4 - 2*t**3 + 6*t**2 + 2. Find p such that r(p) = 0.
-3, -1, 4
Let f(x) be the second derivative of 13*x**5/40 - 115*x**4/24 + 43*x**3/6 + 4*x**2 - 216*x. Factor f(r).
(r - 8)*(r - 1)*(13*r + 2)/2
Let x(g) be the first derivative of -g**6/90 + g**4/18 - g**2/6 - 2*g + 10. Let q(n) be the first derivative of x(n). Factor q(w).
-(w - 1)**2*(w + 1)**2/3
Factor 6302 - 867*n + 28143 + 5*n**2 + 37*n.
5*(n - 83)**2
Let w(j) be the second derivative of -10/9*j**2 + 0 - 11/27*j**3 + 5*j - 1/54*j**4. Factor w(s).
-2*(s + 1)*(s + 10)/9
Let r(v) = -4*v - 6 + 2*v + 3*v - 8. Let d be r(16). Factor 2*i**2 + i**4 - 3*i**4 + d*i + 10*i**3 - 12*i**3.
-2*i*(i - 1)*(i + 1)**2
Suppose -3*w - y + 7 = 0, -14 - 3 = -5*w + y. Let i(c) be the first derivative of c**3 - 4 + 4*c**2 + 8 - w*c**2. Factor i(m).
m*(3*m + 2)
Let p(r) = r**2 + 4*r - 14. Let f be p(-6). Let i = f - -11. Find n, given that -n**2 - 2*n**2 - 9 + i*n - 3*n**3 + 6*n = 0.
-3, 1
Determine s, given that 18*s**2 + 3/2*s**4 - 9*s**3 - 12*s + 0 = 0.
0, 2
Let y(s) = -s**4 + s**3 - s**2 + s + 1. Let a(p) = 5*p**5 + 20*p**4 + 45*p**3 - 40*p**2 - 30*p + 10. Let h(v) = a(v) - 10*y(v). Solve h(f) = 0 for f.
-4, -2, -1, 0, 1
Let z(h) be the first derivative of -2/5*h**3 + 2/25*h**5 - 20 + 0*h**2 + 1/5*h**4 + 0*h. What is c in z(c) = 0?
-3, 0, 1
Suppose i = -i + 4. Find g, given that 79*g**i - 104*g - 343*g**2 - 8 - 74*g**2 = 0.
-2/13
Let n(m) be the third derivative of 1/90*m**6 + 1/3*m**3 + 17*m**2 - 1/9*m**4 + 0*m - 1/18*m**5 + 0. Factor n(q).
2*(q - 3)*(q + 1)*(2*q - 1)/3
Let y(a) be the first derivative of 5*a**3/12 - 73*a**2/8 - 15*a/2 + 54. Let y(d) = 0. What is d?
-2/5, 15
Let x(d) be the third derivative of d**6/30 - 8*d**4/3 + 19*d**2 - 1. Solve x(y) = 0.
-4, 0, 4
Factor -60*a - 33*a**2 + 3*a**2 + 33*a**2.
3*a*(a - 20)
Suppose -602 = 2*x + d - 618, -4*d = -2*x - 24. Suppose 1/2*j - 1/4 + 1/4*j**x + 0*j**2 - 1/2*j**3 = 0. Calculate j.
-1, 1
Let q be -1 + (-5 - -1) + 50. Let h be ((-4)/65)/(162/q + -4). Suppose h*p**2 - 2/13 + 2/13*p**3 - 2/13*p = 0. Calculate p.
-1, 1
Let x(f) be the first derivative of -5*f**4/4 + 155*f**3/3 + 80*f**2 + 69. Let x(q) = 0. Calculate q.
-1, 0, 32
Let l(x) be the third derivative of 1/24*x**4 + 0 + 0*x + 0*x**3 - 22*x**2 + 1/420*x**5. Let l(b) = 0. Calculate b.
-7, 0
Let y(s) = -4*s**2 + 19*s - 3. Let t(z) be the first derivative of 4*z**3 - 28*z**2 + 8*z - 2. Let f(l) = -3*t(l) - 8*y(l). Factor f(o).
-4*o*(o - 4)
Find g such that -g**4 + 8/3*g**3 + 10*g**2 + 5/3 + 8*g = 0.
-1, -1/3, 5
Suppose -29 - 241 = -3*u. Let i = u + -90. Factor 1/6*y**2 + 0 + i*y.
y**2/6
Let d(a) be the third derivative of -a**7/35 - a**6/40 + 9*a**5/10 + 9*a**4/8 + 258*a**2. Factor d(u).
-3*u*(u - 3)*(u + 3)*(2*u + 1)
Determine l so that 4/3*l**4 - 4/9*l**2 - 2*l**5 + 0*l + 10/9*l**3 + 0 = 0.
