2/7*x**h.
2*x*(x + 4)/7
Let u(p) be the second derivative of 35*p**4/12 + 1915*p**3/6 - 275*p**2 + 20*p + 45. Factor u(j).
5*(j + 55)*(7*j - 2)
Let c = -233052 + 233052. Factor -5/2*k**3 + c + 1/2*k**4 + 1/2*k**5 + 3/2*k**2 + 0*k.
k**2*(k - 1)**2*(k + 3)/2
Let g(b) be the third derivative of -1/540*b**6 + 230*b**2 - 1/27*b**4 - 2/135*b**5 + 0*b + 0 + 0*b**3. Let g(k) = 0. What is k?
-2, 0
Let x = -865/84 + 485/42. Factor -5/4*q**3 - 5/4 + x*q + 5/4*q**2.
-5*(q - 1)**2*(q + 1)/4
Suppose -1293*l + 81*l - 1474*l = 1699 - 15129. Determine i so that -2/9*i**l + 14/9*i**3 + 0 - 8/9*i**2 + 0*i - 4/9*i**4 = 0.
-4, 0, 1
Let n(z) be the second derivative of -1/120*z**6 + 0*z**2 - 1 + 1/40*z**5 + 1/48*z**4 + 78*z - 1/12*z**3. Factor n(p).
-p*(p - 2)*(p - 1)*(p + 1)/4
Let m = -3808/107 - -12494/321. Let v = 8 + -5. What is g in 2*g**4 + 4/3*g**2 + 0*g + 0 + m*g**v = 0?
-1, -2/3, 0
Let d(o) = 2258*o - 6771. Let j be d(3). Find f, given that 0 + 4/3*f - 22/9*f**2 - 2/9*f**4 + 4/3*f**j = 0.
0, 1, 2, 3
Let g(i) = 27*i**2 + 37*i + 15. Let u(n) = 9*n**2 + 12*n + 5. Let k(s) = 2*g(s) - 7*u(s). Let o(z) = 4*z**2 + 5*z + 3. Let t(c) = -3*k(c) - 7*o(c). Factor t(p).
-(p + 2)*(p + 3)
Let -44/5 - 158/5*t + 6*t**2 + 14/5*t**4 + 158/5*t**3 = 0. What is t?
-11, -1, -2/7, 1
Let t(u) be the third derivative of -u**8/17920 + u**7/3360 - u**6/1920 + 13*u**4/24 + 16*u**2 - 2. Let g(b) be the second derivative of t(b). Factor g(w).
-3*w*(w - 1)**2/8
Let n be 15 + -7 + -5 + -1. Suppose 28*j**2 - 31*j**n - 21*j - 4 - 14 = 0. Calculate j.
-6, -1
Let q(f) = -3*f**2 + f + 2. Let p(k) = 16*k**2 - 1667*k + 690551. Let h(d) = 2*p(d) + 10*q(d). Let h(z) = 0. What is z?
831
Let y be ((-56)/(-102) - 8/(-68))/(40/24). Let p(u) be the first derivative of 4*u**2 - 6*u**3 + 0*u + 8 - y*u**5 + 3*u**4. Factor p(z).
-2*z*(z - 4)*(z - 1)**2
Let f(z) be the second derivative of -z**5/40 - 67*z**4/24 + 143*z**3/4 - 657*z**2/4 + 13*z + 55. Factor f(w).
-(w - 3)**2*(w + 73)/2
Let t(p) = -13*p - 2. Let h be t(0). Let c be (2/(-4))/(h/8). Find y, given that 24/7*y**c + 18/7*y**3 + 8/7*y + 0 = 0.
-2/3, 0
Suppose -22*g - 1844 = 1148. Let b be 34/g*(-1 - (-2)/(-6)). Find k, given that 0*k + 0 + 0*k**2 + b*k**4 + 1/3*k**3 = 0.
-1, 0
Let o(g) be the third derivative of 1/60*g**5 + 0*g**3 + 2*g**2 + 65*g + 0 + 1/8*g**4. What is v in o(v) = 0?
-3, 0
Suppose 52*l = 48*l + 44. Suppose 0*z + z - l = -3*v, -5*v + 11 = -2*z. Find s, given that -s**5 - 2*s + 52*s**v + 1 + s**4 - 49*s**3 - s**2 - 1 = 0.
-1, 0, 1, 2
Suppose 5*i - 5*y = 85, -4*i - y + 55 = -28. Let t be (-15)/(15/5) + i. Factor 10*p**2 - 6 + t + 6 + 35*p + 5 - 5*p**3.
-5*(p - 4)*(p + 1)**2
Suppose -629*x + 590*x + 156 = 0. Let f(l) be the third derivative of 0*l + 1/20*l**5 + 0 - 5*l**2 + 17/24*l**x + 5/3*l**3. Let f(b) = 0. What is b?
