*2 + u.
2*i**3/3
Let z(s) be the first derivative of s**5/10 - 27*s**4/4 - 55*s**3/6 + 727. Solve z(y) = 0 for y.
-1, 0, 55
Let q be -3 - -4*(0 - (-1245)/10). Let g = -493 + q. Solve -6/7*t**3 + 2/7*t**5 + 0*t**4 + 0 + 0*t + 4/7*t**g = 0.
-2, 0, 1
Let m = -1/51887 + 155663/103774. Factor -867/2 - m*w**2 - 51*w.
-3*(w + 17)**2/2
Let c(b) be the third derivative of b**5/270 + b**4/18 + b**3/3 - 12*b**2 - 129. Factor c(r).
2*(r + 3)**2/9
Factor -582/5*u + 3/5*u**2 + 1719/5.
3*(u - 191)*(u - 3)/5
Let j = 58334 + -58333. Factor -8*x**2 + j + 9/2*x**3 + 5/2*x.
(x - 1)**2*(9*x + 2)/2
Let i be (-20)/(4*(-4)/64). Factor 57*t + 3*t**3 - i*t**2 + 7*t**2 + 40*t**2 - 27.
3*(t - 9)*(t - 1)**2
Let k(r) be the first derivative of -5*r**6/3 + 284*r**5/5 + 89*r**4/2 - 116*r**3/3 - 5724. Solve k(w) = 0 for w.
-1, 0, 2/5, 29
Let d(n) be the third derivative of n**6/30 - 16*n**5/15 - 38*n**4/3 - 160*n**3/3 + n**2 - 696. What is c in d(c) = 0?
-2, 20
Let f = -477 + 479. Suppose -3*d + 9 - 1 = -2*q, f*q = -d. Determine v, given that -47/4*v**d - 5/2 - 3/4*v**4 + 23/4*v**3 + 37/4*v = 0.
2/3, 1, 5
Let t = 996128 + -996123. Solve -57/2*v**3 - 6 - 65/8*v**4 - 32*v - 46*v**2 - 7/8*v**t = 0.
-3, -2, -2/7
Let m(y) be the third derivative of y**5/180 + 11*y**4/72 - 481*y**3/9 + 4882*y**2. Find o, given that m(o) = 0.
-37, 26
Let x be 6/26 - 1058/(-4485) - (-6)/(-20). Let q(s) be the first derivative of 0*s**2 - 1/3*s**3 + 0*s - x*s**6 - 16 + 1/4*s**4 + 1/5*s**5. Factor q(g).
-g**2*(g - 1)**2*(g + 1)
Let c(s) = 4*s + 3. Let o(g) = g**2 - 18*g + 150. Let p(m) = 35*c(m) - 5*o(m). Factor p(r).
-5*(r - 43)*(r - 3)
Let g(i) = 6*i**2 + 1. Let q(a) = -11*a**2 - 944*a + 222782. Let s(w) = 2*g(w) + q(w). Factor s(x).
(x - 472)**2
Let m(r) = 2*r**2. Let w be m(1). Let d = 28289/2 - 14143. Factor -5/2*h**3 + 2*h**w + 0 + 2*h - d*h**4.
-h*(h - 1)*(h + 2)*(3*h + 2)/2
Let l(b) be the third derivative of b**5/90 + 73*b**4/36 - 72*b**3 - b**2 - 391*b + 1. Factor l(y).
2*(y - 8)*(y + 81)/3
Let m(o) be the first derivative of o**6/6 - 313*o**5/5 + 24335*o**4/4 + 24649*o**3/3 - 885. Factor m(a).
a**2*(a - 157)**2*(a + 1)
Let w(b) be the third derivative of 1/30*b**5 + 0 + 1/6*b**4 - 2*b + 1/3*b**3 - 75*b**2. Factor w(m).
2*(m + 1)**2
Suppose 0 = m + 2*j - 57, 0*j + 3*j = -4*m + 243. Let z = 67 - m. Factor 47*n**2 - 45*n**2 + 6*n - z*n.
2*n*(n + 1)
Let l be 5 + (4 + -2 - 28/7). Factor -6*s**2 + 6*s**5 - 15*s**3 - 9*s**4 - 9*s**5 - l*s**4.
-3*s**2*(s + 1)**2*(s + 2)
Let g(k) = k**3 - 97*k**2 - 1252*k - 6095. Let s be g(109). Factor -1/2*u**3 - 48*u - s*u**2 - 64.
-(u + 2)*(u + 8)**2/2
Suppose o + 2 = -j, 0 = -2*j + j + 3*o + 2. Let x be (-17634)/(-21) + j/((-14)/4). Find r, given that x*r - 1032*r - 23*r**2 - r**2 - r**3 - 512 = 0.
