*v + 27*v**5 + 9 + x*v**3 + 117*v**4 - 2441*v**2 - 6*v**3 = 0.
-3, -1, 1/3
Let u(m) be the first derivative of -2*m**3/9 - 29*m**2/3 - 308*m/3 + 9. Factor u(w).
-2*(w + 7)*(w + 22)/3
Find f such that -47*f**4 + 97*f**4 - 44*f**2 + 245*f**3 - 25*f**4 - 6*f**2 = 0.
-10, 0, 1/5
Suppose 10 = m - i, 22*m + 5*i = 17*m - 20. Solve -3/7*n**5 - 6*n + 45/7*n**m + 39/7*n**4 + 0 - 39/7*n**2 = 0.
-1, 0, 1, 14
Let u(a) = 32*a**4 - 344*a**3 + 1998*a**2 - 4892*a + 4358. Let x(r) = -11*r**4 + 114*r**3 - 666*r**2 + 1632*r - 1452. Let z(y) = -3*u(y) - 8*x(y). Factor z(q).
-2*(q - 3)**2*(2*q - 9)**2
Suppose 14*v + 2/9*v**2 + 244/9 = 0. Calculate v.
-61, -2
Let j be ((-4345)/30)/(-11) + ((-9)/18)/((-23)/(-460)). Factor -3/2*n**2 + j*n - 1/3.
-(n - 2)*(9*n - 1)/6
Let x(p) be the first derivative of -p**5 + 45*p**4/2 - 25*p**3 - 85*p**2 - 1098. Factor x(s).
-5*s*(s - 17)*(s - 2)*(s + 1)
Factor -2450/23 + 140/23*g - 2/23*g**2.
-2*(g - 35)**2/23
Suppose 2*c - 12 = -g, -5*g + 1378 - 1357 = -3*c. Solve 0 + 2/11*h**4 - 512/11*h + 576/11*h**2 - g*h**3 = 0 for h.
0, 1, 16
Let p(v) be the second derivative of v**6/15 - 7*v**5/10 + 12*v**3 + 2275*v. Solve p(f) = 0 for f.
-2, 0, 3, 6
Let p(n) = -n**2 - 11*n + 82. Let v(o) = -7*o**2 + 33*o - 6. Let w be v(5). Let b be p(w). Factor 0 - 11/2*m**3 + 0*m + m**b.
-m**2*(11*m - 2)/2
Let o(p) = p**2 - 8*p + 17. Let l be o(5). Factor 11*t**2 + 16*t - 91*t**3 + 7*t**3 - 37*t**l - 6*t**2.
-4*t*(3*t + 2)*(7*t - 2)
Factor 2400 + 9709*y**2 - 4859*y**2 + 196*y - 4846*y**2.
4*(y + 24)*(y + 25)
Factor -4825425 + 4*j**5 - 32*j**3 + 4825425 + 8*j**4.
4*j**3*(j - 2)*(j + 4)
Suppose 0 = -2*u - 27 + 35, -5*q + 2728 = 2*u. Let p = q - 539. Find o, given that 0*o + 1/8*o**4 + 1/8*o**3 + 0 - 1/8*o**2 - 1/8*o**p = 0.
-1, 0, 1
Find o, given that 3/7*o**2 + 240/7 + 18*o = 0.
-40, -2
Let c(d) be the first derivative of 2/3*d**6 + d**4 - 4*d**2 - 4*d**3 + 12/5*d**5 + 238 + 0*d. Determine g so that c(g) = 0.
-2, -1, 0, 1
Factor 2*w**2 + 19 + 7 + 43 + 12 + 70*w - 13.
2*(w + 1)*(w + 34)
Let l(c) = 260*c**3 + 3764*c**2 + 2112*c - 1456. Let g(m) = 40*m**3 + 579*m**2 + 325*m - 224. Let v(p) = 32*g(p) - 5*l(p). Factor v(n).
-4*(n + 1)*(n + 14)*(5*n - 2)
Let c be 47/1 + (-135)/3. Factor 3*j**4 + 57/4*j**c - 75/8*j**3 - 3/8*j**5 - 21/2*j + 3.
-3*(j - 2)**3*(j - 1)**2/8
Let y(p) be the third derivative of -103*p**2 - 1/80*p**5 + 5/4*p**3 + 0*p - 3/32*p**4 + 0. Factor y(s).
-3*(s - 2)*(s + 5)/4
Let 477 - 57*n + 45*n**2 + 243*n - 708 = 0. What is n?
-77/15, 1
Suppose -9*y - 36 = -19*y + 4*y. Let d(z) be the first derivative of -38 + 0*z + 0*z**4 - 2/69*z**y + 6/115*z**5 + 0*z**2 - 2/69*z**3. Solve d(c) = 0.
