13*m(k) + 6*n(k). Factor t(b).
-3*b*(b - 2)*(b + 6)
Let s be 8/23 - 21/70*2. Let d = -6/115 - s. Factor 0*t - 4/5*t**2 - d*t**5 + 3/5*t**4 + 0*t**3 + 0.
-t**2*(t - 2)**2*(t + 1)/5
Let f = 324576/55 + -29689/5. Let h = f + 183/5. Suppose 0 + 0*i**2 + 0*i - h*i**3 = 0. Calculate i.
0
Suppose 5*q - 6 = 19. Factor -11*a**2 + a**2 + 2*a**5 - 10*a**q + 3*a**5 + 15*a**3.
-5*a**2*(a - 1)**2*(a + 2)
Let 274*f**2 - 269*f**2 - 11*f - 9*f - 42 + 17 = 0. Calculate f.
-1, 5
Let g(u) be the third derivative of -u**7/504 - u**6/144 + 5*u**4/8 + 18*u**2. Let m(j) be the second derivative of g(j). Solve m(s) = 0 for s.
-1, 0
Let -377 + 377 - 41*g**2 - 4*g**3 + 5*g**2 - 41*g - 15*g = 0. What is g?
-7, -2, 0
Let c be 440/44 - (-44)/(-6). Factor -1/3*r**3 - c*r - 5/3*r**2 - 4/3.
-(r + 1)*(r + 2)**2/3
Let m(g) be the second derivative of -g**5/4 + 25*g**4/12 - 5*g**3 + 41*g - 1. Find y such that m(y) = 0.
0, 2, 3
Let r = 64786/113351 - 2/16193. Determine b so that -8/7*b**3 - r*b**4 + 0*b - 4/7*b**2 + 0 = 0.
-1, 0
Suppose 0 = b - 3*c - 11, 5*b - 11*c = -13*c + 21. Let z be ((-33)/(-5) - 0)*5. Factor -b*n**2 - z*n - 10*n - 80 + 3*n.
-5*(n + 4)**2
Let z(b) = 3*b**3 - 29*b**2 + 36*b - 35. Let j(k) = k**3 - 10*k**2 + 12*k - 12. Let u(i) = 11*j(i) - 4*z(i). Suppose u(r) = 0. Calculate r.
2
Solve 0*j**2 + 0 + 0*j**3 + 0*j - 2/7*j**4 = 0.
0
Let g(l) be the first derivative of -3*l**4/4 + 3*l**3 - 3*l**2 + 116. Solve g(r) = 0 for r.
0, 1, 2
Let i = -8654 + 8656. Factor 4/11 + 8/11*n + 3/11*n**i.
(n + 2)*(3*n + 2)/11
Let m be ((-5)/6)/1 - 933/(-622). Solve m*f - 2/3*f**2 + 4/3 = 0 for f.
-1, 2
Let n(m) be the second derivative of 0*m**3 + 7/40*m**5 + 1/24*m**4 + 2/15*m**6 + 0 - 4/21*m**7 + 0*m**2 - 9*m. Factor n(y).
-y**2*(y - 1)*(4*y + 1)**2/2
Let 2/5*w**5 - 10 + 28/5*w**2 + 22/5*w**4 + 68/5*w**3 - 14*w = 0. What is w?
-5, -1, 1
Let z(k) be the second derivative of k**5/90 - 5*k**4/18 + 16*k**3/9 + 64*k**2/9 + 3*k - 3. Factor z(i).
2*(i - 8)**2*(i + 1)/9
Suppose -22 = -5*s + 2*i, -5*s + 6 = 5*i - 9. Suppose 0*j - r + 8 = j, 3*j = 2*r + s. Factor -1 + 12*q + 2*q**2 - j*q + 5 + 2.
2*(q + 1)*(q + 3)
Factor -14/5 - 1/5*x**2 - 3*x.
-(x + 1)*(x + 14)/5
Let t(n) be the third derivative of 5*n**8/336 - 13*n**6/24 - n**5 + 28*n**2 - 1. Determine y so that t(y) = 0.
-3, -1, 0, 4
Let t be 3 - ((-3)/(-1) + -3). Determine q, given that -7*q - 4 + 1 - q**t + 36*q**2 - 41*q**2 = 0.
-3, -1
Let n(y) be the second derivative of 8/3*y**3 + 9*y + y**4 - 8*y**2 + 2/15*y**6 + 0 - 4/5*y**5. Solve n(c) = 0 for c.
-1, 1, 2
Let j be (-60)/550*2/4. Let k = j + 69/55. Suppose 3/5*r**2 + 3/5 + k*r = 0. What is r?
-1
Suppose 2*a - z + 2 = 0, 5*a + 44 = -2*z + 48. Solve 2/5*j**3 + 2/5*j**4 - 2/5*j**2 - 2/5*j + a = 0 for j.
