. Let b(x) be the first derivative of d(x). Factor b(k).
(k - 1)*(k + 1)*(7*k + 2)/3
Let p be -2 - ((-1269)/235 - 4/(-10)). Factor -8/3*v**2 + 16/3*v - 4*v**p + 10/3*v**4 + 0 - 2/3*v**5.
-2*v*(v - 2)**3*(v + 1)/3
Let q(v) = v**3 + 4*v**2 - 27*v + 32. Let g(o) = o. Let b(a) = -g(a) + q(a). Factor b(k).
(k - 2)**2*(k + 8)
Let i = 40 + -37. Suppose -n**i + n**3 - 2*n**3 - n**3 = 0. Calculate n.
0
Factor 114*u**2 - 165*u - 10 + 16 + 45*u**2.
3*(u - 1)*(53*u - 2)
Let c = -38 + 54. Suppose -6*w + 2*w = -c. Factor -2*t - t**4 - 7*t**w + 14*t**3 - 3*t**2 - t**2 + 0*t**4.
-2*t*(t - 1)**2*(4*t + 1)
Let v be (-89)/(-15) - (-1 - (-16)/10). Let p = v - 5. Solve 0 - 1/3*l**4 - p*l**3 + 1/3*l + 1/3*l**2 = 0.
-1, 0, 1
Factor -28/5 + 38/15*l + 2/15*l**2.
2*(l - 2)*(l + 21)/15
Let q(j) be the first derivative of 3*j**4/28 + 12*j**3/7 + 33*j**2/14 + 223. Let q(i) = 0. Calculate i.
-11, -1, 0
Factor -19*s**3 - 12*s - 98*s**2 - 8*s**3 + s**3 + 8 - 15*s**3 - 4*s**3.
-(s + 2)*(5*s + 2)*(9*s - 2)
Let w(c) be the second derivative of 1/24*c**4 + 16*c + 0 + 1/3*c**3 + 3/4*c**2. Factor w(q).
(q + 1)*(q + 3)/2
Let v(l) = -l**2 + l. Let m(t) = -5*t**2 + 8*t. Let w(i) = m(i) - 6*v(i). Let j be w(-6). Factor -7 - 36*d**2 - 18*d + 3 - 1 + 2 - j*d**3.
-3*(2*d + 1)**3
Let w(v) be the first derivative of -49*v**4/22 + 182*v**3/33 - 51*v**2/11 + 18*v/11 + 197. Factor w(t).
-2*(t - 1)*(7*t - 3)**2/11
Let v be (-45)/27 - (-110)/12. Suppose 0 - 3/2*s**2 - 3*s**4 + 3*s - v*s**3 = 0. Calculate s.
-2, -1, 0, 1/2
Let h = 131 + -129. Factor -4 - 4*p**h + 4 + 3*p - 9*p + 2*p**5 + 4*p**3 + 6*p**4 - 2.
2*(p - 1)*(p + 1)**4
Factor 7/5*h - 1/5*h**2 + 0.
-h*(h - 7)/5
Let w(r) = -3*r**3 - 26*r**2 - 73*r - 46. Let q(o) = -21*o**3 - 183*o**2 - 510*o - 321. Let i(n) = 4*q(n) - 27*w(n). Factor i(g).
-3*(g + 1)*(g + 2)*(g + 7)
Let v(b) be the second derivative of -5*b**4/12 + 370*b**3/3 - 13690*b**2 - 6*b + 2. Factor v(q).
-5*(q - 74)**2
Let f(v) = -2*v - 12. Suppose -2*r - 4*u = 34, -10 = 5*r - 7*u + 2*u. Let z be f(r). Determine q so that -49/6*q**z - 8/3 - 28/3*q = 0.
-4/7
Suppose 0 = -6*h + 11*h - 60. Factor -28*s**2 + 47*s**2 + h*s - 22*s**2 + 3*s - 12.
-3*(s - 4)*(s - 1)
Factor 14/9*k**2 - 2/9*k**3 - 32/9 - 16/9*k.
-2*(k - 4)**2*(k + 1)/9
Let u = 834 + -825. Let l(h) = h**2 - 3*h - 2. Let w be l(6). Determine i so that -2 - u*i**2 + 15*i**3 - 1 - 31*i + 12*i**4 + w*i = 0.
-1, -1/4, 1
Let n(s) be the first derivative of -4 + 1/5*s**5 + s**4 + s**2 + 0*s + 5/3*s**3. Find l such that n(l) = 0.
-2, -1, 0
Factor 2*v**4 + 48*v - 107*v + 5*v**2 + 53*v + 6*v**2 + 20*v**3 + v**4.
v*(v + 1)*(v + 6)*(3*v - 1)
Let g(f) = -f**3 + 7*f**2 + 2*f - 3. Let w be g(7). Let l be (-8)/(-1) - (w + -14). Factor -4*y**2 + y - 8*y - 3 + l + 3*y.
