 1/2*p**i + 11/2*p - 13.
(p - 2)*(p + 13)/2
Let x be 23/(-460)*15 + 11/4. Let m(d) be the first derivative of 25/3*d - 5/12*d**4 + 5/6*d**x - 2 - 25/9*d**3. Suppose m(b) = 0. What is b?
-5, -1, 1
Suppose -139 = -99*w + 455. Let j(t) be the second derivative of 0 + w*t**2 + 7/2*t**3 - 7/4*t**4 + 3/16*t**5 + 2*t. Factor j(z).
3*(z - 4)*(z - 2)*(5*z + 2)/4
Suppose -12 + 22 = 5*c. Suppose 5*u + c*u - 196 = 0. Factor 24 + 83*l**2 + 92*l**2 - u*l - 171*l**2.
4*(l - 6)*(l - 1)
Factor 172/5 - 342/5*g + 168/5*g**2 + 2/5*g**3.
2*(g - 1)**2*(g + 86)/5
Suppose 73*c = 45*c - 56. Let x(n) = n**2 + 3*n + 4. Let t be x(c). Factor -3/2*u**t - 18*u - 54.
-3*(u + 6)**2/2
Let i(b) be the second derivative of 3*b**7/14 - 4*b**6 + 579*b**5/20 - 99*b**4 + 152*b**3 - 96*b**2 + 19*b - 4. Determine p so that i(p) = 0.
1/3, 1, 4
Let d(v) = -5*v**2 - 47*v + 9. Suppose 42 - 33 = 3*m. Let p(a) = 11*a**2 + 93*a - 21. Let w(g) = m*p(g) + 7*d(g). Factor w(o).
-2*o*(o + 25)
Let n = -411711 - -411713. Suppose 9/2*y**n + 1/4*y**4 - 27/4 + 2*y**3 + 0*y = 0. What is y?
-3, 1
Let a(n) be the first derivative of -1/16*n**6 + 0*n + 0*n**3 + 16 - 9/20*n**5 - 27/32*n**4 + 0*n**2. Factor a(w).
-3*w**3*(w + 3)**2/8
Suppose 0 = -6*o + 5*o - 3*g + 335, -3*o + 1055 = -g. Find w, given that -o - 32*w**5 - 98 - 480*w**3 - 244*w**4 + 864*w - 1530*w**2 + 1746*w**2 + 124 = 0.
-3, 3/8, 1
Let v(w) be the second derivative of -w**4/90 - 1082*w**3/15 - 878043*w**2/5 - 3436*w. Find a, given that v(a) = 0.
-1623
Determine b, given that 90 - 1323*b**3 + 649*b**3 + 677*b**3 - 3*b - 90*b**2 = 0.
-1, 1, 30
Suppose 27*x = -31*x - 21*x + 93*x. Factor 0*k - 12/7*k**3 + 9/7*k**2 + x + 3/7*k**4.
3*k**2*(k - 3)*(k - 1)/7
Let h(d) be the third derivative of d**6/780 + 271*d**5/390 - 68*d**4/39 - 3*d**2 - 35*d + 24. Factor h(x).
2*x*(x - 1)*(x + 272)/13
Let r(m) = -5*m**2 - 2*m + 15. Let j(d) = 14*d**2 + 6*d - 41. Suppose o = 3*g + 8 - 4, 2*g = 0. Let u(q) = o*j(q) + 11*r(q). Factor u(s).
(s + 1)**2
Let s(n) be the first derivative of -3*n**5/80 + 3*n**4/16 + 9*n**3/8 + 15*n**2/8 - 35*n + 85. Let q(w) be the first derivative of s(w). Factor q(v).
-3*(v - 5)*(v + 1)**2/4
Let m(o) be the third derivative of 0 + o**3 + 0*o - 1/90*o**6 - 1/6*o**4 + 1/15*o**5 + 26*o**2. Let h(c) be the first derivative of m(c). Factor h(q).
-4*(q - 1)**2
Let y(i) = i**3 + i**2 - i - 8. Let a be y(2). Suppose 2*p + 2*p + 24 - 4*p + a*p + 4*p - 3*p**2 = 0. What is p?
-2, 4
Factor 5/3*y**4 + 0 - 80/3*y**3 - 70/3*y + 145/3*y**2.
5*y*(y - 14)*(y - 1)**2/3
Factor 2/7*h**3 + 138/7*h**2 + 774/7*h + 162.
2*(h + 3)**2*(h + 63)/7
Suppose 2*o + 2*o = u - 1646, 1645 = u - 5*o. Let p be 2/(-10)*u/60 + 6. Find y such that 0 + p*y**5 + 1/2*y**4 - 1/2*y**3 - 1/2*y**2 + 0*y = 0.
