= 0.
-154, -2/5, 1, 2
Factor -20*m**2 + 64/3*m + 8/3*m**3 + 16.
4*(m - 6)*(m - 2)*(2*m + 1)/3
Let n(k) be the second derivative of 2*k**6/15 + 4*k**5/5 + k**4/3 - 4*k**3 + 3*k - 1031. Factor n(m).
4*m*(m - 1)*(m + 2)*(m + 3)
Let f(i) = -i**2 + 7. Let q be f(0). Let r(g) = -1 + 12 - 5 - q - g**2. Let v(u) = 3*u**2 + 5. Let y(h) = 20*r(h) + 5*v(h). Find s such that y(s) = 0.
-1, 1
Let s(v) = 501*v**2 - 4*v - 244*v**2 - 73 - 256*v**2. Let y be s(11). Factor 20/3*u**3 + 500/3*u + 50*u**2 + 625/3 + 1/3*u**y.
(u + 5)**4/3
Let c(x) = 40*x**3 + 744*x**2 - 756*x + 14. Let a(f) = 14*f**3 + 248*f**2 - 252*f + 5. Let y(w) = -14*a(w) + 5*c(w). Solve y(s) = 0 for s.
-63, 0, 1
Solve -9/4*i**4 - 183/4*i**2 - 195/4*i - 69/4*i**3 - 18 = 0 for i.
-3, -8/3, -1
Let a(f) = 113*f**3 - 2*f**2 + f. Let u be a(1). Factor t**4 + 2*t**5 - u*t**2 + 13*t**4 + 98*t**2 - 2*t**3.
2*t**2*(t - 1)*(t + 1)*(t + 7)
Let f(i) = 13*i**2 - 11*i - 4. Let o(a) = 2*a. Let t(w) = -f(w) - o(w). Let x(n) = 37*n**2 - 26*n - 11. Let q(c) = -17*t(c) - 6*x(c). Factor q(g).
-(g - 2)*(g - 1)
Let a be 4 - ((-1628)/(-777))/((-44)/12 - -3). Factor 24/7 - 16*f + 110/7*f**2 + a*f**3.
2*(f + 3)*(5*f - 2)**2/7
Suppose 0 = m + 5*p - 52, m = -2*m - 4*p + 178. Let c = -58 + m. Find u such that 10*u + 135*u**3 + 56*u**2 - 121*u**2 + 8*u**5 + 27*u**5 - 115*u**c = 0.
0, 2/7, 1
Let h = 422 - 418. Factor -h*p**3 + 12*p**2 + p**3 + 692*p - 678*p + p**3.
-2*p*(p - 7)*(p + 1)
Let m(c) be the third derivative of c**6/30 + 27*c**5/10 - 41*c**4/12 - c**2 + 93. Determine g, given that m(g) = 0.
-41, 0, 1/2
Let n(v) be the third derivative of v**6/420 + 29*v**5/90 + 355*v**4/126 + 128*v**3/21 - 5*v**2 - 6*v + 7. Find q, given that n(q) = 0.
-64, -3, -2/3
Let r(q) be the first derivative of -2*q**3/33 + 1022*q**2/11 - 738. Find t, given that r(t) = 0.
0, 1022
Let p be (-531)/(-126) - (-2)/7 - (-1121)/177. Factor 17/3*j**2 - p*j - 1/6*j**3 + 16/3.
-(j - 32)*(j - 1)**2/6
Let v(g) = -31*g**4 - g**2 - g - 1. Let b(x) = 234*x**4 - 102*x**3 + 92*x**2 + 40*x + 8. Let j(q) = -b(q) - 8*v(q). Factor j(c).
2*c*(c - 1)*(c + 8)*(7*c + 2)
Let q(l) = -l**2 + l + 2. Let t(g) = 2*g**2 - 13*g - 8. Let p(a) = 5*a**2 - 39*a - 25. Let b(k) = -2*p(k) + 7*t(k). Let f(x) = b(x) + 3*q(x). Factor f(s).
s*(s - 10)
Let a(q) be the first derivative of 17/3*q**3 + 1/10*q**5 + 0*q**2 + 3/8*q**4 + 0*q + 1/120*q**6 + 7. Let r(c) be the third derivative of a(c). Factor r(v).
3*(v + 1)*(v + 3)
Let b = -230359/20 - -11518. Let w(u) be the first derivative of -b*u**4 - 21/25*u**5 - 31 - 2/5*u + 23/15*u**3 + 1/10*u**2. Solve w(q) = 0 for q.
-1, -1/3, 2/7, 1
Let h(j) be the third derivative of j**8/168 + j**7/15 + 7*j**6/60 - 19*j**5/30 - 4*j**4/3 + 20*j**3/3 - 5246*j**2. Find s such that h(s) = 0.
