Suppose -5*r + 11 = t - 3*r, -3*r = 5*t - 34. Solve l**2 + 14*l**2 - t + 3*l**3 + 24*l + 17 = 0 for l.
-2, -1
Let l(q) be the first derivative of 36 + 3*q**3 + 7/2*q**2 - 2*q. Factor l(o).
(o + 1)*(9*o - 2)
Let v(f) = -12*f**3 + 2*f**2 + 4*f + 9. Let w be v(-2). Let h = 108 - w. Suppose 3/5*p**h + 1/5*p - 1/5*p**4 - 3/5*p**2 + 0 = 0. What is p?
0, 1
Let k(b) be the first derivative of 1/6*b**6 - b**3 + 1/4*b**4 + 3/5*b**5 - b**2 + 0*b - 6. Factor k(z).
z*(z - 1)*(z + 1)**2*(z + 2)
Let l(p) be the third derivative of 0*p + 0 - 2/5*p**3 + 9/40*p**4 - 9*p**2 + 1/200*p**6 - 3/50*p**5. Suppose l(k) = 0. What is k?
1, 4
Let d(r) = -r**2 + 5*r. Let q(s) = -2*s**3 - 50*s**2 - 208*s + 110. Let j(u) = 3*d(u) + q(u). Factor j(l).
-(l + 5)*(l + 22)*(2*l - 1)
Let g(y) be the first derivative of 2*y**7/147 + 8*y**6/35 + 48*y**5/35 + 64*y**4/21 + 6*y - 10. Let i(p) be the first derivative of g(p). Factor i(z).
4*z**2*(z + 4)**3/7
Let m(v) be the third derivative of v**7/70 - v**6/8 + 7*v**5/20 - 3*v**4/8 - 37*v**2. Determine a, given that m(a) = 0.
0, 1, 3
Factor 0 + l - 7/8*l**2 - 1/8*l**3.
-l*(l - 1)*(l + 8)/8
Let p(t) be the first derivative of 9 + 0*t**3 + 1/2*t**2 - 1/12*t**4 - 2/3*t. Factor p(b).
-(b - 1)**2*(b + 2)/3
Let o(h) be the first derivative of h**4/12 + h**3 + 10*h**2/3 + 4*h - 79. Factor o(x).
(x + 1)*(x + 2)*(x + 6)/3
Suppose 3*y - 12 = 3. Suppose -3*b - 12 = -q, y*b = -4*q + 29 + 36. Suppose 11*x**3 + 124*x**4 + 60*x**5 - 9*x**4 - 5*x + 34*x**3 - q*x**2 + 0*x = 0. What is x?
-1, -1/4, 0, 1/3
Factor 152/7*t + 0 - 2/7*t**2.
-2*t*(t - 76)/7
Suppose 5*t + 3*i + 4 = 0, -5*i = t - 2*i - 4. Let y = t - -2. Determine r, given that -2/13*r**3 + y*r**2 + 0 + 2/13*r = 0.
-1, 0, 1
Suppose 0 = -10*x + 3*x + 28. Let s(z) = 6*z**2 - 77*z + 301. Let f(m) = -3*m**2 + 38*m - 151. Let j(h) = x*s(h) + 7*f(h). Factor j(p).
3*(p - 7)**2
Let n(u) be the first derivative of -20*u**3/3 - 6*u**2 - 318. Find a such that n(a) = 0.
-3/5, 0
Find t such that -22*t - 5*t**2 + 15/2*t**3 - 1/2*t**5 + 2*t**4 - 12 = 0.
-2, -1, 2, 6
Let i(z) be the third derivative of z**7/280 - z**6/60 - z**5/40 + z**4/4 + 4*z**3/3 - 2*z**2. Let v(f) be the first derivative of i(f). Factor v(a).
3*(a - 2)*(a - 1)*(a + 1)
Let t be (-156)/(-9) + 2/3. Let h be 1/2 + t/4. Factor -4*x + 6*x**3 + h*x**2 + 3 + 0*x**3 - 5*x**3 + 11*x.
(x + 1)**2*(x + 3)
Factor 6/13 - 16/13*i**2 - 10/13*i.
-2*(i + 1)*(8*i - 3)/13
Suppose -5*t + 2*t + 16 = -s, 0 = -5*s - t - 32. Let c be (4/(-7))/(2/s). Factor 3*x - x + 0*x**2 - x**2 - x**c.
-2*x*(x - 1)
Solve 358*n**5 + 51*n**4 + 88*n - 362*n**5 - 31*n**4 - 68*n**2 - 4*n**3 - 32 = 0.
-2, 1, 4
Let v be 5 - 0 - (444/36 - 8). Suppose 1/3*h**2 + 1/3 - v*h = 0. What is h?