-4*(y - 1)*(y + 2)
Let s(n) be the first derivative of -n**7/735 + n**5/70 - n**4/42 + 7*n**2/2 + 5. Let y(p) be the second derivative of s(p). Factor y(f).
-2*f*(f - 1)**2*(f + 2)/7
Let v = 20 + -12. Let y(x) = -x**2 + 7*x + 11. Let u be y(v). Factor -2*i**2 - i**5 + i**u + 8*i**2 - 4 + i**2 - 3*i**4.
-(i - 1)**2*(i + 1)*(i + 2)**2
Let j be 2/(-1) - (-71 + 7 + 2). Solve j*w**2 + 5*w**3 + 51*w - 6*w - 10*w**2 = 0.
-9, -1, 0
Let p(s) be the second derivative of -1/6*s**6 + 5/2*s**2 + 0*s**4 + 0 + 1/2*s**5 + s - 5/3*s**3. Factor p(y).
-5*(y - 1)**3*(y + 1)
Let i(s) = 2*s**3 - 13*s**2 - 3. Let r(a) = 0*a**2 + a**2 + a**3 - 44 + 45. Let y(k) = -i(k) - 3*r(k). Factor y(j).
-5*j**2*(j - 2)
Let n(t) = 5*t**4 + 5*t**3 - 5*t**2 - 5*t. Suppose 0 = -3*w + 4*w + 4. Let k(a) = -3*a**4 - 3*a**3 + 3*a**2 + 3*a. Let p(r) = w*n(r) - 7*k(r). Factor p(m).
m*(m - 1)*(m + 1)**2
Factor 0 - 2/3*k**2 + 2/3*k.
-2*k*(k - 1)/3
Let v(c) = c**3 - 4*c**2 + 2*c. Let u be v(2). Let p = -1 - u. Factor -p*b + 0*b**2 + 0*b - 2*b**2 + b.
-2*b*(b + 1)
Let z(k) be the third derivative of -17*k**8/2520 - k**7/75 + k**6/30 + 4*k**5/225 - 2*k**2 + 6*k. What is y in z(y) = 0?
-2, -4/17, 0, 1
Let u(s) be the first derivative of -s**6/33 - 2*s**5/11 - 3*s**4/11 + 4*s**3/33 + 7*s**2/11 + 6*s/11 - 18. Determine c, given that u(c) = 0.
-3, -1, 1
Suppose f - 5 = -41. Let j = 43 + f. What is h in 17/3*h - 1 - 3*h**3 - j*h**2 = 0?
-3, 1/3
Let u(b) be the third derivative of 3/8*b**4 + 0*b - 17*b**2 + 1/10*b**5 - 2 + 1/120*b**6 + 2/3*b**3. Factor u(r).
(r + 1)**2*(r + 4)
Let u(q) = -126*q**5 + 369*q**4 - 99*q**3 - 510*q**2 + 243*q + 159. Let f(n) = -2*n**5 - n**4 + n**3 + n**2 - 1. Let g(h) = 3*f(h) - u(h). Solve g(j) = 0 for j.
-1, -2/5, 3/2
Let t(o) be the first derivative of -2/45*o**5 + 0*o**3 + 1/9*o**4 + 0*o + 4 + o**2 + 1/180*o**6. Let i(u) be the second derivative of t(u). Factor i(h).
2*h*(h - 2)**2/3
Suppose 0*c + 28 = 14*c. Factor -4*s**4 - 15*s**2 + 6*s**c + 25*s**2 + s**3 - 13*s**3.
-4*s**2*(s - 1)*(s + 4)
Factor -24 + 30*r**2 - 1 - 5*r**3 + 36*r**2 + 45*r - 81*r**2.
-5*(r - 1)**2*(r + 5)
Let 15/7 + 3/7*t**2 + 18/7*t = 0. What is t?
-5, -1
Let g = -1455/7 + 208. Let c(n) be the first derivative of -1/21*n**6 + 8/35*n**5 + 0*n - g*n**2 - 3/7*n**4 + 3 + 8/21*n**3. Factor c(o).
-2*o*(o - 1)**4/7
Let i(c) be the second derivative of -c**7/1400 - c**6/200 - c**5/100 - 5*c**3/6 + 6*c. Let h(p) be the second derivative of i(p). Factor h(w).
-3*w*(w + 1)*(w + 2)/5
Let a = -2/67 + 550/469. Factor -4/7*p**2 - a + 12/7*p.
-4*(p - 2)*(p - 1)/7
Let p = 11/13 + -317/390. Let c(l) be the first derivative of 6 - 2/15*l**2 + 0*l + p*l**4 - 2/45*l**3. Solve c(x) = 0.