-5, -2, 1
Let m = 4949 + -4949. Let k(z) be the second derivative of -2*z + 0*z**2 + m + 1/150*z**5 + 1/45*z**4 + 1/45*z**3. Factor k(g).
2*g*(g + 1)**2/15
Let k(r) be the first derivative of r**7/7140 + r**6/3060 - r**5/1020 - r**4/204 - 68*r**3/3 + 85. Let j(h) be the third derivative of k(h). Factor j(d).
2*(d - 1)*(d + 1)**2/17
Suppose 0 = -2*u + 11 - 9, c + u = 253. Let f = c - 249. Determine d, given that -4/7 + 2/7*d - 2/7*d**f + 4/7*d**2 = 0.
-1, 1, 2
Solve -193*w**4 - 1683*w**3 + 732*w - 318*w**2 + 1848*w**2 + 677*w**4 + 72 - 121*w**4 = 0.
-2/11, 2, 3
Let s(x) be the third derivative of -x**6/480 - x**5/30 + 11*x**4/96 + 3*x**3/4 - 9513*x**2 + 2*x. Factor s(n).
-(n - 2)*(n + 1)*(n + 9)/4
Determine w so that -16/5*w**4 + 0*w**3 + 4/5*w**5 - 64/5*w + 64/5*w**2 + 0 = 0.
-2, 0, 2
Let x = -34559 - -103679/3. Determine v so that -v**3 - 1/3*v**2 + 0 + x*v + 1/3*v**4 + 1/3*v**5 = 0.
-2, -1, 0, 1
Solve 3468*w**2 - 542207 + 92*w**3 + 4*w**4 - 8*w**4 - 78608*w - 794129 + 44*w**3 = 0 for w.
-17, 34
Let g(q) be the third derivative of -q**5/570 + 149*q**4/57 - 88804*q**3/57 + 10*q**2 - 10*q. Factor g(b).
-2*(b - 298)**2/19
Suppose 11*k - 12*k = 25*k. Let o(y) be the second derivative of -y**2 + k + 21*y - 1/6*y**4 - 2/3*y**3. Determine b, given that o(b) = 0.
-1
Factor -9/5*n**2 + 0 + 1/5*n**4 + 3/5*n**3 + n.
n*(n - 1)**2*(n + 5)/5
Let b(d) be the first derivative of 3*d**5/5 - 1311*d**4/4 + 1305*d**3 - 3909*d**2/2 + 1302*d + 2205. Let b(v) = 0. What is v?
1, 434
Let d(c) be the second derivative of -57*c + 0*c**2 + 0 - 7/18*c**3 - 1/18*c**4. What is i in d(i) = 0?
-7/2, 0
Factor 1/5*i**3 + 4032/5 + 48*i - 41/5*i**2.
(i - 24)**2*(i + 7)/5
Solve 4*d**4 + 7200/7 - 2/7*d**5 + 512/7*d**3 - 7228/7*d**2 - 510/7*d = 0 for d.
-16, -1, 1, 15
Suppose 4*w - 56 = -3*l, -5*w - 7 + 2 = 0. Suppose 37*n = 41*n - l. Factor -4*u + 8*u**3 + 4 + 8*u**2 - 8*u + 0*u - 12*u**4 + 4*u**n + 0.
4*(u - 1)**4*(u + 1)
Let j(s) be the first derivative of -s**4/10 - 56*s**3/15 + 59*s**2/5 - 12*s + 264. Factor j(z).
-2*(z - 1)**2*(z + 30)/5
Let k(i) = -9*i**3 + 90*i**2 + 1660*i - 10130. Let z(m) = 2*m**3 - m**2 - 17*m + 1. Let x(y) = 3*k(y) + 15*z(y). Determine v, given that x(v) = 0.
-45, 5
Factor -2/17*p**2 - 6/17 - 8/17*p.
-2*(p + 1)*(p + 3)/17
Let s(l) be the first derivative of -8/5*l**2 + 0*l + 2/15*l**3 + 28. Solve s(k) = 0.
0, 8
Let m(w) be the third derivative of w**7/1680 + w**6/240 - 29*w**5/480 + w**4/8 + 2*w**2 - 1976*w. Find k such that m(k) = 0.
-8, 0, 1, 3
Suppose 0 = -3*c - 5*g - 13, -2*c + g + 11 + 2 = 0. Factor 81*q - 65*q + 14*q**4 + 0*q**4 - 40*q**2 - c*q**3 - 4*q**4.
2*q*(q - 2)*(q + 2)*(5*q - 2)
Suppose 3*m = 4*v - 18, -32 = -4*v - 3*m - m. Factor 0*h + 12*h**3 - 2*h - v*h - 2*h - 14*h**3 + 12*h**2.