-1/2, 0, 1
Let o(q) be the third derivative of -48*q**2 + 1/36*q**5 + 1/9*q**3 + 0*q + 0 - 11/72*q**4. Solve o(w) = 0.
1/5, 2
Let j(h) be the second derivative of -h**5/80 - 7*h**4/48 - 2*h**3/3 - 3*h**2/2 - 92*h + 1. Factor j(f).
-(f + 2)**2*(f + 3)/4
Let c = 230 - 227. Determine i, given that -102*i**3 + 124*i**3 - 183 + 3 + 20*i**4 - 600*i + 535*i**2 + 203*i**c = 0.
-6, -1/4, 1
Let r(p) = -p + 17. Let b be r(3). Suppose -b*t + 16*t - 6 = 0. Factor -3*k - 12 + 7*k + 7*k - t*k**3 + 3*k**2 + k.
-3*(k - 2)*(k - 1)*(k + 2)
Factor 328050*m - 88573500 - 405*m**2 + 1/6*m**3.
(m - 810)**3/6
Let q(w) be the third derivative of -w**8/168 + w**6/30 - w**4/12 - 3223*w**2. Factor q(r).
-2*r*(r - 1)**2*(r + 1)**2
Suppose 2*x = -2671*d + 2670*d + 4, -1 = d - 3*x. Find g, given that -6/11 - 2/11*g**d - 8/11*g = 0.
-3, -1
Let y = -408043 - -2040217/5. Suppose -y + 37/5*s - 7*s**2 = 0. What is s?
2/35, 1
Let t(g) be the first derivative of g**5 - 3305*g**4/2 + 2184605*g**3/3 + 3498. Factor t(b).
5*b**2*(b - 661)**2
Let f(z) = -7. Let a(b) = -10*b**2 - 189*b - 2. Let s(o) = a(o) - 3*f(o). Factor s(p).
-(p + 19)*(10*p - 1)
Let k(p) = 2*p**3 + 30*p**2 - 5*p - 27. Let b be k(-15). Factor -17*v + 38 - 433*v + 55*v**2 + b - 6.
5*(v - 8)*(11*v - 2)
Factor 0*p**2 + 117*p + 2*p**2 - 3*p - 59*p + 246*p - 151.
(p + 151)*(2*p - 1)
Let v(w) = 8*w**2 + 152*w + 2870. Let z(l) = 7*l**2 + 152*l + 2873. Let g(a) = -a**2 + 14*a - 45. Let o be g(10). Let x(j) = o*v(j) + 6*z(j). Factor x(u).
2*(u + 38)**2
Let i(s) be the second derivative of s**4/30 + 6*s**3/5 + 56*s**2/5 + 2365*s. Find a, given that i(a) = 0.
-14, -4
Let 5050386 + 85346*v**2 + 141212 + 1854897*v + 968*v**3 + 491719*v + 4669182 + 4*v**4 - 5714*v**2 = 0. What is v?
-79, -5
Let p(t) be the third derivative of -t**6/30 - 4*t**5/15 + t**4/2 + 12*t**3 + 1525*t**2. What is x in p(x) = 0?
-3, 2
Let i(z) be the third derivative of z**5/12 + 245*z**4/2 + 72030*z**3 - 3*z**2 - 3*z - 70. Find l such that i(l) = 0.
-294
Find n, given that -10*n**4 - 2015/2*n**3 - 51495/2*n**2 - 18500*n + 6250 = 0.
-50, -1, 1/4
Suppose -z - f = -2, 0*f - 8 = -4*z - 2*f. Suppose 0 = 5*j - 3*u - 18, 0 = -z*j + 4*j - 4*u - 10. Factor -5 - 16*d**2 - 3 - 4*d**3 - 23*d + j*d.
-4*(d + 1)**2*(d + 2)
Let t(d) be the third derivative of -d**7/630 - 19*d**6/360 + 92*d**5/45 - 125*d**4/6 + 64*d**3 + 2*d**2 - 1105. Suppose t(q) = 0. Calculate q.
-32, 1, 6
Find s such that 940/9*s - 2/9*s**2 + 1888/9 = 0.
-2, 472
Let w(k) be the second derivative of k**5/170 + 3*k**4/34 - 25*k**3/51 - 33*k**2/17 - 32*k - 3. Factor w(q).
2*(q - 3)*(q + 1)*(q + 11)/17
Suppose -1214*f = -1212*f - 10. Factor -2 - 6*p**2 + f + 84*p**3 - 87*p**3 + 3*p + 3.