1
Let q be ((-20708)/(-21))/(14/(-21)). Let w = q - -1483. Factor 0 - 66/7*h**3 - 24/7*h**4 - 72/7*h**2 - 3/7*h**5 - w*h.
-3*h*(h + 1)**2*(h + 3)**2/7
Let k(g) be the first derivative of 0*g + 7/6*g**4 + 0*g**2 + 4/9*g**3 + 2/5*g**5 - 18. Factor k(b).
2*b**2*(b + 2)*(3*b + 1)/3
Suppose 4*n - 15 = n. Factor 151 + n*d**2 - 30*d - 34*d + 105 - d**2.
4*(d - 8)**2
Let d(p) = -12*p**3 - 2*p**2 - 5. Let r be d(4). Let v be (-713)/r + (-2)/7. Solve -3/5*s**2 - 6/5*s - v = 0 for s.
-1
Let y(x) be the second derivative of x**6/1800 + x**5/200 - x**4/30 + 3*x**3/2 - 5*x. Let i(k) be the second derivative of y(k). Suppose i(a) = 0. Calculate a.
-4, 1
Suppose 28 = s - 4*z, 1292 = -4*z + 1268. Suppose -3/4*q**s - 9/4*q**2 - 3*q**3 + 0 + 0*q = 0. What is q?
-3, -1, 0
Let w be (-902)/(-540) + (-100)/60. Let m(f) be the third derivative of 0 - 9*f**2 + 0*f**4 + 1/27*f**3 - w*f**5 + 0*f. Factor m(h).
-2*(h - 1)*(h + 1)/9
Let y(n) be the first derivative of 2*n**3/39 - 6*n**2/13 - 12. Factor y(t).
2*t*(t - 6)/13
Suppose -y - 5*z = -2*z - 143, 409 = 3*y + 4*z. Let g = 133 - y. Find o, given that -32/3*o - 10/3*o**g - 8/3 + 14/3*o**3 = 0.
-1, -2/7, 2
Let u(s) be the third derivative of 1/315*s**7 + 0*s**3 + 0 - 1/90*s**5 - 1/18*s**4 + 0*s + 1/90*s**6 + 2*s**2. What is v in u(v) = 0?
-2, -1, 0, 1
Let m(j) be the third derivative of -j**8/1512 + j**7/135 - 19*j**6/540 + 5*j**5/54 - 4*j**4/27 + 4*j**3/27 - 86*j**2. Determine u so that m(u) = 0.
1, 2
Let r(f) = 65*f - 65. Let c(i) = -3*i**2 + 74*i - 63. Let t(h) = 5*h**2 - 146*h + 127. Let w(b) = 7*c(b) + 4*t(b). Let d(l) = 6*r(l) + 5*w(l). Factor d(q).
-5*(q - 11)*(q - 1)
Let v = -6926/171 - -816/19. Factor -128/9*f + 8*f**3 + v*f**4 + 32/9*f**2 + 0 + 2/9*f**5.
2*f*(f - 1)*(f + 4)**3/9
Let s(w) be the first derivative of w**3/6 + 15*w**2/4 - 38*w + 546. Let s(h) = 0. What is h?
-19, 4
Let a(s) be the first derivative of s**4/4 - 86*s**3/3 + 966*s**2 - 3528*s - 430. Let a(q) = 0. What is q?
2, 42
Let h(k) = 12*k - 58. Suppose -5*j - 2*g + 20 = -g, -4*j = -g - 25. Let x be h(j). Factor -3/2*p**x + 3/2*p + 3.
-3*(p - 2)*(p + 1)/2
Let d(u) be the second derivative of u**6/30 + u**5/2 + 11*u**4/4 + 22*u**3/3 + 10*u**2 + 260*u. Factor d(z).
(z + 1)*(z + 2)**2*(z + 5)
Let h(w) be the third derivative of w**5/180 - w**4/6 + 10*w**3/9 - 2*w**2 + 45*w. Factor h(v).
(v - 10)*(v - 2)/3
Let o(i) = -i**2 - 7*i - 4. Let l be o(-6). Find h such that -39*h**2 + l*h + 48*h**2 - 3*h**3 + 10*h = 0.
-1, 0, 4
Factor 11*a + 34*a - 275 - 1 - 2*a**2 + 59*a - 2*a**2.
-4*(a - 23)*(a - 3)
Suppose -19*u = -1417 - 350. Suppose 14*h - u + 37 = 0. Factor 1/9*z**5 - 2/9*z**2 + 2/9*z**h + 0 + 0*z - 1/9*z**3.
z**2*(z - 1)*(z + 1)*(z + 2)/9
Let z(u) be the third derivative of u**8/50400 + u**7/4200 + 4*u**5/5 - 11*u**2. Let l(r) be the third derivative of z(r). Factor l(p).
