 - 0)/(14/(-35)). Suppose 0 + 8/15*n**c + 8/15*n + 2/15*n**3 = 0. Calculate n.
-2, 0
Suppose -3*j = -2*m + 3, -5*m + 2*j + 11 = -2*j. Solve 3*w - 3*w**2 - 12*w**5 - 9*w**4 + 9*w**5 - 9*w**m - 3*w = 0.
-1, 0
Let d be 4/(10/(-5)) + 7. Let j(v) be the second derivative of 0 + 2*v - 1/4*v**4 + 1/3*v**3 + 0*v**2 + 1/20*v**d. What is s in j(s) = 0?
0, 1, 2
Let f(w) be the third derivative of w**7/420 + w**6/120 - w**5/120 - w**4/24 + 26*w**2. Find j, given that f(j) = 0.
-2, -1, 0, 1
Let q(w) = -4860*w**4 + 6985*w**3 - 2435*w**2 + 205*w - 35. Let h(m) = -405*m**4 + 582*m**3 - 203*m**2 + 17*m - 3. Let d(