-1, 0, 1
Let t(l) be the second derivative of 0*l**3 + 0 - 7/144*l**4 - 1/240*l**5 + 1/6*l**2 + 1/120*l**6 - 5*l + 1/504*l**7. Determine v, given that t(v) = 0.
-2, -1, 1
Suppose 2*f - 6 + 10 = 4*p, -6*f + 2*p + 8 = 0. Factor -28/11*i**3 - 18/11*i - 12/11*i**4 - 2/11*i**5 - 4/11 - 32/11*i**f.
-2*(i + 1)**4*(i + 2)/11
Suppose -800/3*t + 82/3*t**3 - 2/3*t**4 + 10/3*t**2 - 2/3*t**5 + 1000/3 = 0. Calculate t.
-5, 2, 5
Let g(y) = 5*y**3 + 10*y**2 + 27*y + 3. Let m(j) = 36*j**3 + 68*j**2 + 190*j + 22. Let v(d) = 44*g(d) - 6*m(d). Factor v(n).
4*n*(n + 2)*(n + 6)
Let k(l) = l**3 - 2*l**2 - 13*l + 8. Let i be k(-3). Factor 8/3*n + 0 + 0*n**2 - 2/3*n**4 - i*n**3.
-2*n*(n - 1)*(n + 2)**2/3
Let v be 2/(((-2)/12)/((-4)/16)). Suppose 24 = 3*c + v*u, -5*u = 2*c - 2*u - 20. Find f, given that 0*f**2 + 0*f**3 - 3/2*f**c + 0 - 3/4*f**5 + 0*f = 0.
-2, 0
Let i = 35 - 38. Let g be 2 + i - 2/(-16)*10. Factor -1/2*z**3 + 0*z**2 + 1/4*z + g*z**5 + 0 + 0*z**4.
z*(z - 1)**2*(z + 1)**2/4
Let x(n) be the third derivative of 0*n**3 + 10*n**2 + 1/18*n**4 - 1/90*n**5 + 0*n - 1/180*n**6 + 0. Determine g, given that x(g) = 0.
-2, 0, 1
Suppose 5*s = -5*t - 5, 3*s - t - 5 = -0*s. Let b be (-3 + s + -2)/(-1). Find a, given that -1/2*a**b + 0 - a**3 + a + 1/2*a**2 = 0.
-2, -1, 0, 1
Let k(d) be the third derivative of d**6/30 + 7*d**5/15 + 4*d**4/3 - 32*d**3/3 - 369*d**2. Suppose k(r) = 0. What is r?
-4, 1
Let i = 2/32565 - -293077/130260. What is q in -3/4*q**3 + 0*q + 0 + i*q**2 = 0?
0, 3
Let l(o) be the second derivative of -o**5/20 - o**4/12 + o**3 - 42*o. Let l(p) = 0. What is p?
-3, 0, 2
Let b = 7 + -1. Let p = 9 - b. Suppose 38*u - 39*u + 2*u**3 - p*u**3 + 2*u**2 = 0. Calculate u.
0, 1
Let g = -40 - -42. Let 26*i**g - 35 - 140*i**2 - 75*i**3 + 11 - 3*i**5 - 84*i - 24*i**4 = 0. Calculate i.
-2, -1
Suppose z**2 + 20*z**3 + 3*z**2 - 4*z**4 + 0*z**2 - 4*z**2 = 0. Calculate z.
0, 5
Let r(q) be the first derivative of -3*q**5/25 + 57*q**4/20 - 21*q**3 + 471*q**2/10 - 42*q + 651. Let r(i) = 0. Calculate i.
1, 7, 10
Let f = 10397/17345 - -2/3469. Let 0 + 0*g + 0*g**2 + 3/5*g**4 + f*g**3 = 0. Calculate g.
-1, 0
Let u(x) be the second derivative of -8/105*x**7 + 0*x**4 + 0 + 7*x - 2/15*x**3 + 13/20*x**5 + 0*x**2 + 0*x**6. Find t such that u(t) = 0.
-2, -1/4, 0, 1/4, 2
Let m = 6 - 3. Suppose -m*j = -2*j. Suppose -5*b + 3 - 7*b + j*b - 3*b**2 - 15 = 0. What is b?
-2
Let n = 1659 + -1657. Let 2/9*m**n - 4/9 + 2/9*m = 0. What is m?
-2, 1
Factor -114*g**4 + 16*g**2 - 25*g**3 + 5*g**5 + 119*g**4 - g**2.
5*g**2*(g - 1)**2*(g + 3)
Let f = -490 + 490. Let y(j) be the second derivative of 0 + f*j**2 + 1/30*j**4 + 5*j + 1/25*j**5 - 2/15*j**3 - 1/75*j**6. Determine p, given that y(p) = 0.
-1, 0, 1, 2
Let i(j) = j**3 + 84*j**2 + 467*j - 74. Let o be i(-78). Find m such that -4*m**o + 0 - 36/5*m**3 - 28/5*m**2 - 4/5*m**5 - 8/5*m = 0.