2*p*(p + 3)/5
Suppose -17*t**2 - 74/5*t - 1/5*t**5 - 11/5*t**4 - 24/5 - 9*t**3 = 0. What is t?
-4, -3, -2, -1
Let f be 7/2*(-2)/(-3). Let j be 4/(-6) + (-160)/(-48). Solve 1/3 + 14/3*m**2 - j*m**3 - f*m = 0.
1/4, 1/2, 1
Suppose -5*x - 2*t = -6*t + 39, 3 = -x - 4*t. Let o be (-110)/(-35) + 2/x - 2. Solve 1/7*m**4 + o*m**3 + 12/7*m + 13/7*m**2 + 4/7 = 0 for m.
-2, -1
Solve -68/3 + 548/3*n + 64/3*n**3 - 1120/3*n**2 = 0.
1/4, 17
Suppose -6*a = -86 + 26. Suppose 4*t = a + 2, k - 16 = -4*t. Find m, given that 32/5*m + 24/5*m**3 - 220*m**k - 280*m**5 + 176/5*m**2 + 0 = 0.
-1/2, -2/5, -2/7, 0, 2/5
Find q, given that -1715/4 - 12705/4*q**2 + 8085/4*q + 6655/4*q**3 = 0.
7/11
Let l(f) be the third derivative of 1/25*f**5 + 1/525*f**7 + 1/75*f**6 + 1/15*f**3 + 0 - 10*f**2 + 1/15*f**4 + 0*f. Solve l(s) = 0.
-1
Let u be -1 + 2 + 0 + (-4446)/4394. Let a = u - -356/1521. Suppose 0 - 4/9*b - a*b**2 = 0. What is b?
-2, 0
Let s = 26 - 16. Let h be ((-15)/60)/(2/(-16)). Let -o - 2*o + 13*o + 0*o**4 - s*o**3 + 5*o**4 - 5*o**h = 0. What is o?
-1, 0, 1, 2
Factor -5 - 9*a**3 - 331*a**2 + 8*a**4 - 203 - 281*a**2 - 4*a**4 + 205*a**3 + 620*a.
4*(a - 1)**3*(a + 52)
Let r(i) be the first derivative of -3*i**5/5 + 9*i**4/2 - 12*i**3 + 15*i**2 - 9*i + 153. Suppose r(l) = 0. What is l?
1, 3
Let b(q) be the first derivative of 1/35*q**5 + 3/7*q**3 - 3/14*q**4 - 1 - 2/7*q**2 + 0*q. Factor b(r).
r*(r - 4)*(r - 1)**2/7
Let t(i) be the first derivative of -1 - 32/21*i**3 + 0*i + 8/7*i**2 + 3/7*i**4. Factor t(k).
4*k*(k - 2)*(3*k - 2)/7
Let k be 4/6*(4 - 1). Let t be (21 + 3)*2/8. Solve -3*c**k - 6*c - 2*c + 2*c - 3*c - t = 0 for c.
-2, -1
Let q = 63 - 44. Solve -4*t**2 - q - 7 + 10 + 3*t + 13*t = 0 for t.
2
Suppose 6*k - 3*k = 0. Let f = -8567 + 8570. Factor -6/5 + k*q**2 + 3/5*q**f - 9/5*q.
3*(q - 2)*(q + 1)**2/5
Let g(t) = 4*t - 12 - 4 + 11. Let a be g(2). Solve -5*i**3 + a*i**3 - 25*i**4 + 27*i**4 = 0 for i.
0, 1
Suppose 139 + 181 = 10*b. Let h be b/(-306) + (-20)/(-90). Factor 0 - h*w + 4/17*w**2.
2*w*(2*w - 1)/17
Let r(l) = l**2 + 7*l - 96. Let j be r(-14). Let u(p) be the first derivative of 8 + 4/5*p**5 + 4*p - 8/3*p**3 - j*p**2 - 2/3*p**6 + 2*p**4. Factor u(a).
-4*(a - 1)**3*(a + 1)**2
Let c(f) = -6*f**2 - 26*f + 32. Suppose -8*x = -6*x + 8. Let u be 20*1*x/(-16). Let g(q) = 2*q**2 + 9*q - 11. Let n(p) = u*c(p) + 14*g(p). Factor n(s).
-2*(s - 1)*(s + 3)
Let t(o) be the third derivative of -o**7/350 + 3*o**6/100 + 6*o**5/25 - 28*o**4/5 + 192*o**3/5 + 111*o**2 - 5*o. Determine g so that t(g) = 0.
-6, 4
Factor 165/2*s**2 + 5/2*s**3 + 0 + 155*s.
5*s*(s + 2)*(s + 31)/2
Let f be 1/(104/(-12) + 9). Let r(t) be the second derivative of -5/2*t**f + 9/2*t**2 + 0 - 1/20*t**5 + 