 Let c(w) = -10*i(w) + 3*r(w). Factor c(m).
-4*(m + 2)*(m + 23)
Let x = -169/4 + 45. Let z(g) be the second derivative of 2*g**3 + 0 + 6*g**2 - x*g**4 - 9/10*g**5 + 7*g. Factor z(r).
-3*(r + 2)*(2*r + 1)*(3*r - 2)
Factor 1336*t**2 - 4340*t - 1080*t**2 + 9674 - 1986 - 4*t**3.
-4*(t - 31)**2*(t - 2)
Let g be -2*(4 - (-22)/(-4)). Factor 15*y - 44*y + 21*y + 10*y**g - 2*y**2 - 14*y**2.
2*y*(y - 2)*(5*y + 2)
Let o(d) = d**4 - 19*d**3 - 78*d**2 - 4*d + 104. Let r(z) = z**4 - 20*z**3 - 78*z**2 - 4*z + 104. Let g(a) = -3*o(a) + 4*r(a). Suppose g(x) = 0. What is x?
-2, 1, 26
Let f be (6/(-6) + 6)*1. Let z(x) be the first derivative of -7/2*x**2 + 2*x + 5/3*x**3 - f. Factor z(a).
(a - 1)*(5*a - 2)
Let c be (-12108)/(-21) - (9 - 5). Let w = 574 - c. Find r such that 6/7*r**4 - w*r**3 - 2/7*r**2 + 10/7*r - 4/7 = 0.
-1, 2/3, 1
Suppose 5*q - 3 = 4*q. Solve -q*d**2 + 3 - 14*d + 10*d + 4*d = 0 for d.
-1, 1
Let m = 4473 - 8945/2. Let -1/4*g**4 - 5/4*g**2 + g**3 + m*g + 0 = 0. Calculate g.
0, 1, 2
Factor 0 - 4/5*y**2 - 24*y.
-4*y*(y + 30)/5
Let r(i) be the third derivative of i**8/336 - i**7/30 + 19*i**6/120 - 5*i**5/12 + 2*i**4/3 - 2*i**3/3 - 265*i**2. Factor r(w).
(w - 2)**2*(w - 1)**3
Let p = -421/2 - -1283/6. Suppose -p*w + 4/3 + 7/3*w**2 - 1/2*w**3 = 0. What is w?
2/3, 2
Find t, given that -10*t**3 + 3*t**3 - 5*t**2 + 8*t**3 + 4*t**3 = 0.
0, 1
Let o(k) be the first derivative of 20*k**2 + 5/3*k**3 + 6 + 80*k. Factor o(f).
5*(f + 4)**2
Let y(v) be the second derivative of -v**5/50 - 19*v**4/30 + v**3/15 + 19*v**2/5 + 26*v - 7. Factor y(m).
-2*(m - 1)*(m + 1)*(m + 19)/5
Suppose -3*f = -r + 2, -3*r + 2*f = -3*f - 6. Find q, given that q**3 + 3*q**3 - 236*q + 232*q - 4 + 4*q**r = 0.
-1, 1
Let f be (8/7)/((-60)/(-70)). Let a(s) be the first derivative of f*s**5 - 43/18*s**4 + 8 + 0*s + 16/9*s**3 - 4/9*s**2 - 7/27*s**6. Suppose a(v) = 0. What is v?
0, 2/7, 1, 2
Let m(f) be the third derivative of 14*f**2 + 1/6*f**5 + 1/6*f**6 + 0 - 25/24*f**4 + 5/336*f**8 + 5/3*f**3 + 0*f - 2/21*f**7. Suppose m(i) = 0. Calculate i.
-1, 1, 2
Let r be (-3)/120*5/(-2). Let j(u) be the first derivative of 0*u - r*u**4 + 1/12*u**3 - 1 + 0*u**2. Let j(d) = 0. Calculate d.
0, 1
Let f(a) be the second derivative of -2/3*a**3 - 1/7*a**7 + 0 + 1/3*a**6 - 5/6*a**4 + 0*a**2 + 11*a + 1/2*a**5. Solve f(c) = 0.
-1, -1/3, 0, 1, 2
Let x = -707/43100 - -20/431. Let j(d) be the third derivative of 4*d**2 - x*d**5 + 1/200*d**6 + 0*d + 3/40*d**4 - 1/10*d**3 + 0. Factor j(v).
3*(v - 1)**3/5
Let n = -216833/34 - -6377. Let r = 1/17 - n. Find y, given that 1/4*y**4 - 1/2*y - 1/4 + 0*y**2 + r*y**3 = 0.
-1, 1
Let p be (-7986)/(-5841) - (-1 - 0)*-1. Let l = p + -2/59. Factor -l*q**2 + 0 - 1/6*q - 1/6*q**3.