-2/3, 0, 1/3, 1
Let g(h) = h**2 - 2*h + 2. Let l be g(3). Factor 2 - n**2 + l*n**3 - 12*n + 7*n - n**2.
(n - 1)*(n + 1)*(5*n - 2)
Let d be ((-2)/(-3))/((-624)/(-117)). Let x(u) be the first derivative of -d*u**2 - 3/16*u**4 - 1/20*u**5 + 0*u - 1/4*u**3 - 7. Solve x(g) = 0 for g.
-1, 0
Let c = 919/5 - 182. Let z(k) be the second derivative of 2/15*k**4 + 4/5*k**3 + 0 + 2*k + c*k**2. Factor z(n).
2*(2*n + 3)**2/5
Let q be (1 - -3)/(15 + -13). Let a(o) be the first derivative of 1/14*o**6 + 0*o**q + 0*o**3 + 0*o + 3/35*o**5 + 0*o**4 + 4. Suppose a(f) = 0. Calculate f.
-1, 0
Let v(z) = -5*z**3 - 2*z**2 + z - 10. Let o(c) = -c + 4*c**2 + 2 - 3 - c**3 - 3*c**2. Let a(j) = -40*o(j) + 5*v(j). Factor a(s).
5*(s - 2)*(s - 1)*(3*s - 1)
Suppose p - 60 = -5*p. Suppose 8 + 15*x**2 - 5*x + p*x**4 - 15*x**4 + 5*x**3 - 18 = 0. What is x?
-1, 1, 2
Solve -64/7*g + 16/7*g**3 - 48/7 + 4/7*g**4 - 4/7*g**2 = 0.
-3, -2, -1, 2
Let j be 14/70 - 14/(-5). Factor 4*u**3 - 6*u**2 + 2*u**5 - 3*u**4 - 3*u + 9*u**4 - 2*u**j - u.
2*u*(u - 1)*(u + 1)**2*(u + 2)
Determine k, given that 1/4*k**3 + 3 - 1/4*k**2 - 2*k = 0.
-3, 2
Let n(p) be the second derivative of p**6/150 + 4*p**5/25 + 2*p**4/5 - 32*p**3/15 - 56*p**2/5 + 245*p + 1. Let n(u) = 0. Calculate u.
-14, -2, 2
Let q(p) be the second derivative of -p**4/21 + 4*p**3/21 + 6*p**2/7 + 163*p. Let q(y) = 0. Calculate y.
-1, 3
Suppose -5*t + z + 12 = 3*z, 4*t - z - 7 = 0. Suppose -5*o + 3*u = 2, -3*o - 10 = t*u - 6*u. Factor 2/3*x**o + 0 + 2/3*x.
2*x*(x + 1)/3
Let a(v) be the first derivative of -105*v**4/4 + 10*v**3/3 + 105*v**2/2 - 10*v - 381. Suppose a(g) = 0. Calculate g.
-1, 2/21, 1
Let p(j) = -2*j**2 + j**2 + j**3 + 4 - 3*j**3 + 3*j**3. Let u be p(0). Factor -7*c**2 + 7*c**2 - 8 + 3*c**3 + 9*c**2 - u.
3*(c - 1)*(c + 2)**2
Let w(o) be the third derivative of -o**6/15 - o**5/5 + 7*o**4/6 + o**3/3 + 16*o**2. Let l(r) = r**3 - r - 1. Let h(j) = -10*l(j) - w(j). Factor h(k).
-2*(k - 4)*(k - 1)**2
Let q(s) = s**2 + 11*s - 14. Let u(i) = -i + 1. Let w(z) = -q(z) - 6*u(z). Let m be w(-6). Solve -3/2*h**m + 0 + 3/2*h**4 + 0*h**3 + 0*h = 0 for h.
-1, 0, 1
Factor -2/3*s - 2/15*s**2 - 8/15.
-2*(s + 1)*(s + 4)/15
Let q(f) be the first derivative of -f**6/15 - 2*f**5/25 + 7*f**4/10 + 26*f**3/15 + 6*f**2/5 + 124. Suppose q(l) = 0. What is l?
-2, -1, 0, 3
Solve 1/9*j**2 + 0 - 14/9*j = 0.
0, 14
Let d(k) = 9*k - 112. Let q be d(13). Let o(j) be the first derivative of 6/7*j**2 + 6/7*j**3 + 3/7*j**4 + 6 + 3/35*j**q + 3/7*j. Suppose o(p) = 0. What is p?
-1
Let d(h) be the second derivative of 13*h + 0 + 1/5*h**4 + 1/50*h**5 + 4/5*h**2 + 3/5*h**3. Factor d(a).