-3*(p - 1)*(p + 1)*(p + 2)
Let s(l) = -2*l**4 - l**3 + 2*l**2 + 2*l. Let h(i) = -7*i**4 + 11*i**3 + 61*i**2 - 50*i - 204. Let w(u) = 4*h(u) - 12*s(u). Suppose w(t) = 0. What is t?
-3, -2, 2, 17
Suppose -121*u + 26*u = 527*u + 26*u. Factor 0 + u*a + 8/5*a**2 + 2/5*a**3.
2*a**2*(a + 4)/5
Let y = 5 + -2. Suppose 90 = 13*p + 25. Find t, given that -p*t - 3*t + y*t + 5*t**2 = 0.
0, 1
Let i(p) be the first derivative of p**6/30 + 7*p**5/25 - 2*p**4/5 + 1227. Find k such that i(k) = 0.
-8, 0, 1
Let f(v) be the first derivative of -v**4/3 + 10*v**3/3 - 12*v**2 - 212*v + 224. Let k(t) be the first derivative of f(t). Factor k(l).
-4*(l - 3)*(l - 2)
Solve -36*c**3 + 95*c - 6 + 349*c**5 - 121*c - 351*c**5 - 44*c**2 - 14*c**4 = 0.
-3, -1
Let r(n) = -n**3 - 10*n**2 + 12*n + 11. Let x be r(-11). Suppose 7*t + t - 32 = x. Find g, given that -9*g**3 - 6*g**3 + 16*g**3 - g**t = 0.
0, 1
Let y(m) be the first derivative of m**4 - 2152*m**3/3 - 1082*m**2 + 4312*m + 4422. Factor y(k).
4*(k - 539)*(k - 1)*(k + 2)
Let f(u) be the first derivative of -u**6/60 + u**5/5 - 2*u**4/3 - 45*u**2/2 - 299. Let i(x) be the second derivative of f(x). What is o in i(o) = 0?
0, 2, 4
Let v(b) be the second derivative of -b**5/10 - 23*b**4/6 - 160*b**3/3 - 300*b**2 - 1030*b. Suppose v(k) = 0. Calculate k.
-10, -3
Let t be (7 - 54786/7824)*556/(-6). Let j = 6/163 + t. Factor -1/4*k + 1/4*k**4 - j*k**2 + 1/4*k**3 + 0.
k*(k - 1)*(k + 1)**2/4
Let r(b) be the second derivative of b**5/180 - b**4/9 - 110*b**3/27 + b + 1201. Factor r(k).
k*(k - 22)*(k + 10)/9
Let w(b) be the first derivative of b**7/21 - b**6/3 + 3*b**5/5 + 2*b**4/3 - 8*b**3/3 + 33*b + 33. Let q(s) be the first derivative of w(s). Factor q(d).
2*d*(d - 2)**3*(d + 1)
Let p(q) be the first derivative of -1/4*q**4 - q**3 + 9/2*q**2 - 25*q - 39. Let x(r) be the first derivative of p(r). Determine c, given that x(c) = 0.
-3, 1
Factor 277*h + h**5 - 28*h**4 + 162*h**3 - 93*h**2 - 235*h**2 - 225 + 141.
(h - 21)*(h - 4)*(h - 1)**3
Let d be 252/15 + (6/22 - (-4050)/(-330)). What is l in 8/5*l**3 - d*l - 4/5*l**4 + 4*l**2 + 0 = 0?
-2, 0, 1, 3
Let b(s) be the third derivative of -s**6/180 - 11*s**5/270 - s**4/108 + 5*s**3/9 - 6*s**2 + 98. Factor b(c).
-2*(c - 1)*(c + 3)*(3*c + 5)/9
Let c(m) be the second derivative of m**7/14 - 7*m**6/5 - 33*m**5/4 + 17*m**4 - 512*m. Determine k so that c(k) = 0.
-4, 0, 1, 17
Let s = 4090/3 + -1362. Let t(a) be the first derivative of 100*a - 16 - 20*a**2 + s*a**3. Factor t(z).
4*(z - 5)**2
Let q(a) be the second derivative of 1 + 3/70*a**5 - a**4 + 100/21*a**3 - 72/7*a**2 + 9*a + 1/105*a**6. Suppose q(w) = 0. What is w?
-9, 2
Suppose 32*s = 65*s. Let f be ((-6)/(-42))/(2/8). Factor f - 4/7*d**2 + s*d.
-4*(d - 1)*(d + 1)/7
Let d(p) = -p**5 - 38*p**4 + 27*p**3 - p**2 - 13*p + 13. Let k(f) = -f**4 - 2*f**2 + f + 1. Let q(v) = -2*d(v) + 26*k(v). Let q(b) = 0. What is b?
-26, -1, 0, 1
Suppose -10 = -5*