-q*(q + 1)**2/6
Factor 0*f + 2/13*f**5 + 2/13*f**3 + 0*f**2 + 4/13*f**4 + 0.
2*f**3*(f + 1)**2/13
Suppose -m = -5*k - 2 + 5, 5*m = -k - 15. Let s be 4 - (m + -2 + 3)*-1. Let -2/3*z**s - 2/9*z**3 - 2/3*z - 2/9 = 0. What is z?
-1
Let a(o) be the third derivative of -o**7/42 + 5*o**6/24 - 2*o**5/3 + 5*o**4/6 - 69*o**2 - 2*o. Determine m so that a(m) = 0.
0, 1, 2
Let s(a) be the third derivative of -a**6/240 + a**5/20 - 5*a**4/48 + 12*a**2 + 4*a. Factor s(g).
-g*(g - 5)*(g - 1)/2
Suppose -m - m - 20 = -7*m. Find z, given that 4/3*z**5 + 20/3*z**m + 144 + 0*z - 20/3*z**3 - 60*z**2 = 0.
-3, 2
Suppose -18*t = -41 - 49. Suppose t - 5 = 8*g. Factor g*m - 1/2*m**2 + 0.
-m**2/2
Let l = 3515 + -3515. Factor -2/3*o**2 - 2/3*o + l.
-2*o*(o + 1)/3
What is d in 4/5*d**2 + 72/5 + 44/5*d = 0?
-9, -2
Let j(g) be the third derivative of -g**2 + 0*g - 1/20*g**4 + 0*g**3 + 1/100*g**5 + 1/200*g**6 + 0. Factor j(p).
3*p*(p - 1)*(p + 2)/5
Let x(f) = -f**3 + 30*f**2 - 30*f + 43. Let n be x(29). Let d be ((-4)/n)/((-12)/84). Determine k, given that -1/2*k - 1/2*k**4 + 1/2*k**3 + 1/2*k**d + 0 = 0.
-1, 0, 1
Let o = 49 - 341/5. Let t = 682/35 + o. Factor 0*x + 0 - 2/7*x**4 + t*x**2 + 0*x**3.
-2*x**2*(x - 1)*(x + 1)/7
Suppose -22*t + 79*t - 2*t**2 + 2*t**2 - 3*t**2 = 0. Calculate t.
0, 19
Let z(u) be the first derivative of 2*u**5/15 + 11*u**4/3 + 242*u**3/9 + 412. Factor z(c).
2*c**2*(c + 11)**2/3
Let v(u) be the third derivative of -u**5/5 + 46*u**4/3 - 40*u**3 + 101*u**2. Factor v(w).
-4*(w - 30)*(3*w - 2)
Let a(z) = z**2 - 9*z + 7. Let p be a(-5). Let n = -223/3 + p. Factor -2/3*w**2 - n - 10/3*w.
-2*(w + 1)*(w + 4)/3
Let k(x) = -10*x**2 + 3*x + 11. Let j be k(5). Let c = j + 2024/9. Solve -16/9*m**3 + 8/9*m - 2/9 + 4/9*m**2 - 2/9*m**4 + c*m**5 = 0.
-1, 1/4, 1
Let r(i) = -106*i - 210. Let f be r(-2). What is n in -2/7*n**3 + 0 + 0*n**f + 0*n = 0?
0
Let k(a) be the third derivative of a**7/1260 + a**6/180 - a**4/9 + a**3/3 + 16*a**2. Let j(y) be the first derivative of k(y). Determine r so that j(r) = 0.
-2, 1
Suppose -12 = 4*f, -z - 20 + 18 = 2*f. Let k(r) be the second derivative of 0 + r**2 - r + 1/96*r**z - 1/6*r**3. Factor k(w).
(w - 4)**2/8
Let u(k) = 55*k + 57. Let j be u(-1). Find s such that 2/5*s**5 + 0*s + 0 + 2/5*s**4 + 0*s**j + 0*s**3 = 0.
-1, 0
Let k(c) be the third derivative of -c**5/80 - 13*c**4/32 + 10*c**2 + 4*c. Factor k(p).
-3*p*(p + 13)/4
Suppose 19/4*r - 3 + 1/4*r**3 - 2*r**2 = 0. Calculate r.
1, 3, 4
Let z(g) = -9*g**3 + g**2 - g + 1. Let k be z(1). Let i(d) = 2*d**2 + 17*d + 11. Let m be i(k). Factor 0*f**m - 1/2*f**4 + 0 + f + 3/2*f**2.
-f*(f - 2)*(f + 1)**2/2
Let g(p) be the second derivative of -p**5/25 + 2*p**4/15 + 6*p**3/5 - 36*p**2/5 - 228*p + 2. Solve g(m) = 0 for m.
