c**4.
c**3*(c + 1)**2/8
Let n(f) = -4*f**2 - 60*f + 64. Let k(v) = 3*v**2 + 40*v - 43. Let l(x) = 7*k(x) + 5*n(x). Factor l(r).
(r - 19)*(r - 1)
Suppose 3*s = 3*w + 12, -w - 2 = w. Factor 14*u**4 + u - 38*u**s - u + 16*u**2 + 8*u + 0*u.
2*u*(u - 2)*(u - 1)*(7*u + 2)
Let x(h) be the third derivative of -h**5/15 - 5*h**4/6 - 8*h**3/3 - 2*h**2. Solve x(y) = 0 for y.
-4, -1
Let r be (-1)/4 - (-22)/(-8). Let l be (1*(3 + r))/2. Factor 1/3*m**3 + 0*m**2 + l - 1/3*m.
m*(m - 1)*(m + 1)/3
Let w(n) = 6*n - 2*n + 10 - 3*n. Let v be w(-6). Solve -v*o**5 - o**4 + 0*o**5 - 5*o**4 - 2*o**3 = 0 for o.
-1, -1/2, 0
Suppose 102 = 4*f + 82. Solve -5/3*b**4 - 10/3*b**3 - 10/3*b**2 - 1/3*b**f - 5/3*b - 1/3 = 0.
-1
Let f be (-8)/5 - (-6)/(-15). Let j(q) = q**2 + q - 1. Let m be j(f). Factor t + m + 1/4*t**2.
(t + 2)**2/4
Let m(u) = u + 1. Let l(d) = -4*d**2 + 4*d - 12. Let r(i) = -l(i) - 6*m(i). Factor r(j).
2*(j - 1)*(2*j - 3)
Let n(h) = h + 4. Let y be n(-2). Find r such that -3*r**y - 2*r**3 + 2*r - 2*r**2 + 3*r**2 + 2*r**4 = 0.
-1, 0, 1
Suppose 5 = o - 5*w + 2*w, -o - 3 = 5*w. Factor -4 - t**3 + t + t**2 - o + 6 - 1.
-(t - 1)**2*(t + 1)
Let p(z) = -z + 5. Let q be p(1). Factor 1/5*f**q - 4/5*f - 4/5*f**3 + 1/5 + 6/5*f**2.
(f - 1)**4/5
Let i(f) = -8*f**2 - 2*f - 14. Let t(k) = -15*k**2 - 5*k - 27. Let l(c) = 11*i(c) - 6*t(c). Solve l(v) = 0.
-2
Suppose -3 - 5*z**2 - 3*z**4 + 11*z**2 - 2*z**5 - z**5 - 3*z + 6*z**3 = 0. What is z?
-1, 1
Let u(a) = -4*a**2 - 3*a. Let p(k) = -2*k**2 - 2*k. Let m(w) = 10*p(w) - 4*u(w). Factor m(j).
-4*j*(j + 2)
Let w = 7 + -4. Solve m**w + m + m - 2 + 2*m**2 - 3*m**3 = 0.
-1, 1
Let p = 131 + -261/2. Factor 0 + p*j - 1/2*j**3 + 0*j**2.
-j*(j - 1)*(j + 1)/2
Factor 3/2*a**3 - 1 + 3*a - 1/4*a**4 - 13/4*a**2.
-(a - 2)**2*(a - 1)**2/4
Let x(r) be the second derivative of -r**7/27 - 2*r**6/135 + 7*r**5/90 + r**4/27 + 9*r. Let x(h) = 0. Calculate h.
-1, -2/7, 0, 1
Let f = -1253999/300 + 4180. Let c(w) be the third derivative of 0*w + 0*w**4 - f*w**5 + 0 + 1/1050*w**7 + 2*w**2 + 0*w**6 + 0*w**3. Factor c(g).
g**2*(g - 1)*(g + 1)/5
Let o(b) be the third derivative of -b**6/60 - b**5/30 + b**4/12 + b**3/3 + 16*b**2. Let o(i) = 0. Calculate i.
-1, 1
Let d = -3 + 3. Let g = -445 + 448. Find l, given that d*l - 1/3*l**4 + 0*l**g + 0 + 1/3*l**2 = 0.
-1, 0, 1
Let n(o) be the third derivative of -3*o**7/980 + o**6/140 - o**5/210 + o**3/6 - 2*o**2. Let b(i) be the first derivative of n(i). Determine r so that b(r) = 0.
0, 1/3, 2/3
Suppose -g + 4*g = 12, g = 3*l - 2. Factor -8/17*z + 0 - 2/17*z**l.
-2*z*(z + 4)/17
Factor -2/5*n**2 - 72/5 + 24/5*n.
