e -1026 - 4977 + 4*p**2 - 333 - 480*p = 0 for p.
-12, 132
Let b(a) = -a**2 + 28*a - 27. Let i(p) = 8*p**2 - 244*p + 216. Let g(r) = 17*b(r) + 2*i(r). Factor g(s).
-(s + 3)*(s + 9)
Let u(w) be the first derivative of w**4/36 + 16*w**3/27 + 5*w**2/6 + 564. Let u(t) = 0. Calculate t.
-15, -1, 0
Solve -819*y**3 - 101*y**4 + 827*y**3 - 2*y**5 + 89*y**4 + 112*y**2 - 256 = 0 for y.
-4, -2, 2
Let u be 1/(-7)*2 + 247/7. Suppose 0 = 64*q - 65*q + u. Factor -25*p**3 + 7 + 2*p**4 - q*p - 3 + 6 + 45*p**2 + 3*p**4.
5*(p - 2)*(p - 1)**3
Let n(b) be the second derivative of -b**6/135 - 29*b**5/90 + 61*b**4/54 - 31*b**3/27 + 66*b + 10. Solve n(z) = 0.
-31, 0, 1
Let w = 186 + -156. Suppose 53*j + w = 63*j. Solve -3/2*z**2 - 4*z + 2 + 5/2*z**j + z**4 = 0.
-2, 1/2, 1
Let q(m) be the second derivative of 13*m**5/15 - 128*m**4/9 - 664*m**3/9 - 32*m**2 - 5568*m. Solve q(g) = 0.
-2, -2/13, 12
Factor 228*j - 1/2*j**2 - 25992.
-(j - 228)**2/2
Find q, given that -2621*q - 106 - 7*q**2 - 2333*q + 8018*q - 2691*q = 0.
2/7, 53
Let c(w) be the first derivative of w**3 - 2637*w**2 + 2317923*w - 149. Factor c(s).
3*(s - 879)**2
Let q = 10 - 8. Let u(p) be the first derivative of 14*p - 21*p - 3 + 16*p**q - 4*p**3 - 13*p. Factor u(n).
-4*(n - 1)*(3*n - 5)
Let n(z) be the third derivative of z**8/1848 + z**7/1155 - z**6/132 - z**5/66 + z**4/33 + 4*z**3/33 + 8*z**2 - 1. Suppose n(a) = 0. Calculate a.
-2, -1, 1, 2
Let d(t) = -3*t - 122. Let b(p) = 2*p + 80. Let i(w) = 8*b(w) + 5*d(w). Let y be i(-26). Factor 0 - 2/3*o**3 - 2/9*o**5 - 2/9*o**2 - 2/3*o**y + 0*o.
-2*o**2*(o + 1)**3/9
Let w(s) be the second derivative of -s**4/27 - 304*s**3/9 - 2*s - 104. What is j in w(j) = 0?
-456, 0
Let x(r) = -4*r**3 + 50*r**2 - 96 - 10*r**3 + 4*r**3 + 11*r**3 + 47*r. Let k be x(-49). Suppose -6/5*l**3 + 36/5 + 33/5*l**k - 12*l = 0. Calculate l.
3/2, 2
Suppose -j - 4*j + 5 = -2*p, 0 = -j + p - 2. Determine t so that -4*t**5 - 20*t**2 + 4*t**2 - 17*t**3 - 15*t**j - 20*t**4 = 0.
-2, -1, 0
Let u = 89864/3 - 29952. Factor u*c**2 + 2/3*c**3 + 2*c + 0.
2*c*(c + 1)*(c + 3)/3
Suppose -490*y = -488*y + 60. Let n be (y/10)/(4/((-16)/6)). Determine t so that 6/5*t**n + 3/5*t**4 + 0 + 0*t + 9/5*t**3 = 0.
-2, -1, 0
Let g(y) be the third derivative of 1/21*y**7 - 1/3*y**5 + 9*y**2 + 5/24*y**4 + y - 1/12*y**6 + 0 + 5/336*y**8 + 5/3*y**3. Solve g(d) = 0.
-2, -1, 1
Let w = 20 + 5. Find g such that -6*g**3 - g**3 + 18*g**3 - 25 - 6*g**3 - 5*g + w*g**2 = 0.
-5, -1, 1
Let m(v) be the third derivative of -v**6/360 - 167*v**5/180 - 310*v**4/9 - 4832*v**3/9 + 453*v**2 - 1. Determine i so that m(i) = 0.
-151, -8
Suppose 0 = -u - 23*m + 26*m + 1077, -5*u + 5365 = 5*m. Suppose 1076*w**5 + 9*w - u*w**5 - 16*w**3 + 2*w**4 + 12 - 12*w**2 + 5*w - 2*w**4 = 0. Calculate w.
