 4*a**2 + 17*a**3.
-4*a**2*(a - 1)
Let z(u) be the first derivative of -63/4*u**4 - u**3 + 3*u**2 + 3 + 0*u. Factor z(w).
-3*w*(3*w + 1)*(7*w - 2)
Let h(m) be the third derivative of -m**5/150 - m**4/30 + 5*m**2. Solve h(g) = 0 for g.
-2, 0
Let n be 23/15 - (-72)/(-54). Find s such that 0*s**3 + 0 - 1/5*s**5 - 2/5*s**2 + 2/5*s**4 + n*s = 0.
-1, 0, 1
Let u(g) be the third derivative of -21*g**6/160 + 5*g**5/8 + 37*g**4/32 + 3*g**3/4 + 10*g**2. Find y such that u(y) = 0.
-1/3, -2/7, 3
Solve -8 - 6*u + 38*u**2 - 36*u**2 + 0*u = 0.
-1, 4
Let h(q) = 4*q**3 - 3*q + 5. Let s(l) = -9*l**3 + 6*l - 11. Suppose -n - 2*n + 42 = 0. Let i(b) = n*h(b) + 6*s(b). Suppose i(u) = 0. What is u?
-2, 1
Factor -2*x - 3 - 1/3*x**2.
-(x + 3)**2/3
Let k(y) = 2*y**3 + 205*y**2 + 1082*y - 7. Let s(a) = a**3 + 68*a**2 + 361*a - 2. Let i(h) = 2*k(h) - 7*s(h). Factor i(g).
-3*g*(g + 11)**2
Let z(u) be the third derivative of -6*u**2 + 1/180*u**6 + 0*u**4 + 0*u + 0*u**3 + 0 + 1/90*u**5. Factor z(i).
2*i**2*(i + 1)/3
Let f(d) be the first derivative of 0*d - 1/2*d**2 - 1 - 1/3*d**3. Solve f(t) = 0.
-1, 0
Find n, given that 9*n**3 + n + 9*n**4 + 2*n**2 - 5*n**4 + 4*n**2 = 0.
-1, -1/4, 0
Let g(w) = 4*w**3. Let m(u) = 0*u**4 + 4*u**3 + u**4 - 3*u**3. Suppose 3*y = -z + 5 + 11, 5*y = 3*z + 22. Let d(s) = z*g(s) - 6*m(s). Factor d(f).
-2*f**3*(3*f + 1)
Let d(h) = -h**2 + 4*h + 4. Let s be d(4). Factor -6*l**4 + 2*l**4 - s*l + l**3 + 8*l**2 + 2*l**3 - 5*l**4.
-l*(l + 1)*(3*l - 2)**2
Let w(d) be the first derivative of -3*d**5/5 + 3*d**4/4 - d**3/4 + 8. Factor w(f).
-3*f**2*(2*f - 1)**2/4
Let v(t) = -3*t - 4*t + 5*t. Let l be v(-2). Factor -l*g + g**2 - g + 4*g.
g*(g - 1)
Let t be -2*(2/(-2) + -3). Let m(f) = -9*f**2 + 9*f + 5. Let k(x) = -14*x**2 + 14*x + 8. Let y(a) = t*m(a) - 5*k(a). Factor y(q).
-2*q*(q - 1)
Let u = -2/1831 - 67735/10986. Let n = u - -20/3. Find y such that 0*y - 1/2 + n*y**2 = 0.
-1, 1
Find c such that 2/3*c - 2/3 + 2/3*c**2 - 2/3*c**3 = 0.
-1, 1
Let a be (8 - (-56)/(-7)) + 0. Find w, given that 2/7*w**5 + a*w + 0 + 0*w**3 + 0*w**2 + 2/7*w**4 = 0.
-1, 0
Let f(b) = 12*b**4 + 46*b**3 + 42*b**2 + 8*b + 6. Let t(h) = h**3 + h**2 + 1. Let y(s) = -f(s) + 6*t(s). Suppose y(l) = 0. Calculate l.
-2, -1, -1/3, 0
Let a(z) be the first derivative of 2*z**3/9 + z**2 - 4. Factor a(m).
2*m*(m + 3)/3
Let a be ((-2)/6)/((-5)/10). Let s = 1/6 + 1/2. Factor 0*m + a*m**2 - s.
2*(m - 1)*(m + 1)/3
Let s(j) be the second derivative of -j**7/14 - 4*j. Solve s(c) = 0 for c.
0
Let v = 4 + -19/5. Solve 0*j + v*j**3 - 2/5*j**2 + 0 = 0 for j.
0, 2
Let c(p) be the first derivative of -p**4/21 - 8*p**3/21 - 6*p**2/7 - 5*p + 10. Let a(f) be the first derivative of c(f). Factor a(q).