-1, 0, 2
Let h be 396/(-176) - 114/(-40). Find t, given that -12/5*t**2 - 3*t - 6/5 - h*t**3 = 0.
-2, -1
Let s(i) be the second derivative of 3*i**5/10 - 17*i**4/12 + 2*i**3/3 + 6*i**2 + 269*i. Suppose s(m) = 0. What is m?
-2/3, 3/2, 2
Let j be (52/(-143))/(6/(-33)). Suppose 3*p - t - 45 = -6, -t - 27 = -2*p. Let p*o**j + 15/2*o**3 + 6*o + 0 + 3/2*o**4 = 0. What is o?
-2, -1, 0
Factor 10/3*y**3 - 4*y**2 - 8/3*y - 2/3*y**4 + 16/3.
-2*(y - 2)**3*(y + 1)/3
Factor 2*h + 2/3*h**3 + 2/3*h**4 - 10/3*h**2 + 0.
2*h*(h - 1)**2*(h + 3)/3
Suppose 0 = 3*x + 3*i - 3, x - 2*i = 4*x - 4. Factor -8*r**3 + x*r**2 + 6*r**4 + 92*r - 2*r**3 - 90*r.
2*r*(r - 1)**2*(3*r + 1)
Let k(q) be the first derivative of q**7/70 - 3*q**6/40 + q**4/2 - 9*q**2 + 14. Let t(b) be the second derivative of k(b). Find m such that t(m) = 0.
-1, 0, 2
Let t(f) be the first derivative of 0*f**2 + 2/5*f**5 + 0*f + 15 - 2/3*f**3 - 1/4*f**4 + 1/6*f**6. Determine d so that t(d) = 0.
-2, -1, 0, 1
Suppose -4*a - 18 = j, -4*a = -4*j + 10 + 18. Factor 39*i**j + 60*i - 20*i**2 - 2 - 18 + 16*i**2.
5*(i + 2)*(7*i - 2)
Let d = 14 + -17. Let n = d - -5. Factor g + 3*g**3 - 159*g**2 + 161*g**n - 2*g**3.
g*(g + 1)**2
Let s = 113363/62985 - -2/12597. Factor s + 3/5*r**5 - 3/5*r**4 + 3*r - 18/5*r**3 - 6/5*r**2.
3*(r - 3)*(r - 1)*(r + 1)**3/5
Let b be (-236)/210*-7 + (-2)/(-15). Let q(i) be the first derivative of -b + 0*i - 4/9*i**3 + 4/15*i**5 - 2/3*i**2 + 1/3*i**4. Suppose q(g) = 0. Calculate g.
-1, 0, 1
Let p be 27/16*(-13 + (-8 - 737/(-33))). Factor p + 15/8*y - 3/8*y**2.
-3*(y - 6)*(y + 1)/8
Let m = 1580/113 + 355746/1243. Let s = -300 + m. Suppose s*u**5 - 2/11*u**3 + 0 + 0*u**4 + 0*u + 0*u**2 = 0. What is u?
-1, 0, 1
Let m(c) be the second derivative of 5*c**4/12 - 20*c**3 + 360*c**2 + 268*c. Factor m(b).
5*(b - 12)**2
Let l(v) be the first derivative of -4*v**3/15 + 98*v**2/5 + 170. What is c in l(c) = 0?
0, 49
Suppose 0 = 5*o + 3*v - 555, 4*v - 128 = -6*o + 5*o. Factor 0 - 24*w**3 - 126*w - 45*w**2 + o*w + 3.
-3*(w + 1)**2*(8*w - 1)
Suppose 14*s + 3*j = 16*s - 21, -2*s + 19 = -j. Factor -3/2*t**4 + 6*t + 0 - 27/2*t**2 + s*t**3.
-3*t*(t - 4)*(t - 1)**2/2
Suppose -149 - 26 = -5*t. Let g be (-5)/t*-23 + (0 - 1). Determine v, given that -6/7*v**4 + g*v**3 + 0*v - 12/7*v**2 + 2/7 = 0.
-1/3, 1
Let j(z) be the second derivative of z**4/12 + 13*z**3/3 - 27*z**2/2 - z - 42. Solve j(s) = 0 for s.
-27, 1
Let o(v) be the second derivative of -v**6/15 - 13*v**5/5 - 169*v**4/6 - 29*v. Factor o(l).
-2*l**2*(l + 13)**2
Let c(q) be the first derivative of -q**6/960 - 3*q**5/160 - 5*q**4/64 + 28*q**3/3 + 29. Let u(y) be the third derivative of c(y). Let u(z) = 0. Calculate z.
-5, -1
Let z be -8 - (-4 - (-104)/(-16)). Let w(v) be the second derivative of 0*v**2 - 1/4*v**5 - z*v**3 + 0 + 1/6*v**6 + 7*v - 25/12*v**4. Factor w(g).
5*g*(g