-5, -2/3
Suppose 7*z = 13*z + 18. Let o be (z + 4)*(-1 - -2) + 2. Find d, given that -468*d**2 + 21*d**o - 54 + 276*d + 144*d**3 + 6 + 75*d**4 = 0.
-4, 2/5, 1
Let m(z) = 17*z**3 + 2616*z**2 + 5223*z + 2617. Let f(k) = -25*k**3 - 3925*k**2 - 7835*k - 3925. Let i(h) = 7*f(h) + 10*m(h). Factor i(y).
-5*(y + 1)**2*(y + 261)
Let s = -514577/5 + 102916. Let z be (-32)/(-24)*3/10. Factor -s*g**3 + 0*g + 0 - 1/5*g**4 - z*g**2.
-g**2*(g + 1)*(g + 2)/5
Suppose -18*w + 75 = -4*n + 177, 2*n - 21 = 3*w. Factor -30 - 500/3*j**n - 215*j - 1300/3*j**2.
-5*(j + 2)*(10*j + 3)**2/3
Factor -32 - 22 - 266*v**2 + 262*v**2 - 104*v**3 + 104*v + 58.
-4*(v - 1)*(v + 1)*(26*v + 1)
Suppose -3*d + 4 = -13 + 5. Let i(t) be the third derivative of -8*t**2 - 3/16*t**d + 0 - 9/8*t**3 + 0*t - 1/80*t**5. Suppose i(l) = 0. What is l?
-3
Suppose 4*c - 9*h - 16 = -4*h, -20 = -5*c + 2*h. Let m(l) be the first derivative of 3/5*l**5 + 3*l**2 - 3*l - 7 - 3/2*l**c + 0*l**3. Solve m(w) = 0 for w.
-1, 1
Factor 2464/5*w**2 - 2/5*w**3 - 152274*w + 302580.
-2*(w - 615)**2*(w - 2)/5
Suppose 0 = -4*s + 3*n + 18, 2 = -s + 6*n - 2*n. Let a be s/(-4) - (-112)/32. Factor -6*f**a - 3*f**3 + 3*f**4 + 479 - 479.
3*f**2*(f - 2)*(f + 1)
Let o(r) be the second derivative of 2 + 1/5*r**3 + 1/30*r**4 - 4/5*r**2 + 45*r. Factor o(t).
2*(t - 1)*(t + 4)/5
Let s(x) be the second derivative of -x**7/126 + x**6/9 - 3*x**5/5 + 29*x**4/18 - 43*x**3/18 + 2*x**2 - x + 17. Let s(r) = 0. What is r?
1, 3, 4
Let a(l) be the third derivative of -l**5/80 + 39*l**4/32 - 27*l**3/2 + 1048*l**2. Factor a(z).
-3*(z - 36)*(z - 3)/4
Suppose -99/2*x - 1/6*x**3 + 162 + 5*x**2 = 0. What is x?
9, 12
Let z = 36 + -36. Suppose 0 = 5*c, 4*u + 513*c = 515*c + 8. Factor -1/5*n**4 - 2/5*n**u + 0 - 3/5*n**3 + z*n.
-n**2*(n + 1)*(n + 2)/5
Let p(t) = -12*t**4 + 19*t**3 - 27*t**2 - 58*t + 33. Let k(h) = -h**4 - h**2 - 2*h + 3. Let s(b) = -44*k(b) + 4*p(b). Factor s(r).
-4*r*(r - 18)*(r - 2)*(r + 1)
Factor -133*n**2 + 5829*n + 15*n**3 + 7*n**2 - 70 - 14*n**2 - 5574*n.
5*(n - 7)*(n - 2)*(3*n - 1)
Factor 0*k**4 + 32*k**3 + 28*k**2 - 7*k**4 - 18*k**2 - 24*k**2 + 9 - 20*k**2.
-(k - 3)*(k - 1)**2*(7*k + 3)
Suppose -14*m = -31*m + 8670. Let p be 56/(-35) - (-5016)/m. Factor -32/17 - p*k + 14/17*k**3 - 94/17*k**2.
2*(k - 8)*(k + 1)*(7*k + 2)/17
Let w(d) be the first derivative of -2/3*d**3 + 12*d + 5*d**2 + 61. Find g, given that w(g) = 0.
-1, 6
Let l(n) be the second derivative of -53030/3*n**4 - 37*n - 49000*n**2 + 145600/3*n**3 - 312*n**5 - 3/2*n**6 - 1. Factor l(z).
-5*(z + 70)**2*(3*z - 2)**2
Find p such that -5796*p + 504561 + 3*p**2 + 569148 + 1725759 = 0.
966
Factor -17161/9 + 262/9*q - 1/9*q**2.