-2, -1, 1, 3
Let r(w) = -2*w**2 - 9608*w - 5779212. Let c(l) = 3*l**2 + 19212*l + 11558422. Let z(t) = 2*c(t) + 5*r(t). Factor z(p).
-4*(p + 1202)**2
Factor -6682*p**2 - 875*p + 6097*p**2 - 10*p**3 - 390 - 5*p**4 - 95*p**3.
-5*(p + 1)**2*(p + 6)*(p + 13)
Suppose -27 = -101*p + 52*p + 120. Find j, given that -8/5 - p*j - 6/5*j**2 + 1/5*j**3 = 0.
-1, 8
Find a such that -230/7*a - 116/7 + 2/7*a**3 - 16*a**2 = 0.
-1, 58
Let k(q) be the first derivative of -q**6/2 - 108*q**5/5 - 1053*q**4/4 + 148*q**3 + 15048*q**2 - 29376*q - 4942. Let k(p) = 0. Calculate p.
-17, -12, 1, 4
Let z(u) be the first derivative of 1/5*u**3 + 24*u + 33/5*u**2 - 133. Factor z(w).
3*(w + 2)*(w + 20)/5
Let w(n) be the second derivative of 1/210*n**6 - 22*n + 2/105*n**5 + 0*n**3 + 5*n**2 + 1/42*n**4 + 0. Let z(s) be the first derivative of w(s). Factor z(i).
4*i*(i + 1)**2/7
Let r be ((-7)/(-2))/((-2)/6 + (-172)/(-12)). Let w(y) be the third derivative of -r*y**5 + 0 + 19*y**2 + 5/144*y**6 + 0*y**3 - 5/18*y**4 + 0*y. Factor w(f).
5*f*(f - 4)*(5*f + 2)/6
Suppose -2240 - 216*i - 3/4*i**2 + 1/4*i**3 = 0. Calculate i.
-16, 35
Let a(s) be the third derivative of -1/20*s**6 - 58*s**2 + 1/3*s**4 + 1/105*s**7 + 0*s**3 + 0*s**5 + 0*s + 0. Factor a(b).
2*b*(b - 2)**2*(b + 1)
Factor -1/2*h**2 + 435/2 + 71*h.
-(h - 145)*(h + 3)/2
Suppose 169 - 163 = 2*g. Factor g*i**3 - 96*i**2 - 8*i - i + 102*i**2.
3*i*(i - 1)*(i + 3)
Let w(h) = 9300*h + 37203. Let d be w(-4). Suppose -18/5 + 33/5*k + 48/5*k**4 - 9/5*k**5 + 18/5*k**2 - 72/5*k**d = 0. Calculate k.
-2/3, 1, 3
Let z(w) be the third derivative of 25/6*w**3 - 1/12*w**5 + 0 - 4*w**2 + 0*w + 5/6*w**4. Find j, given that z(j) = 0.
-1, 5
Suppose -4406 = -4*j + 5*r, 2630 = 4*j + r - 1764. Suppose -1102*d**2 - 3*d**5 + j*d**2 - 12*d**4 - 9*d**3 + 3*d**4 = 0. What is d?
-1, 0
Suppose 7*u - 71 = -4*f, -2*f = 3*u - 22071 + 22040. Factor -3*q - 13/4*q**3 + 1/4*q**4 - 18 + 23/2*q**f.
(q - 6)**2*(q - 2)*(q + 1)/4
Let n(h) be the third derivative of -1 - 1/60*h**5 + 50*h**2 + 0*h + 0*h**3 + 3/8*h**4. Factor n(x).
-x*(x - 9)
Let z = 77525/103388 - -4/25847. Suppose -z*w + 0 + 9/2*w**3 - 15/4*w**2 = 0. Calculate w.
-1/6, 0, 1
Let o(h) be the second derivative of 0*h**3 + 0*h**2 - 61*h - 1 + 1/25*h**5 + 1/225*h**6 - 7/90*h**4. Find q such that o(q) = 0.
-7, 0, 1
Let y(x) be the second derivative of -x**4/8 + 13*x**3/4 - 30*x**2 + 1548*x. Factor y(h).
-3*(h - 8)*(h - 5)/2
Factor 217/9*g + 24 + 1/9*g**2.
(g + 1)*(g + 216)/9
Let y(g) be the third derivative of g**6/24 + g**5/3 - 25*g**4/24 - 7*g**2 + 50*g. Let y(u) = 0. What is u?
-5, 0, 1
Let r be 10/55 + 20/11 - (-6)/(-4). Let j = 1211/4 + -301. Solve r*f + j*f**3 - 9/4*f**2 + 0 = 0.