-2, -1, 0
Let r(q) = 2*q**4 - 2*q - 1. Let w(i) = -5*i**4 - 9*i**3 + 8*i**2 + 6*i + 3. Let p(h) = 3*r(h) + w(h). Factor p(t).
t**2*(t - 8)*(t - 1)
Let a(p) be the second derivative of -8*p - 3/4*p**4 - 3/20*p**5 - p**3 + 0*p**2 + 0. Find t such that a(t) = 0.
-2, -1, 0
Let p be (-1)/(-4)*(-24)/(-30). Factor 0 - p*l - 1/5*l**2.
-l*(l + 1)/5
Let h be 20 - -8 - (58 - 32). Find m such that 1/5*m**h + 8/5*m - 9/5 = 0.
-9, 1
Let d(v) be the second derivative of -10*v + 1/12*v**3 + 1/48*v**4 + 0*v**2 + 0. Factor d(t).
t*(t + 2)/4
Let m be 2/15 + (-14)/105. Factor 2*u + 0*u + m*u**3 + 2*u**3 - 4*u**3 + u**2 - 1.
-(u - 1)*(u + 1)*(2*u - 1)
Let t(y) = 13*y**3 + 45*y**2 + 37*y - 5. Suppose p + 18 - 15 = 0. Let k(q) = -7*q**3 - 23*q**2 - 19*q + 3. Let j(v) = p*t(v) - 5*k(v). Solve j(o) = 0 for o.
-4, -1, 0
Let k(i) be the third derivative of -i**7/210 - i**6/60 + 7*i**5/60 + 5*i**4/6 + 2*i**3 + i**2 - 18. Factor k(h).
-(h - 3)*(h + 1)*(h + 2)**2
Let z = 13566/5 + -2075183/765. Let f = 13/17 - z. Suppose -2/9*y + 0 + 2/9*y**3 - f*y**2 + 2/9*y**4 = 0. What is y?
-1, 0, 1
Let t(q) = 14*q + 34. Let z be t(12). Suppose -z*w**3 + 217*w**3 - 15*w**5 - 4*w**4 + 6*w**2 - 2*w**4 = 0. Calculate w.
-1, -2/5, 0, 1
Let f(u) = 16*u**4 + 168*u**3 - 1944*u**2 + 6252*u - 4312. Let l(q) = -q**4 - 6*q**2 - q - 1. Let g(d) = -f(d) - 20*l(d). Factor g(r).
4*(r - 19)**2*(r - 3)*(r - 1)
Let d(l) = -5*l**4 - 13*l**3 + 117*l**2 - 200*l + 104. Let b(n) = -n**4 + n**3 + n**2. Let f(t) = 6*b(t) - 2*d(t). Factor f(y).
4*(y - 2)**2*(y - 1)*(y + 13)
Let q(h) = -35*h**2 - 20*h + 25. Let o(r) be the third derivative of 3*r**5/20 + 5*r**4/24 - r**3 - 8*r**2. Let b(s) = -15*o(s) - 4*q(s). Factor b(g).
5*(g - 1)*(g + 2)
Let o = -11068/5 + 22141/10. Factor 3/5*s + 0 + 1/10*s**3 - o*s**2.
s*(s - 3)*(s - 2)/10
Suppose 15 - 21 = -2*z. Let a = 242/3 - 80. Factor a*f + 1/3*f**2 - 2/3*f**z - 1/3.
-(f - 1)*(f + 1)*(2*f - 1)/3
Let i(t) be the third derivative of t**6/120 - t**5/10 + 11*t**4/24 - t**3 - 94*t**2. Factor i(w).
(w - 3)*(w - 2)*(w - 1)
Let n be 0/((10/4)/((-200)/160)). Find c such that 1/10*c**3 + 0*c**4 - 1/10*c**5 + 0*c + n + 0*c**2 = 0.
-1, 0, 1
Solve 4*z**2 + 11/6*z + 1/2*z**5 + 1/3 + 13/3*z**3 + 7/3*z**4 = 0 for z.
-1, -2/3
Suppose -10*a - 292 = -322. Solve 28/5*u**2 - 4/5*u**4 + 0 - 8/5*u**a - 16/5*u = 0 for u.
-4, 0, 1
Let o(u) be the second derivative of -u**4/42 - 2*u**3/7 - 5*u**2/7 + 201*u. Let o(t) = 0. What is t?
-5, -1
Let p be 542*(-1)/6 + (-8)/(-24). Let i be (-15 - -3)/4 + p/(-24). Suppose -i*s + 3*s**3 + 0 + 9/4*s**2 = 0. Calculate s.
-1, 0, 1/4
Let r(t) = 3*t - 17. Let q be r(7). Suppose 5*k - 4*o = 10, 0*o - 6 = -3*k - q*o. Supp