-8
Suppose 29 = 2*w - 5*v, -5*w + 13*v = 12*v - 15. Let z(s) be the second derivative of 0*s**w + 0 - 1/10*s**5 - 22*s - 1/3*s**4 + s**3. Let z(t) = 0. What is t?
-3, 0, 1
Let j(f) be the second derivative of 11*f**6/255 + 23*f**5/85 + 26*f**4/51 + 8*f**3/51 + 2693*f. Let j(d) = 0. What is d?
-2, -2/11, 0
Factor 0*t - 2*t**2 - 11/5*t**4 + 41/10*t**3 + 0 + 1/10*t**5.
t**2*(t - 20)*(t - 1)**2/10
Factor -1/4*o**3 + 112 - 9/4*o**2 + 12*o.
-(o - 7)*(o + 8)**2/4
Let p(y) = 3*y**2 + 198*y + 204. Let c(n) = -3*n**2 - 194*n - 203. Let h(j) = -3*c(j) - 4*p(j). Factor h(m).
-3*(m + 1)*(m + 69)
Let h(k) be the first derivative of 2*k**5/15 - 7*k**4/3 + 22*k**3/9 + 26*k**2/3 + 1662. Suppose h(m) = 0. Calculate m.
-1, 0, 2, 13
Solve 6750/11 + 675/11*n + 0*n**2 - 1/11*n**3 = 0 for n.
-15, 30
Let p = 460/3 + -3172/21. Suppose p*y + 4/7*y**5 - 16/7 + 20/7*y**2 - 4/7*y**4 - 20/7*y**3 = 0. What is y?
-2, -1, 1, 2
Suppose -c - c = -6. Let g(l) = l**3 + 3*l**2 - 3*l - 6. Let t be g(-3). Factor 13*d**c - d**t - 15*d**4 - 6*d**3.
-3*d**3*(5*d - 2)
Suppose 120 = -7*a + 12*d, 21*d - 40 = 4*a + 17*d. Factor 16/5*z**3 - 4/5*z**4 + 0*z + 0 + a*z**2.
-4*z**3*(z - 4)/5
Solve 189*n - 9*n**3 + 30 - 30 - 173*n - n**4 - 6*n**2 = 0 for n.
-8, -2, 0, 1
Suppose 34*a = 15*a - 32*a. Factor a*m**3 + 3/4*m**4 + 3/4 - 3/2*m**2 + 0*m.
3*(m - 1)**2*(m + 1)**2/4
Let q(i) = 19*i**2 - 43*i + 11. Let n(z) = 10*z**2 - 22*z + 6. Suppose 5*s = 4*y + 18, -y = s + 4 - 13. Let p(h) = s*q(h) - 13*n(h). Factor p(m).
-4*(m - 1)*(4*m - 3)
Suppose 2*u - 93 = t, 5*u + 43 - 293 = -t. Suppose u*k - 40 = 29*k. Factor 1/2*a - 2*a**k + 3/2.
-(a - 1)*(4*a + 3)/2
Let -o**4 + 182*o**2 + 333*o**3 - 299*o**3 + 0*o**4 + 294*o + o**4 + 2*o**4 = 0. What is o?
-7, -3, 0
Let b = -1/44050 + 198227/88100. Factor b + 33/8*q - 3/4*q**2.
-3*(q - 6)*(2*q + 1)/8
Let 813/4*p**3 - 921/4*p**2 - 69/2*p - 9/2*p**4 + 66 = 0. Calculate p.
-1/2, 2/3, 1, 44
Factor -20*x**2 - 297 - 2706*x - 358 - 963*x + 1044*x.
-5*(x + 131)*(4*x + 1)
Factor -13*y - 2830*y**2 + 6*y - 816*y**3 + 811*y**3 + 7*y.
-5*y**2*(y + 566)
Let x(f) be the first derivative of -20/11*f + 10/33*f**3 - 23/11*f**2 - 58. Factor x(y).
2*(y - 5)*(5*y + 2)/11
Let m(j) = 2*j**2 + 2*j + 3. Let i be m(3). Factor 52*k - 20*k**2 - 4*k**4 + 24*k**3 - 25*k - i*k.
-4*k**2*(k - 5)*(k - 1)
Let o = -768430 + 768432. Let -42/5*f**o + 44/5*f - 2/5*f**3 + 0 = 0. What is f?
-22, 0, 1
Let u(g) be the first derivative of -4*g**5/25 - 13*g**4 - 988*g**3/15 - 366*g**2/5 - 4990. Suppose u(t) = 0. What is t?
-61, -3, -1, 0
Let q(h) be the third derivative of h**7/70 - h**6/20 + h**5/20 + 511*h**2 - 1. Factor q(p).