-2*(n - 6)**2/5
Let g(d) be the second derivative of 3*d**5/130 + 8*d**4/39 - d**3/3 - 6*d**2/13 - 16*d. Suppose g(j) = 0. Calculate j.
-6, -1/3, 1
Let o(f) be the third derivative of -f**6/40 + f**5/10 + f**4/8 - f**3 - 24*f**2. Suppose o(j) = 0. What is j?
-1, 1, 2
Let u(s) = -2*s**3 - 5*s**2 + 8*s + 5. Let j(o) = -3*o**3 - 10*o**2 + 17*o + 10. Let a(m) = 3*j(m) - 7*u(m). Determine t, given that a(t) = 0.
-1, 1
Let m be (-5)/10 - (-33)/6. Let d(x) be the second derivative of -1/20*x**m + 1/6*x**3 + 0*x**2 + 3*x + 0 - 1/12*x**4 + 1/30*x**6. Factor d(u).
u*(u - 1)**2*(u + 1)
Let n(r) be the first derivative of r**8/1680 - r**6/360 + 4*r**3/3 + 4. Let k(f) be the third derivative of n(f). Factor k(v).
v**2*(v - 1)*(v + 1)
Let x(s) be the third derivative of -s**7/1470 - s**6/210 - s**5/105 - s**2 - 14*s. Suppose x(h) = 0. What is h?
-2, 0
Solve -1/6*t**3 + 0 - 2/3*t - 2/3*t**2 = 0 for t.
-2, 0
Let l(c) be the first derivative of c**8/84 + c**7/30 + c**6/45 + 3*c**3 - 2. Let s(i) be the third derivative of l(i). Factor s(y).
4*y**2*(y + 1)*(5*y + 2)
Let q(c) = -c**4 + 6*c**2 + 4*c - 5. Let o(a) = -2*a**4 + 11*a**2 + 7*a - 9. Let b(t) = -4*o(t) + 7*q(t). Factor b(d).
(d - 1)**2*(d + 1)**2
Suppose -4*v - 2/5*v**2 + 0 = 0. What is v?
-10, 0
Let s = 51/5 - 61/6. Let x(w) be the second derivative of -w + 0 + 0*w**3 + s*w**4 - 1/5*w**2. Factor x(z).
2*(z - 1)*(z + 1)/5
Let j(c) be the third derivative of -c**6/600 - c**5/300 + 2*c**4/15 - 2*c**3/3 - 4*c**2 + 10. Factor j(f).
-(f - 2)**2*(f + 5)/5
Factor v**2 - 1/5*v - 3/5*v**3 - 1/5.
-(v - 1)**2*(3*v + 1)/5
Factor -2/3 + 5/3*c**2 - c.
(c - 1)*(5*c + 2)/3
Suppose -4*z + 4 = -4. Let j(n) be the second derivative of -1/12*n**3 + 13/40*n**5 + 1/12*n**6 + 3/8*n**4 + z*n - 1/2*n**2 + 0. Factor j(q).
(q + 1)**3*(5*q - 2)/2
Let q(w) = -w**3 - 14*w**2 + w + 18. Let x be q(-14). Let o(a) be the first derivative of 7/2*a**4 + 32/3*a**3 + x*a - 2 + 11*a**2. Find y such that o(y) = 0.
-1, -2/7
Let z be (-402)/737 + (-124)/(-66). Solve 4*o**2 - 16/3 + z*o**3 + 0*o = 0 for o.
-2, 1
Let -2/5*u**3 - 24/5*u + 16/5 + 12/5*u**2 = 0. What is u?
2
Let y(u) = 4*u**4 + 8*u**3 + 10*u**2 + 6. Let p(o) = 9*o**4 + 17*o**3 + 20*o**2 - o + 13. Let t(w) = -6*p(w) + 13*y(w). Factor t(a).
-2*a*(a - 3)*(a + 1)**2
Suppose -7 - 11 = -6*j. Let u(p) be the first derivative of -2/21*p**j - 1/7*p**2 + 0*p + 2/35*p**5 + 1/14*p**4 - 3. Factor u(n).
2*n*(n - 1)*(n + 1)**2/7
Let m(t) = t + 13. Let h be m(-6). Let p = 11 - h. Factor -6*s**2 + 4*s**2 + 2*s**3 - p*s**2 + 4*s**2.
2*s**2*(s - 1)
Let x = 2 + 2. Factor -g**4 + g**3 + g**2 + 0*g**x - g**3.
-g**2*(g - 1)*(g + 1)
Let s(r) be the third derivative of 0*r**4 + 0*r**3 - 1/20*r**5 + 0 + 0*r + 7*r**2. Suppose s(p) = 0. What is p?
0
Let s(d) be the second derivative of -d**7/420 + d**6/120 - d**5/80 + d**4/3 + 6*d. Let v(r) be the third derivative of s(r). Factor v(p).
