 8*k**2 - 2*k - 2. Let b(n) = -2*h(n) - 3*r(n). Factor b(m).
-m*(m - 2)**2*(m - 1)
Determine p so that -1/3*p**2 + p - 2/3 = 0.
1, 2
Let h(f) be the second derivative of f**7/21 + 2*f**6/15 - f**4/3 - f**3/3 + 5*f. Factor h(t).
2*t*(t - 1)*(t + 1)**3
Let p(y) = -y**3 + y**2 - 2*y + 2. Let l(k) = -2*k**3 + 2*k**2 - 3*k + 3. Let s(q) = -q**2 + 5*q - 3. Let v be s(5). Let b(r) = v*l(r) + 5*p(r). Factor b(t).
(t - 1)**2*(t + 1)
Suppose 4*h - 2*c - 44 = 0, -2*h + 4*h + 2*c = 10. Let r be (-6)/27 - (-20)/h. Factor n**2 - 4*n**r - n**3 - 2*n**3.
-3*n**2*(n + 1)
Let o(j) = 3*j**2 - 10*j - 13. Let l(f) = 4*f**2 - 10*f - 14. Let v(c) = -4*l(c) + 5*o(c). Let v(n) = 0. Calculate n.
-9, -1
Suppose 5*r = 4*w - 12 - 2, 0 = 3*w + 3*r + 3. Let m(v) be the first derivative of -w - 3/2*v**2 + 0*v - v**3. Factor m(g).
-3*g*(g + 1)
Suppose i = -n - 4, 5*n = 3*i - 4*i - 16. Let v(d) = -3*d**2 + 7*d - 2. Let k(z) = -2*z**2 + 6*z - 1. Let t(a) = n*v(a) + 4*k(a). Factor t(p).
(p + 1)*(p + 2)
Let i(r) be the third derivative of r**6/160 - r**5/80 - 5*r**2. Let i(n) = 0. Calculate n.
0, 1
Suppose k - 4 = -k. Factor -1/2*v**4 + 0*v - 1/2*v**3 + 0*v**k + 0.
-v**3*(v + 1)/2
Let s(g) be the second derivative of -g**10/60480 + g**9/15120 - g**8/13440 - g**4/3 - 4*g. Let h(r) be the third derivative of s(r). Factor h(a).
-a**3*(a - 1)**2/2
Let v(o) = 5*o**5 - 11*o**4 + 13*o**3 - 7*o**2. Let j(h) = -h**5 + h**4 - h**3 + h**2. Let i(n) = 3*j(n) + v(n). Factor i(d).
2*d**2*(d - 2)*(d - 1)**2
Let s(x) = -x**3 - 5*x**2 - 4*x + 2. Let v be s(-4). Let f be 4*(-2)/(-30)*3/2. Determine a so that -4/5*a**v + f*a + 2/5*a**3 + 0 = 0.
0, 1
Let f = 4 + -1. Determine c so that -4*c**2 + 0*c + 6*c**f - 4*c**4 + c + 3*c**5 - 2*c**5 = 0.
0, 1
Let w be ((-11)/(429/52))/((-4)/1). Let -2/3 - w*v**3 - 5/3*v - 4/3*v**2 = 0. What is v?
-2, -1
Suppose 0 = 39*g - 37*g. Solve a**4 + 1/2*a**2 + 5/4*a**3 + 1/4*a**5 + 0*a + g = 0.
-2, -1, 0
Let a be 32/(-12) - (-2)/3. Let c be ((-18)/4 - -3)*a. Let 8/5*x**2 - 2/5*x + 0 - 8/5*x**4 + 2/5*x**c = 0. Calculate x.
-1, 0, 1/4, 1
Let o(r) be the first derivative of -7*r**6/720 - r**5/48 + r**4/24 + r**3 + 1. Let p(l) be the third derivative of o(l). Factor p(k).
-(k + 1)*(7*k - 2)/2
Let s(u) be the second derivative of 7*u**6/600 + u**5/60 - u**4/60 - 3*u**2/2 + 4*u. Let y(w) be the first derivative of s(w). Factor y(v).
v*(v + 1)*(7*v - 2)/5
Factor 1/4*l + 1/2*l**4 + 3/4*l**2 - 1/4 - 5/4*l**3.
(l - 1)**3*(2*l + 1)/4
Let w = -10 + 14. Factor 0*t**2 - t**4 - t**3 - t + t**2 + 2*t**3 + 0*t**w.
-t*(t - 1)**2*(t + 1)
Suppose 0 = -4*t - t + 5. Let i = 11 + t. Factor -8*v**2 - 16*v**4 - i*v**4 - 22*v**4 + 7*v**3 - 47*v**3.
-2*v**2*(5*v + 2)**2
Let q = -245 + 247. Factor -8/5 - 8/5*y - 2/5*y**q.