-4*(q + 1)*(q + 3)/7
Let q be (-3341)/771 + 5*1. Let w = -2/105 + 352/105. Let 8*j**5 + 0 + w*j**4 + 0*j + q*j**2 - 4*j**3 = 0. What is j?
-1, 0, 1/4, 1/3
Let g = 62/7 - 241/28. Factor 1/2*w**2 - g*w**3 + 0 + 0*w - 1/4*w**4.
-w**2*(w - 1)*(w + 2)/4
Suppose 147/4*x + 1/4*x**3 - 343/4 - 21/4*x**2 = 0. What is x?
7
Let z = -2 + 4. Let a(c) be the first derivative of 0*c + 0*c**3 - 1/12*c**4 + 1/15*c**5 + 0*c**z - 1. Determine v, given that a(v) = 0.
0, 1
Let x be 1/(-5) + (-98)/(-90). Factor 8/9*j**2 + 2/9*j**3 - 2/9*j**4 - x*j + 0.
-2*j*(j - 2)*(j - 1)*(j + 2)/9
Let j be 0 + (0 - -6)/(15/10). Let w(x) be the first derivative of 3/4*x**j - 1/5*x**5 - 3 - 1/6*x**6 + 0*x + 5/3*x**3 + x**2. Determine i, given that w(i) = 0.
-1, 0, 2
Suppose p + 9*p = 0. Determine d, given that 0*d + 0*d**3 + 0 + p*d**2 + 8/11*d**5 - 2/11*d**4 = 0.
0, 1/4
Let f be -1*(2 - 1)*3. Let y be 3 - (-3 + (-10)/f). Solve -2/3*l**2 - 8/3*l - y = 0.
-2
Let v(n) be the third derivative of n**7/42 - n**6/8 + n**5/12 + 5*n**4/8 - 5*n**3/3 - 9*n**2. Factor v(g).
5*(g - 2)*(g - 1)**2*(g + 1)
Let f = 20 + -11. Solve -89*z**2 - 6 - 12*z**4 - 36*z**4 - 73*z**3 - z**2 - f*z**5 - 39*z - 23*z**3 = 0 for z.
-2, -1, -1/3
Let l(u) = 16*u**3 + 16*u**2 - 28*u - 82. Let d(a) = a**3 - a + 1. Let h(c) = -36*d(c) + 2*l(c). Factor h(v).
-4*(v - 5)**2*(v + 2)
Let s(x) be the third derivative of -x**5/390 + x**4/156 + 2*x**3/39 + 4*x**2. Suppose s(c) = 0. What is c?
-1, 2
Let r(u) be the first derivative of u**6/30 + u**5 + 47*u**4/4 + 203*u**3/3 + 196*u**2 + 1372*u/5 + 18. Factor r(v).
(v + 2)**2*(v + 7)**3/5
Let y = 2 - 2. Factor -z**4 - 2 + z**3 + y*z + 2 - z + z**2.
-z*(z - 1)**2*(z + 1)
Let t = -31 + 33. Solve 1/2*z**t + 0*z + 0*z**3 + 0 - 1/2*z**4 = 0 for z.
-1, 0, 1
Suppose -5*c**4 + 135*c - 135*c - 30*c**2 - 25*c**3 + 0*c**3 = 0. What is c?
-3, -2, 0
Suppose 0 = 2*z - 4. Solve -6*d**z + 0*d**5 - 3*d + 3*d**5 - 4*d**4 + 10*d**4 = 0 for d.
-1, 0, 1
Let q be -1 + 37/(-108)*-3. Let s(l) be the second derivative of 0 - l + 0*l**3 + q*l**4 + 0*l**2. Determine v so that s(v) = 0.
0
Let i(m) be the third derivative of 0 + 1/165*m**5 - 2/33*m**3 + 0*m - 1/660*m**6 + 1/132*m**4 + 2*m**2. Factor i(k).
-2*(k - 2)*(k - 1)*(k + 1)/11
Determine z so that -6/7 - 2/7*z**2 - 8/7*z = 0.
-3, -1
Factor 0 + 0*d**2 + 3/5*d**5 - 6/5*d**4 + 0*d + 3/5*d**3.
3*d**3*(d - 1)**2/5
Let b be ((-4)/4)/(-3) + (-4)/(-12). Let p be 2/4*4/3. Factor b*j**2 + p + 4/3*j.
2*(j + 1)**2/3
Let w be (48/32)/(2*4/16). Solve 10/11*r - 8/11*r**w + 16/11*r**4 - 12/11*r**2 - 2/11 = 0.
-1, 1/2
Let r(x) be the first derivative of 2 + 0*x - 1/300*x**5 + 0*x**3 + x**2 + 0*x**4. Let t(n) be the second derivative of r(n). Factor t(i).