-3*(2*p - 1)**2/2
Let y(c) be the third derivative of -c**5/390 + 4*c**3/39 - 8*c**2. Suppose y(p) = 0. Calculate p.
-2, 2
Let m(k) = -6*k. Let n be m(1). Let i be 24/9 + 4/n. Factor 2*f + f**i - 6*f**2 - 2*f**2.
-f*(7*f - 2)
Let p(o) = -7 + 3*o - 15*o**2 + 4*o**2 + 9. Let l(v) = 10*v**2 - 2*v - 2. Let f = 16 - 10. Let s(w) = f*l(w) + 5*p(w). Solve s(x) = 0 for x.
-1, 2/5
Let u = 1459061 + -898781363/616. Let y = 1/56 + u. Factor 0 + 2/11*t**2 + y*t.
2*t*(t + 2)/11
Let v(m) be the second derivative of 0*m**2 - 9/40*m**5 + 3/20*m**6 - 1/28*m**7 + 0 + 0*m**3 - 5*m + 1/8*m**4. Solve v(u) = 0 for u.
0, 1
Let d(z) be the first derivative of 2*z**5/65 - 5*z**4/26 + 14*z**3/39 - 3*z**2/13 + 31. Solve d(h) = 0.
0, 1, 3
Let a be (-2)/(-2) + -5 + 6. Factor -n - 2*n**a + 1 + 3*n**2 - n.
(n - 1)**2
Factor 0 + 4/7*d - 2/7*d**2.
-2*d*(d - 2)/7
Let y be -71*5/180 - (-2 + 0). Let d(i) be the second derivative of 0*i**2 - 3*i + 0 - 1/9*i**3 - y*i**4. Factor d(z).
-z*(z + 2)/3
Find u such that 5*u**3 - 27 - 20*u**3 + 18*u**2 + 7*u**3 + u**4 = 0.
-1, 3
Suppose -6*o - 15 = -11*o. Suppose 0 = o*r - 1 - 8. Suppose 0 - g**r - 1/3*g**4 - g**2 - 1/3*g = 0. What is g?
-1, 0
Factor 2/7*k**4 + 16/7 + 8/7*k - 12/7*k**2 - 2/7*k**3.
2*(k - 2)**2*(k + 1)*(k + 2)/7
Let d(z) = z**3 + 3*z**2 - z - 3. Let h be (-21)/14*(-2)/(-1). Let p be d(h). Factor 2/5*m - 4/5*m**2 + p + 2/5*m**3.
2*m*(m - 1)**2/5
Factor 40/11*n**4 + 0*n**2 + 0*n + 50/11*n**5 + 8/11*n**3 + 0.
2*n**3*(5*n + 2)**2/11
Let v(p) be the second derivative of p**7/350 - p**6/200 - p**5/100 + p**4/40 + 3*p**2/2 + 2*p. Let m(g) be the first derivative of v(g). Factor m(i).
3*i*(i - 1)**2*(i + 1)/5
Suppose 25 = 5*p + 5*w, 0 = -w + 3*w - 4. Factor 4/3*q**2 + 1/3*q**p - 4/3*q**4 - 1/3*q + 0.
-q*(q - 1)*(q + 1)*(4*q - 1)/3
Let i(b) = 5*b**4 - b**3 - 5*b**2 + 3*b. Let f(d) = 66*d**4 - 12*d**3 - 66*d**2 + 39*d. Let v(k) = -2*f(k) + 27*i(k). Find c, given that v(c) = 0.
-1, 0, 1
Let a(g) be the second derivative of g**4 + 2*g**3 + 0 + 1/5*g**5 + 2*g**2 - 4*g. Solve a(q) = 0 for q.
-1
Factor -2/3*p**2 - 2/3*p**5 + 2/3*p**3 + 0*p + 2/3*p**4 + 0.
-2*p**2*(p - 1)**2*(p + 1)/3
Let q(s) = s + 24. Let r be q(-24). What is z in 2/5*z**2 + r - 2/5*z = 0?
0, 1
Suppose 3 + 45*i**3 - 25*i**4 + 5*i**5 - 35*i**2 + 1104*i - 3 - 1094*i = 0. What is i?
0, 1, 2
Let h(n) be the third derivative of -n**9/52920 - n**8/23520 + n**4/24 - 5*n**2. Let x(m) be the second derivative of h(m). Find d such that x(d) = 0.
-1, 0
Let a(o) be the third derivative of -o**9/241920 + o**8/26880 - o**7/10080 - o**5/20 - 2*o**2. Let y(j) be the third derivative of a(j). Factor y(g).
-g*(g - 2)*(g - 1)/4
Let r(z) be the third derivative of z**7/294 - z**6/280 - z**5/35 - z**4/42 - 10*z**2. Determine d, given that