-2*(y + 2)**2/5
Let s(y) be the third derivative of 1/24*y**4 + 1/210*y**7 + 1/40*y**6 + 0 - 5*y**2 + 0*y + 0*y**3 + 1/20*y**5. Factor s(r).
r*(r + 1)**3
Let f(t) be the first derivative of t**4/2 + 52*t**3/3 + 7*t**2 - 14*t - 3. Let k(l) = -l**3 - 17*l**2 - 5*l + 5. Let g(a) = 3*f(a) + 10*k(a). Factor g(u).
-2*(u + 2)**2*(2*u - 1)
Suppose 2*z - 3 = -1. Let m be 3*z/(-3)*-2. Solve -6*r**m + 3*r**2 + r**2 = 0.
0
Let c(y) = 9*y**4 + 7*y**3 + 23*y**2 - 39*y - 7. Let z(d) = -4*d**4 - 4*d**3 - 11*d**2 + 19*d + 3. Let s(l) = 3*c(l) + 7*z(l). Suppose s(b) = 0. Calculate b.
-4, 0, 1
Suppose -2*p = 1 + 33. Let x = 17 + p. Factor 0*u + 0*u**3 + x - 2/5*u**4 + 2/5*u**2.
-2*u**2*(u - 1)*(u + 1)/5
Let a(p) be the third derivative of -3*p**2 + 0 + 0*p**7 + 0*p - 1/60*p**6 + 1/24*p**4 + 0*p**5 + 0*p**3 + 1/336*p**8. Factor a(c).
c*(c - 1)**2*(c + 1)**2
Suppose -8 - 12 = -5*v. Let d(k) = 9*k**2 - 8*k. Let y be d(6). Find i such that -80*i - 98*i**5 - y*i**3 + 189*i**2 + 350*i**v - 194*i**3 + 101*i**2 + 8 = 0.
2/7, 1
Let g(n) be the third derivative of n**5/210 + n**4/28 + 23*n**2. Solve g(s) = 0 for s.
-3, 0
Let f(m) be the third derivative of -m**8/8400 + m**7/4200 + m**6/900 - 2*m**3/3 - 2*m**2. Let j(c) be the first derivative of f(c). Solve j(x) = 0 for x.
-1, 0, 2
Let n(w) be the first derivative of w**3 - 33*w**2/2 - 14. Factor n(a).
3*a*(a - 11)
Let k be (-2)/(-10)*16/16. Find v such that 1/5*v**2 + 0*v + k*v**5 + 0 - 1/5*v**4 - 1/5*v**3 = 0.
-1, 0, 1
Let b be 10/6 - (-242)/(-154). Let d(a) be the first derivative of 2/7*a**2 - 2/7*a - b*a**3 - 2. Solve d(m) = 0.
1
Suppose -3*x = 3, 4*b - 10 = 5*x - 3*x. Let v be (-2)/1 + 2 + 2. Find z, given that -2*z - 3 + v*z**b + 0 - 1 = 0.
-1, 2
Let u(v) be the second derivative of v**4/21 - 4*v**3/7 + 10*v**2/7 + 26*v. What is m in u(m) = 0?
1, 5
Let b(o) be the third derivative of o**6/2 - 22*o**5/15 + 5*o**4/6 + 4*o**3/3 - 11*o**2. Factor b(p).
4*(p - 1)*(3*p - 2)*(5*p + 1)
Let c = 53/154 + 12/77. Solve 0 - c*a**2 + 0*a = 0.
0
Let w be (2 - (-3 + 4))*2. What is t in -t - t**3 - t + 2*t + t**w = 0?
0, 1
Let h = -65 + 68. What is f in 0 + 1/5*f**4 + 0*f**2 + 0*f + 1/5*f**h = 0?
-1, 0
Let n = -1621/3 + 541. Suppose 0 + 0*k**2 + 0*k + n*k**3 = 0. What is k?
0
Let t be ((-3)/(-3))/(2/4). Let v(o) be the third derivative of 0*o - 1/12*o**4 - 1/60*o**5 - 2*o**t + 0 + 0*o**3. Suppose v(u) = 0. What is u?
-2, 0
Suppose -s - s = 2*x - 6, 13 = 4*s + 3*x. Determine k so that -3*k**4 + s*k**4 - 4*k**4 = 0.
0
Let w(f) be the first derivative of 0*f**2 + 0*f - 1/21*f**6 - 4/21*f**3 + 4/35*f**5 + 1/14*f**4 - 3. Suppose w(c) = 0. What is c?
-1, 0, 1, 2
Let f(k) = k**4 - k**3 - k**2 + k - 1. Let h(u) = 2*u**3 - 2*u - 2. Let d(g) = 2*f(g) - h(g). Find a, given that d(a) = 0.