-(q - 131)**2/9
Suppose 0 = 3*h - 5*r - 17, 4*h + 0*r + 3*r - 13 = 0. Solve -12*q**3 - 88*q + 96*q + h*q**4 - 4*q**2 + 3*q**5 + q**5 = 0.
-2, -1, 0, 1
Let u be 0/(33*(972/(-198))/9). Let 5/2*h**3 + u*h**2 + 15 - 35/2*h = 0. Calculate h.
-3, 1, 2
Let q(p) = 11*p**2 - 2622*p + 552123. Let d(x) = -4*x**2 + 876*x - 184041. Let r(t) = 8*d(t) + 3*q(t). Factor r(b).
(b - 429)**2
Let o(d) be the first derivative of 2*d**3/3 + 42*d**2 + 82*d + 923. Factor o(i).
2*(i + 1)*(i + 41)
Factor 9/11*r + 1/11*r**2 - 162/11.
(r - 9)*(r + 18)/11
Let h(t) be the first derivative of 2*t + 1/15*t**5 + 7/12*t**4 + 17/9*t**3 + 17/6*t**2 - 52. Factor h(j).
(j + 1)**2*(j + 2)*(j + 3)/3
Let d(y) be the second derivative of -y**4/4 + 84*y**3 - 421*y + 1. Factor d(p).
-3*p*(p - 168)
Let i(d) be the first derivative of -9*d**4 + 448*d**3 - 872*d**2 + 576*d + 2111. Factor i(w).
-4*(w - 36)*(3*w - 2)**2
Let j(t) be the third derivative of 91*t**2 + 1/36*t**5 + 0 + 9245/18*t**3 + 0*t + 215/36*t**4. Suppose j(m) = 0. What is m?
-43
Let k = 5 + 7. Let t = -465 + 468. Factor -3*l**4 - 64*l**2 - 3*l**3 + k*l**t + 55*l**2 + 3*l.
-3*l*(l - 1)**3
Let v be 1/(-4 + 7 + 24/(-6)). Let p(d) = -8*d**3 - 74*d**2 + 24*d + 8. Let k(x) = x**2 + x + 2. Let m(z) = v*p(z) + 4*k(z). Factor m(q).
2*q*(q + 10)*(4*q - 1)
Let t(o) be the third derivative of -2*o - 11*o**2 + 0 - 1/200*o**6 - 3/20*o**4 + 0*o**3 - 7/100*o**5. Determine q, given that t(q) = 0.
-6, -1, 0
Suppose 3963*a = 8023*a - 3998*a - 124. Determine f, given that f - 1/2*f**4 + 0*f**3 + 3/2*f**a + 0 = 0.
-1, 0, 2
Let k(b) = 191*b + 385. Let j be k(-2). Find g, given that 5/2*g**2 - 1/6*g**4 - g**j - 4/3*g + 0 = 0.
-8, 0, 1
Let o(t) be the second derivative of -11*t**4/21 + 488*t**3 + 1864*t**2/7 - 6*t + 98. Determine r, given that o(r) = 0.
-2/11, 466
Let a = -203768 + 203768. Suppose -1/2*f**4 + a + 0*f + 1/2*f**2 - 2*f**3 + 2*f**5 = 0. Calculate f.
-1, 0, 1/4, 1
Let j(y) = 15*y**3 + 337*y**2 + 281*y - 578. Let r(t) = -4*t**3 - 85*t**2 - 70*t + 144. Let m(o) = -6*j(o) - 22*r(o). Factor m(p).
-2*(p - 1)*(p + 2)*(p + 75)
Suppose 784/13*l**2 + 0 - 2/13*l**3 + 786/13*l = 0. Calculate l.
-1, 0, 393
Let h(o) be the second derivative of o**8/8400 - o**7/1400 - o**6/75 - 7*o**5/150 - 43*o**3 + 43*o. Let u(f) be the second derivative of h(f). Factor u(q).
q*(q - 7)*(q + 2)**2/5
Suppose -30*c = -37*c + 21. Factor -54 - c*r**2 + 25 - 21*r + 53.
-3*(r - 1)*(r + 8)
Let r be 140/18 - (-106)/477. Suppose -14*p = -r*p. Find s such that p + 1/3*s - 1/6*s**3 + 1/2*s**4 - 1/6*s**5 - 1/2*s**2 = 0.
-1, 0, 1, 2
Let x = -180 - -184. Determine v so that -37 + 6*v**4 - 2*v**4 - 364*v + 26*v**3 - 141*v**2 - 159 - 5*v**x = 0.
-1, 14
Let n be (2*20/192)/(90/8). Let g(l) be the second derivative of 0*l**2 + n*l**4 + 2/27*l**3 - 1/90*l**5