0, 2/7, 1
Let r(p) = 7*p**3 - 170*p**2 + 204*p + 346. Let x(j) = 3*j**3 - 86*j**2 + 99*j + 174. Let b(l) = -2*r(l) + 5*x(l). Factor b(s).
(s - 89)*(s - 2)*(s + 1)
Let l(w) be the third derivative of w**8/21 - 1672*w**7/105 + 14699*w**6/10 - 43472*w**5/15 + 5408*w**4/3 - 177*w**2 - w. Factor l(j).
4*j*(j - 104)**2*(2*j - 1)**2
Factor 279 - 30/7*b - 3/7*b**2.
-3*(b - 21)*(b + 31)/7
Let s(b) be the second derivative of b**4/6 + 384*b**3 + 331776*b**2 - 1612*b. Solve s(c) = 0.
-576
Let -18586*k - 13865*k - 6177*k**3 - 3517*k - 6303 + 38576*k**2 + 16575 + 18*k**4 - 5439*k**3 = 0. Calculate k.
2/3, 2, 642
Let k = -8893 + 8893. Let a(b) be the second derivative of -19*b + k + b**3 - 1/8*b**4 - 9/4*b**2. Factor a(y).
-3*(y - 3)*(y - 1)/2
Factor -3/5*x + 96/5 + 3/5*x**3 - 96/5*x**2.
3*(x - 32)*(x - 1)*(x + 1)/5
Let u(c) be the first derivative of -8836/5*c - 4/15*c**3 + 127 - 188/5*c**2. Find o such that u(o) = 0.
-47
Let g = 274 - -296. Let i = g - 564. Factor -128 - 1/4*m**3 - 48*m - i*m**2.
-(m + 8)**3/4
Solve -4/5*i - 64/5 + 4/5*i**3 + 64/5*i**2 = 0 for i.
-16, -1, 1
Find n, given that 0 - 1/3*n**3 + 257*n + 254/3*n**2 = 0.
-3, 0, 257
Let a(l) = -7*l**4 + 21*l**3 - 14*l**2 - 114*l - 72. Let u(d) = -3*d**4 + 11*d**3 - 7*d**2 - 57*d - 36. Let g(y) = 2*a(y) - 5*u(y). Factor g(s).
(s - 12)*(s - 3)*(s + 1)**2
Let i(b) = 3*b**2 + b + 14. Let l be i(0). Let -44*y + l*y**2 - 16*y + 29*y**3 + 20 + 51*y**2 - 59*y**3 + 5*y**4 = 0. Calculate y.
1, 2
Let b(o) be the second derivative of 0 + 5/6*o**4 - 1/6*o**6 - 45/2*o**2 - 10*o**3 + o**5 + 57*o. Factor b(q).
-5*(q - 3)**2*(q + 1)**2
Let h(t) be the second derivative of t**6/60 + 7*t**5/10 + 55*t**4/8 - 75*t**3/2 + 11296*t. Let h(k) = 0. What is k?
-15, 0, 2
Let z(b) be the third derivative of -2*b**7/105 + 107*b**6/30 + 36*b**5/5 + 6297*b**2. Factor z(d).
-4*d**2*(d - 108)*(d + 1)
Suppose -158 = -3*h + 5*y, -25*h - 2*y + 49 = -24*h. Determine k so that -12*k**3 - 9 + 17*k + h*k**2 + 21*k**3 + 0*k - 18*k**2 - 2*k = 0.
-3, -1, 1/3
Let w(u) = -8*u + u**2 + 5 + 21*u - 2*u**2. Let q(b) = -453*b + 5*b**2 + 433*b - 8 - 3*b**2. Let l(r) = 5*q(r) + 8*w(r). Let l(p) = 0. What is p?
-2, 0
Let q = 44980 + -136079/3. Let b = -379 - q. Suppose -b - 4/3*l - 2/3*l**2 = 0. Calculate l.
-1
Let a be (-7)/(-3)*60/(-10). Let f(z) = -z - 1. Let h be f(a). Factor 3*r**2 - r + 5*r**3 - h*r + 7*r**2 - 40 - 6*r.
5*(r - 2)*(r + 2)**2
Let l(g) = 15*g**2 + 305*g - 300. Let r(p) = 26*p**2 + 611*p - 602. Let h(b) = -7*l(b) + 4*r(b). Factor h(w).
-(w - 308)*(w - 1)
Determine l, given that 3*l**4 + 198 + 2*l**2 + 291*l - 587*l**3 - 11*l**2 + 488*l**3 = 0.
-1, 2, 33
Let b be 1*-6 - (7 + 1855/(-70)). Find d, given that -3/2*d**2 + 0 + b*d = 0.
0, 9
Factor -186*a - 159/2*a**3 + 189*a**2 + 60 + 12*a**4.
3*(a - 2)**3*(8*a - 5)/2
Let x(j) = 10*