3*p**2*(p - 1)**2
Let x(g) = -2*g - 29. Let y be x(-17). Let f(k) = k**2 - 5*k + 5. Let o be f(y). Determine l so that -2*l**2 + 0*l + 4*l**2 + 2 - o*l + l = 0.
1
Let j(t) be the third derivative of -t**6/90 - 2*t**5/9 + 13*t**4/6 - 43*t**2 - 3. Factor j(u).
-4*u*(u - 3)*(u + 13)/3
Let j = -504429 - -504432. Factor 2*l + 2/15*l**j + 10/3 - 6/5*l**2.
2*(l - 5)**2*(l + 1)/15
Solve 16 + 135*u**3 + 39*u - 52 + 130*u**3 - 394*u**3 + 126*u**3 = 0 for u.
-4, 1, 3
Let d(q) = -65*q**2 + 22273*q - 22230. Let f(s) = -35*s**2 + 11138*s - 11115. Let n(z) = -6*d(z) + 11*f(z). Factor n(o).
5*(o - 2223)*(o - 1)
Let a be 744/(-403) + 6 - (-3 + 7). Factor -8/13*d**2 + a*d**4 + 8/13*d - 2/13*d**3 + 0.
2*d*(d - 2)*(d - 1)*(d + 2)/13
Let c(p) be the second derivative of p + 1/2*p**3 - 1/2*p**2 - 51 - 1/120*p**6 + 3/40*p**5 - 13/48*p**4. Factor c(h).
-(h - 2)**2*(h - 1)**2/4
Let -3*s**5 - 167*s - 6*s**4 - 352 + 899*s**2 + 249*s**3 - 875*s**2 - 128 - 541*s = 0. Calculate s.
-10, -1, 2, 8
Let s(v) be the first derivative of 3*v**6/2 - 246*v**5/5 + 504*v**4 - 1862*v**3 + 4887*v**2/2 - 1080*v + 1641. What is x in s(x) = 0?
1/3, 1, 3, 8, 15
Let p(v) = v**2 - 6*v - 9. Let h be p(6). Let m be (-2)/h + (-17256)/(-108). What is j in 2*j**2 - j**2 - m*j + 155*j = 0?
0, 5
Let c be (2337/(-24) + 98)*(1 - -1). Suppose 55*y - c*y**2 - 605 = 0. What is y?
22
Factor 1244*a**3 - 2*a**4 + 98560*a**2 + 69499*a + 6*a**4 + 172875*a + 87113*a - 44895*a.
4*a*(a + 3)*(a + 154)**2
Factor -7606564/13 + 424*z**2 - 3792250/13*z - 2/13*z**3.
-2*(z - 1379)**2*(z + 2)/13
What is f in -5*f**3 + 4*f**3 - 54*f + 88*f + 376*f**2 + 343*f = 0?
-1, 0, 377
Let z(p) be the third derivative of -p**8/336 - p**7/210 + 3*p**6/20 + 13*p**5/15 + 5*p**4/3 - 1840*p**2. Find t, given that z(t) = 0.
-2, 0, 5
Let a(x) be the third derivative of 2*x**3 + 5*x**2 + 0*x + 0*x**4 + 0 + 1/24*x**5 - 1/144*x**6. Let b(m) be the first derivative of a(m). Solve b(f) = 0.
0, 2
Let k(u) be the first derivative of -2*u**6/3 - 4*u**5/5 + 18*u**4 + 208*u**3/3 + 80*u**2 + 2031. Let k(y) = 0. Calculate y.
-2, 0, 5
Solve -75 + 232*l**3 + 21 - 48*l**4 + 20 - 368*l**2 + 252*l - 4*l**5 - 30 = 0.
-16, 1
Let n(j) be the first derivative of -34/11*j**2 + 0*j - 60 + 2/33*j**3. Suppose n(f) = 0. What is f?
0, 34
Let o(d) be the second derivative of -1/270*d**6 + 1/4*d**4 - 245*d - 7/180*d**5 + 5/9*d**2 - 29/54*d**3 + 0. Factor o(i).
-(i - 1)**3*(i + 10)/9
Let f = -2/341165475 - -662429632079/248027300325. Let o = -3/727 + f. Factor o*t**3 - 2*t - 2/3 + 0*t**2.
2*(t - 1)*(2*t + 1)**2/3
Factor -5978314*n + 94*n**2 - 24*n**2 + 5978313*n + 3*n**3 - 70 - 2*n**3.
(n - 1)*(n + 1)*(n + 70)
Find a such that -10*a**2 - 32*a + 5*a**2 + 4*a**2 + 3*a**2 = 0.
0, 16
Suppose -33*z - 142 + 368 - 127 = 0. Solve -5488/15 - 28/5*u**2 + 392/5*u + 2/15*u**z = 0 for u.
14
Let w(o) = 17. Let i(s) = -s - 1. Let n(m) = 5*i(