2*(a + 1)**2*(a + 4)/5
Suppose 67 = -t + h, 3*h + 67 = -t - 12. Let i = t + 85. Factor -i*q**2 + 18*q - 4 + 7/2*q**3.
(q - 2)**2*(7*q - 2)/2
Let s(j) be the third derivative of 4*j**5/15 + j**4/6 - 12*j**3 - 12*j**2 + 2. Solve s(x) = 0 for x.
-9/4, 2
Let s(r) = -3*r**2 - 80*r - 61. Let l(x) = 3*x**2 + 78*x + 63. Let c(i) = 4*l(i) + 3*s(i). Let c(h) = 0. Calculate h.
-23, -1
Factor 99*q**4 + 141*q**4 - 344*q**4 - 116*q**2 + 12*q**5 + 256*q**3 - 12*q**2.
4*q**2*(q - 4)**2*(3*q - 2)
Let t(k) be the second derivative of 3*k**5/10 - 29*k**4/30 - 2*k**3/15 + 242*k. What is f in t(f) = 0?
-1/15, 0, 2
Factor -1/2*o**3 + 15/2 + 1/2*o - 15/2*o**2.
-(o - 1)*(o + 1)*(o + 15)/2
Let d(y) be the second derivative of -1/4*y**6 + 0 - 3/4*y**2 - 2*y + 1/28*y**7 + 5/4*y**3 - 5/4*y**4 + 3/4*y**5. Suppose d(o) = 0. What is o?
1
Let y(j) be the third derivative of j**5/15 - 61*j**4/3 + 7442*j**3/3 - 2*j**2 - 86*j. Factor y(m).
4*(m - 61)**2
Let h(n) be the first derivative of 9/4*n**2 + 0*n - 1/4*n**3 - 11. Factor h(u).
-3*u*(u - 6)/4
Let y be -157 - -136 - (-260)/12. Suppose -8*h**2 - 32/9*h**4 - 8/9 + y*h**5 + 68/9*h**3 + 38/9*h = 0. Calculate h.
1, 4/3
Suppose 37*a - 41*a = -16. Suppose a*s + 4 = 6*s. Solve -11/4*z + z**s - 3/4 = 0.
-1/4, 3
Let p(f) be the second derivative of f**4/54 + 4*f**3/27 + 4*f**2/9 + 71*f. Solve p(z) = 0 for z.
-2
Factor -2 - 464*s**3 + 19*s**2 + 231*s**3 + 234*s**3 + 2.
s**2*(s + 19)
Let x(h) be the third derivative of h**6/540 + 151*h**5/270 + 1406*h**4/27 - 5776*h**3/27 - 445*h**2. Factor x(w).
2*(w - 1)*(w + 76)**2/9
Let y = -1/600 - 4949/600. Let u = y - -131/12. Solve -4/3*s + u + 1/6*s**2 = 0 for s.
4
Let q(f) be the second derivative of -f**2 - f + 0 - 1/12*f**4 + 0*f**3 - 1/30*f**5. Let b(w) be the first derivative of q(w). Factor b(m).
-2*m*(m + 1)
Let r(y) = -31*y**2 - 15*y + 1. Suppose 4*q - 3*c = c - 92, -4*q = -5*c + 89. Let f(u) = -125*u**2 - 60*u + 5. Let v(k) = q*r(k) + 6*f(k). Factor v(j).
2*(4*j + 1)*(7*j + 2)
Suppose -21*i = -77 + 14. Let p be ((-2)/i)/((-12)/27). Factor 1 + 1/2*z**2 + p*z.
(z + 1)*(z + 2)/2
Factor -6*y**2 - 21/2*y - 1/2*y**3 - 5.
-(y + 1)**2*(y + 10)/2
Let u(v) = -39 + 188 + 78 - 5*v**2 - 72*v. Let r(x) = -2*x**2 - 24*x + 76. Let k(l) = 11*r(l) - 4*u(l). Factor k(n).
-2*(n - 6)**2
Let i(v) be the second derivative of -v**5/4 - 2*v**4/3 - v**3/2 + v**2 + 7*v. Let x(f) = 6*f**3 + 9*f**2 + 3*f - 3. Let p(l) = 3*i(l) + 2*x(l). Solve p(d) = 0.
-1, 0
Let d(u) be the first derivative of -u**6/240 + u**4/96 - 11*u + 15. Let c(k) be the first derivative of d(k). Suppose c(o) = 0. What is o?
-1, 0, 1
Let w(d) be the third derivative of 0 + 3*d**2 - 1/30*d**5 + 0*d**4 + 0*d**3 + 0*d. Suppose w(x) = 0. Calculate x.
0
Suppose -5*v = -3*v + 120. Let i be v/(-25) + -1 + (-2 - -1). Find p, given that -2/5*p**4 + i*p - 6/5*