-1, 0, 1
Let s(y) = 6*y**3 - 47*y**2 + 22*y. Let l(f) = 42*f**3 - 327*f**2 + 153*f. Let g(w) = 4*l(w) - 27*s(w). Factor g(k).
3*k*(k - 6)*(2*k - 1)
Let -272 + 904/3*y + 11/3*y**4 - 35*y**3 + 1/3*y**5 + 5/3*y**2 = 0. Calculate y.
-17, -3, 1, 4
Let k be (-18)/66 + 17*(-3749)/(-12903). Let q = 6 - 3. Determine w so that -40/3*w + 16/3 - 52/3*w**2 - k*w**q = 0.
-2, 2/7
Solve -112/3*f + 38/3*f**3 + 6*f**4 + 32 + 2/3*f**5 - 14*f**2 = 0.
-4, -3, 1
Suppose 33 = 468*j - 460*j + s, 4*s = -5*j + 24. Let n(y) be the third derivative of 35*y**2 + 0*y + 0 + 1/7*y**3 - 1/140*y**5 + 1/56*y**j. Solve n(z) = 0.
-1, 2
Let j = 312 + -278. Suppose 15*h - j = -2*h. Factor 13/3*f**2 + 1/3*f**4 + h*f**3 + 4*f + 4/3.
(f + 1)**2*(f + 2)**2/3
Let d(l) = 5*l**2 + 238*l - 343. Let h be d(-49). Factor -2/17*g**4 + h*g**3 + 18/17*g**2 + 0 + 0*g.
-2*g**2*(g - 3)*(g + 3)/17
Let v(r) be the first derivative of r**7/4200 + r**6/450 - r**5/600 - r**4/30 + 64*r**3/3 - 2. Let i(t) be the third derivative of v(t). Factor i(f).
(f - 1)*(f + 1)*(f + 4)/5
Suppose -z**2 - 578/3*z - 128 = 0. What is z?
-192, -2/3
Suppose -2*b - 2*p = -4, -18*b - 4*p - 1 = -17*b. Factor -3*o**3 - 6 - 2*o**3 + 5*o**b + o**3 + 4*o**2 + o.
(o - 1)*(o + 2)*(o + 3)
Let u(r) = r**2 - 2*r - 5. Let x(i) = -i**2 + i + 6. Suppose -2*o - 2 = -8. Suppose 0*t = -o*t + 18. Let j(g) = t*u(g) + 5*x(g). Suppose j(n) = 0. What is n?
0, 7
Let m be 82/369 + 320/18. Let t = -105 + 148. Let -m*r**3 - 49*r**2 + 65*r**2 - 3*r**4 - t*r**2 = 0. What is r?
-3, 0
Let v(k) be the first derivative of 2*k**6/3 + 84*k**5/5 + 99*k**4 - 484*k**3/3 + 957. Factor v(n).
4*n**2*(n - 1)*(n + 11)**2
Suppose -5*n = -q - 11, -5*q - 8 + 3 = 0. Suppose -7 = -n*l - 3. Determine m so that m**4 - 6*m**l + 7*m**2 - 2*m**2 + 6*m**3 - 6*m = 0.
-6, -1, 0, 1
Let b(r) = -14*r**3 + 26*r**2 + 54*r + 10. Let w = -110 - -104. Let u(t) = 4*t**3 - 9*t**2 - 18*t - 3. Let m(o) = w*b(o) - 20*u(o). Factor m(s).
4*s*(s + 3)**2
Factor 242/3 - 122/3*w**2 - 119/3*w - 1/3*w**3.
-(w - 1)*(w + 2)*(w + 121)/3
Let j = -103626 - -103630. Suppose 15*v - j - 19/2*v**2 + 3/2*v**3 = 0. What is v?
1/3, 2, 4
Let -955*y - 15/2*y**3 - 335/2*y**2 - 300 = 0. What is y?
-12, -10, -1/3
Let q(k) be the second derivative of -11*k**4/16 + 339*k**3/8 + 93*k**2/4 - 498*k. Factor q(s).
-3*(s - 31)*(11*s + 2)/4
Let r be -10 + (-11902)/(-18) + 2/(-9). Suppose r - 659 = -4*c. Find n, given that -1/3*n**c + 4/3*n - 4/3 = 0.
2
Let p(t) be the second derivative of t**6/15 + 21*t**5/10 - 25*t**4/3 - 28*t**3 + 184*t**2 - 5*t - 321. Let p(x) = 0. What is x?
-23, -2, 2
Let o = 188359 - 1311192/7. Let q = 1047 - o. Suppose 0 + 6/7*y**2 + 2*y**3 - q*y = 0. What is y?