-i**2/5
Let l(z) be the first derivative of 4*z**3/21 - 3*z**2/7 - 4*z/7 + 25. Suppose l(t) = 0. Calculate t.
-1/2, 2
Suppose 3*q = q + 10. Let a(s) be the third derivative of 0*s**3 + 0*s - s**2 + 1/120*s**q + 0 + 0*s**4. Factor a(r).
r**2/2
Let i(p) be the second derivative of p**8/1120 - p**7/280 + p**6/240 + p**3/3 - 2*p. Let a(n) be the second derivative of i(n). Factor a(q).
3*q**2*(q - 1)**2/2
Let p = 21 + -21. Let m(t) be the first derivative of 0*t**3 - 2 + 4/55*t**5 + p*t - 1/22*t**4 + 0*t**2. Find g, given that m(g) = 0.
0, 1/2
Suppose 0 = -25*p + 28*p - 3. Let x(d) be the first derivative of 0*d - 1/5*d**2 - p - 2/15*d**3. Find h, given that x(h) = 0.
-1, 0
Let d(k) be the third derivative of -k**6/30 - 14*k**5/15 - 49*k**4/6 + 16*k**2. What is p in d(p) = 0?
-7, 0
Let d(m) be the first derivative of 3*m**6/2 + 3*m**5 - 11*m**4/4 - 11*m**3/3 - m**2 - 5. Suppose d(l) = 0. Calculate l.
-2, -1/3, 0, 1
Suppose 3*d = -2*a + 16, 2*d + d + 5*a - 22 = 0. Factor 1/3*o**5 + 1/3 + 1/3*o**d + 1/3*o - 2/3*o**3 - 2/3*o**2.
(o - 1)**2*(o + 1)**3/3
Let a be 2 + -3 - (-2 + 3). Let p be ((-9)/12)/(3/a). Suppose -1/4 - 1/4*j**4 + 0*j**3 + 0*j + p*j**2 = 0. What is j?
-1, 1
Find y, given that -1/3*y**2 + 1/3*y + 2/3 = 0.
-1, 2
Let p(d) = d**3 - d**2 - d. Let g(f) = 15*f**4 - 42*f**3 + 3*f**2 + 42*f - 12. Let m(i) = g(i) + 6*p(i). Let m(t) = 0. Calculate t.
-1, 2/5, 1, 2
Let f(z) be the third derivative of z**7/525 + z**6/300 - z**5/150 - z**4/60 + 8*z**2. Determine x so that f(x) = 0.
-1, 0, 1
Let o = -4889/4 - -1223. Factor 0*k - o*k**3 - 9/4*k**2 + 0.
-3*k**2*(k + 3)/4
Suppose 0 = -2*h - 4*f - 30, -h = -2*f - 3*f - 20. Let n = h - -7. Suppose -6/5*a**n - 2/5*a**3 - 2/5 - 6/5*a = 0. What is a?
-1
Solve -2/21*u**2 + 0*u + 2/21 = 0.
-1, 1
Suppose -2*m + 8 = 2*s, m + 2*m = -2*s + 10. Factor -3*n**2 + m*n**3 - 2*n + n**3 + 2*n.
3*n**2*(n - 1)
Let z(g) = 5 - g**3 - 5*g**3 - 4*g**2 - 2*g**2. Let i(p) = 7*p**3 + 7*p**2 - 6. Let j(f) = -5*i(f) - 6*z(f). Factor j(s).
s**2*(s + 1)
Let o(s) be the first derivative of 5*s**6/2 - 22*s**5 + 95*s**4/2 + 60*s**3 - 405*s**2/2 - 270*s + 21. Factor o(q).
5*(q - 3)**3*(q + 1)*(3*q + 2)
Let u(o) be the second derivative of o**4/15 - 2*o**3/15 - 10*o. Factor u(d).
4*d*(d - 1)/5
Let m(s) be the third derivative of -4*s**7/315 - s**6/20 - s**5/15 - s**4/36 - s**2. Suppose m(p) = 0. Calculate p.
-1, -1/4, 0
Let x = 2397/2 + -1191. Solve 12*m - 21/2*m**2 - x*m**3 + 6 = 0.
-2, -2/5, 1
Let n = 15241/60 - 254. Let x(v) be the third derivative of 1/300*v**6 - 1/150*v**5 + 0*v - 4*v**2 + 0 + 1/15*v**3 - n*v**4. Factor x(h).
2*(h - 1)**2*(h + 1)/5
Factor g**3 + 3*g**3 + 507 + 2*g**4 - 4*g - 509.
2*(g - 1)*(g + 1)**3
Suppose 0*s - 12 = -4*s. Suppose 0 = -s*r + 8 - 2. Solve -1 - 1 + n**2 + n**r = 0 for n.
-1, 1
Suppose k - 4 = 5*p - k, -5*k = 3*p - 10. Factor -2*g**2 + 0*g