-1, 0, 1, 2
Let d(z) be the third derivative of z**7/105 + 7*z**6/240 + z**5/60 - z**4/48 - 3*z**2. Let d(f) = 0. Calculate f.
-1, 0, 1/4
Factor 3*n**2 + 10 - 16 + 3*n + 3*n**4 + 6*n - 9*n**3.
3*(n - 2)*(n - 1)**2*(n + 1)
Let h(p) be the third derivative of p**8/1176 - p**7/105 + 19*p**6/420 - 5*p**5/42 + 4*p**4/21 - 4*p**3/21 - 8*p**2. Determine l so that h(l) = 0.
1, 2
Let b(p) be the first derivative of p**3/8 + 9*p**2/16 + 13. Factor b(s).
3*s*(s + 3)/8
Let g = -3 - -2. Let y be (-7)/(-2) - g/2. Solve -4*w**2 + 0*w**2 - 2*w - y + 5*w**2 + w**2 = 0.
-1, 2
Let k be ((-90)/24)/(2/64). Let b be (-1698)/k + (-2)/(-8). Factor 0 + 8/5*r + 196/5*r**4 + b*r**2 + 42*r**3.
2*r*(2*r + 1)*(7*r + 2)**2/5
Let o(f) = f**2 - 2*f - 6. Let i be o(4). Factor 3*z**i + 6*z + 5*z**2 + 3 + 4*z**2 - 9*z**2.
3*(z + 1)**2
Let h(t) be the second derivative of 0*t**5 + 0 - 5*t + 0*t**2 + 1/20*t**6 - 1/8*t**3 - 1/8*t**4 + 1/56*t**7. Factor h(n).
3*n*(n - 1)*(n + 1)**3/4
Suppose 5 = -2*h + 3*j - 1, 4*h = j - 2. Let g be (h - 0)/(8/4). Determine n, given that g*n - 2/3*n**3 + 0*n**2 + 0 - 2/3*n**4 = 0.
-1, 0
Suppose -7 = 2*r - d - 54, -2*r + 27 = 3*d. Let z(i) = 3*i**2 - 5. Let w(y) = -y**2 + 2. Let q(m) = r*w(m) + 6*z(m). Solve q(g) = 0 for g.
-2, 2
Let i be -5 - -16*(-2)/(-6). Let x(z) be the first derivative of 0*z**2 - z + i*z**3 - 1. Suppose x(n) = 0. Calculate n.
-1, 1
Let i be 2/(-9) - 86/18. Let c(t) = -3*t**2 - 6*t + 9. Let w(p) = p**2 - 3 - 1 - 11*p + 14*p. Let u(v) = i*w(v) - 2*c(v). Factor u(l).
(l - 2)*(l - 1)
Let n = -1087/96 - 11/32. Let u = -169/15 - n. Determine m, given that -u*m - 2/5*m**2 + 2/5*m**3 + 2/5*m**4 + 0 = 0.
-1, 0, 1
Determine x so that 12/5*x + 3/5*x**2 + 12/5 = 0.
-2
Factor 2/3*s + 5/6*s**3 + 1/6*s**4 + 4/3*s**2 + 0.
s*(s + 1)*(s + 2)**2/6
Let z be 19/8 + 6/(-16). Suppose 13*x**4 + 2*x**2 - x**z - 3*x**5 + 1 - 6*x + 17*x**2 - x - 22*x**3 = 0. What is x?
1/3, 1
Let t be -4 + 3 + 2 - (-3)/(-27). Suppose t - 8/9*x + 8/9*x**3 - 2/9*x**4 - 2/3*x**2 = 0. What is x?
-1, 1, 2
Let h = -2551 + 705. Let q = h - -5594/3. Factor 98/3*t**2 + q*t + 8/3.
2*(7*t + 2)**2/3
Let h = 340 - 24479/72. Let x(q) be the third derivative of 0*q**3 + 1/180*q**5 + 0 + 0*q + h*q**4 + q**2. Solve x(n) = 0 for n.
-1, 0
Let r(t) be the third derivative of -t**7/420 - t**6/45 - t**5/12 - t**4/6 + t**3/3 - t**2. Let p(x) be the first derivative of r(x). Factor p(k).
-2*(k + 1)**2*(k + 2)
Let v be ((8/(-6))/(4/(-6)))/6. Determine w so that w**3 - v*w**4 + 0 - w**2 + 1/3*w = 0.
0, 1
Let u(y) = 96*y**3 + 16*y**2 - 4*y + 8. Let v(z) be the first derivative of 8*z**4 + 5*z**3/3 - z**2/2 + 3*z + 7. Let i(a) = 3*u(a) - 8*v(a). Factor i(q).
4*q*(2*q + 1)*(4*q - 1)
Suppose -6*h + 716 = -2*h. Let m = h + -1251/7. Factor 2/7*t**4