-1, 0, 4/7
Let p(q) = q**2 - 105*q - 94. Let h(i) = -i**2 + 100*i + 91. Let a(w) = 6*h(w) + 5*p(w). What is b in a(b) = 0?
-1, 76
Let m(t) = 4*t**2 - 72*t + 2. Suppose -2*f = 4*p - 20, -21*f + p = -26*f + 86. Let s be m(f). Factor -4/3 + 2/3*r**s + 2/3*r.
2*(r - 1)*(r + 2)/3
Let c(o) be the first derivative of -129 - 72/7*o - 2/21*o**3 - 39/14*o**2 + 1/28*o**4. What is g in c(g) = 0?
-3, 8
Let o(q) = q**4 - q - 1. Let g = -29 + 30. Let y(f) = 57*f**4 + 22 + 36*f**4 + 238*f**3 + 36*f**2 - 64*f - 19*f - 1. Let t(m) = g*y(m) + 5*o(m). Factor t(x).
2*(x + 1)*(x + 2)*(7*x - 2)**2
Suppose 182*j = 183*j - 30. Suppose j*z - 12*z = 0. Factor -9/7*m**3 + 3/7*m**5 - 6/7*m**2 + 0 + z*m**4 + 0*m.
3*m**2*(m - 2)*(m + 1)**2/7
Find a such that -40/11 + 10/11*a**5 + 142/11*a**2 - 54/11*a**4 - 10/11*a**3 + 48/11*a = 0.
-1, 2/5, 2, 5
Factor 2081526 - 2356*s + 2/3*s**2.
2*(s - 1767)**2/3
Let k(r) be the third derivative of r**6/120 - 47*r**5/2 + 55225*r**4/2 - 51911500*r**3/3 + 2470*r**2 + 2*r + 2. Let k(f) = 0. Calculate f.
470
Let t(y) be the second derivative of -y**7/14 - 7*y**6/2 + 219*y**5/20 - 37*y**4/4 - 929*y. Factor t(u).
-3*u**2*(u - 1)**2*(u + 37)
Factor 28*g**4 - 910*g**2 + 32*g + 966*g**2 + 33*g**3 - 24*g**4 - 5*g**3.
4*g*(g + 1)*(g + 2)*(g + 4)
Let b(p) = p**3 - 27*p**2 - 112*p + 660. Let n be b(30). Let u(m) be the third derivative of n*m**3 + 1/3*m**4 + 0 + 15*m**2 + 1/5*m**5 + 0*m. Factor u(c).
4*c*(3*c + 2)
Let t = 28 - 23. Suppose t*d = -3*q + 92, q = 4*d - 5*d + 34. Suppose -q*v**4 + 3*v**5 + 41*v**4 + v**3 - v**3 = 0. Calculate v.
-2/3, 0
Let s(x) be the first derivative of -x**3/21 + 19*x**2/7 + 39*x/7 - 1696. Let s(d) = 0. What is d?
-1, 39
Let v(z) = -130*z + 1835. Let w be v(14). Let a(f) be the first derivative of -1/3*f**2 + 1/9*f - w + 4/9*f**3 - 2/9*f**4. Factor a(g).
-(2*g - 1)**3/9
Let i(v) be the first derivative of -v**6/15 - 6*v**5/5 - 6*v**4 + 213*v + 125. Let u(k) be the first derivative of i(k). Find t such that u(t) = 0.
-6, 0
Let f = 2/131851 - -30062018/659255. Suppose 0*b + 0 - f*b**3 + 18*b**4 + 21/5*b**5 - 72/5*b**2 = 0. What is b?
-6, -2/7, 0, 2
Let m(a) be the third derivative of a**6/660 - 6*a**5/55 + 63*a**4/44 - 90*a**3/11 + 2824*a**2 - 1. Find o such that m(o) = 0.
3, 30
Factor 493 + 1943*g**2 - 1940*g**2 - 845 - 665 + 217*g - 547*g.
3*(g - 113)*(g + 3)
Let w = 671 + -672. Let h(d) = 5*d**3 + 10*d**2 + 5*d - 10. Let q(t) = 2*t**3 + t**2 - 1. Let j(b) = w*h(b) + 5*q(b). Factor j(i).
5*(i - 1)**2*(i + 1)
Let y(f) = -30*f**2 + 7854*f - 1290990. Let q(x) = -7*x**2 + 1964*x - 322748. Let v(m) = -9*q(m) + 2*y(m). Let v(a) = 0. What is a?
328
Let n(q) be the first derivative of q**8/2800 + q**7/280 + q**6/100 - 104*q**3/3 - q**2/2 - 57. Let y(f) be the third derivative of n(f). Factor y(w).
3*w**2*(w + 2)*(w + 3)/5
Let i(c) be the second derivative 