-2*h*(h - 5)*(h - 1)
Let a(v) = 6*v**2 + 5*v - 4. Suppose 29*w = 18*w + 55. Let y(r) = -7*r**2 - 5*r + 6. Let i(f) = w*y(f) + 6*a(f). Factor i(l).
(l + 2)*(l + 3)
Let d(l) be the second derivative of -l**5/4 - 35*l**4/6 - 145*l**3/6 + 110*l**2 - 900*l. Solve d(t) = 0 for t.
-11, -4, 1
Suppose -9*c = -2*j - 62, -26 = -2*j - 493*c + 491*c. Let d(p) be the first derivative of 0*p + 9 + 3*p**4 - 6*p**3 + 0*p**2 - 2/5*p**j. Factor d(t).
-2*t**2*(t - 3)**2
Let a(u) be the second derivative of -u**6/30 - 583*u**5/10 - 114071*u**4/4 - 677446*u**3/3 - 675122*u**2 + 2214*u. Let a(y) = 0. What is y?
-581, -2
Let r(i) be the first derivative of -i**6/9 - 32*i**5/15 - 85*i**4/6 - 124*i**3/3 - 48*i**2 + 193. Let r(w) = 0. Calculate w.
-8, -3, -2, 0
Suppose -15*u - 1377 = 1113. Let i = -828/5 - u. Factor 432/5 + 36/5*f**2 + i*f**3 + 216/5*f.
2*(f + 6)**3/5
Let c(o) be the second derivative of o**5/150 - o**4/3 + o**2 + 18*o + 1. Let h(b) be the first derivative of c(b). Factor h(f).
2*f*(f - 20)/5
Let j(f) = f**2 + 1. Let o(q) = -17*q**2 - 15*q. Let y be 3 + 60/(-6) - -4. Let v(k) = y*j(k) - 3*o(k). Suppose v(b) = 0. Calculate b.
-1, 1/16
Suppose -2*c = -4*d - 14, c - d - 7 = -3. Let w be c + ((-90)/63 - 3/(-7)). Solve 0*i**2 - 4/5*i**3 + 4/5*i**4 - 1/5*i**5 + 0*i + w = 0 for i.
0, 2
Let l(t) be the second derivative of -5*t**4/12 + 2105*t**3/3 - 886205*t**2/2 - 3486*t. Factor l(r).
-5*(r - 421)**2
Let m(k) be the third derivative of -k**7/1120 + k**6/480 + k**5/160 - k**4/32 - 9*k**3/2 + k**2 + 16*k. Let o(w) be the first derivative of m(w). Factor o(q).
-3*(q - 1)**2*(q + 1)/4
Let c(q) = 1700*q**2 + 154*q - 90. Let a(w) = 1696*w**2 + 155*w - 87. Let h(j) = 2*a(j) - 3*c(j). Factor h(f).
-4*(7*f + 2)*(61*f - 12)
Let d be ((-70)/(-15))/(-2)*-3. Factor -d*q - q - 42 - 38 + 7*q**2 + 81.
(q - 1)*(7*q - 1)
Let z be 30/18 - (-12623)/(-7293). Let t = 14073/748 + z. Determine j so that -15/4*j**2 + 0 - 9/2*j + t*j**3 = 0.
-2/5, 0, 3/5
Let k(x) be the second derivative of x**5/30 - 16*x**3/3 - 128*x**2/3 + 61*x + 4. Factor k(u).
2*(u - 8)*(u + 4)**2/3
What is v in 9*v**3 + 301*v**2 - 401*v + 225*v**2 - 124*v - 142*v**2 + 132 = 0?
-44, 1/3, 1
Let c(z) = z**3 - 4*z**2 - 5*z - 2. Let y be c(5). Let i be 3 - (6 + -3) - y. Factor -2*n**5 - 14*n**4 - 8 - 38*n**3 - 110*n**2 - 44*n + 12*n + 60*n**i.
-2*(n + 1)**3*(n + 2)**2
Let n(v) be the second derivative of -v**4/20 + 213*v**3/5 - 255*v**2/2 + 494*v - 3. Factor n(d).
-3*(d - 425)*(d - 1)/5
Let t(j) be the second derivative of -1/15*j**4 + 0*j**3 - 1/75*j**6 - 3*j - 10 - 3/50*j**5 + 0*j**2. Suppose t(w) = 0. Calculate w.
-2, -1, 0
Let k be ((-9)/8 + (-228993)/(-115528))/((-3)/(-7)). Determine d, given that 5/6*d**k + 5/3*d - 175/6 = 0.
-7, 5
Factor 3/5*d**