-3, 2, 3
Let b(y) be the second derivative of -y**6/600 + y**5/300 + y**4/24 + y**3/10 - 27*y**2/2 + 10*y. Let n(k) be the first derivative of b(k). Factor n(d).
-(d - 3)*(d + 1)**2/5
Let j(d) = -5*d**4 + 17*d**3 - 69*d**2 + 85*d - 40. Let m(l) = 56*l**4 - 186*l**3 + 760*l**2 - 934*l + 440. Let f(b) = 68*j(b) + 6*m(b). What is n in f(n) = 0?
1, 2, 5
Suppose 0 = -0*s + 3*s - x - 29, 4*x + 44 = 3*s. Find q, given that 35*q**4 + 25*q**5 - 11*q**2 - 14*q**3 - q**2 - s*q**2 - 26*q**3 = 0.
-2, -2/5, 0, 1
Let b(q) be the third derivative of -q**7/22680 - q**6/3240 - q**5/1080 + q**4/6 - 2*q**2. Let n(y) be the second derivative of b(y). Factor n(g).
-(g + 1)**2/9
Let g(s) be the first derivative of -s**5/40 + 3*s**4/8 + 3*s**3/4 - 81*s**2/4 - 729*s/8 + 73. Let g(i) = 0. What is i?
-3, 9
Factor -1/5*g**2 + 69/5 + 68/5*g.
-(g - 69)*(g + 1)/5
Suppose -4/3*n**2 - 368/3*n - 8464/3 = 0. What is n?
-46
Let l(o) be the third derivative of o**6/120 + o**5/40 - 13*o**3/6 + 2*o**2. Let f(u) be the first derivative of l(u). Factor f(s).
3*s*(s + 1)
Find t such that 3*t**2 - 9 - 1 - 56 - 63*t = 0.
-1, 22
Let h = -234778/5 + 46958. Factor -h - 2*c - 2/5*c**2.
-2*(c + 2)*(c + 3)/5
Factor -1/2*u**5 + 1/2 + 1/2*u**4 - u**2 + u**3 - 1/2*u.
-(u - 1)**3*(u + 1)**2/2
Let y(t) = 2*t + 1. Let k be y(1). Let x(n) = 2*n - 4. Let l be x(k). Factor -3 - l*b**2 - 3 + 17*b - 9*b.
-2*(b - 3)*(b - 1)
Let l = 135 - 129. Suppose 5*q + 2 = l*q. Factor -2/5 + 2/5*d + 2/5*d**q - 2/5*d**3.
-2*(d - 1)**2*(d + 1)/5
Let o(f) be the third derivative of f**6/320 + 117*f**5/80 + 4563*f**4/16 + 59319*f**3/2 + 2*f**2 - 247. Determine t, given that o(t) = 0.
-78
Let h(y) = -9*y**3 - 3*y**2 - 9*y - 3. Let b(d) = -8*d**3 - 4*d**2 - 9*d - 3. Suppose -1 = 6*j - 31. Let f(c) = j*h(c) - 6*b(c). Factor f(q).
3*(q + 1)**3
Let m(z) be the second derivative of -1/40*z**5 + 0*z**4 + 0*z**2 + 12*z + 0*z**3 + 1/60*z**6 + 0. Factor m(g).
g**3*(g - 1)/2
Suppose 18 = -5*i - 2, 0 = -3*k - 4*i - 4. Factor -32*p**k - 96*p**2 - 36*p + 1 + 0 - 88*p**3 - 4*p**5 - 1.
-4*p*(p + 1)**2*(p + 3)**2
Let u(m) be the third derivative of m**7/630 - m**6/360 - m**5/180 + m**4/72 - 297*m**2. Factor u(a).
a*(a - 1)**2*(a + 1)/3
Let m(x) be the first derivative of -x**4/36 - 4*x**3/9 - 8*x**2/3 + 11*x - 17. Let h(a) be the first derivative of m(a). Solve h(k) = 0.
-4
Factor 1/7*n**3 - 3/7*n**2 - 3 - 25/7*n.
(n - 7)*(n + 1)*(n + 3)/7
Let v(t) = -7*t**3 - 126*t**2 - 2656*t - 18527. Let u(i) = 3*i**3 + 63*i**2 + 1327*i + 9263. Let p(c) = 5*u(c) + 2*v(c). Factor p(f).
(f + 21)**3
Let l = -8 - -21. Let -l*m**2 - 46*m**4 + 4*m**2 - 15*m**2 - 12*m - 15*m**3 + 43*m**4 = 0. Calculate m.
-2, -1, 0
Let m(y) be the first derivative of 3*y**5/35 + 57*y**4/28 + 51*y**3/7 + 21*y**2/2 + 48*y/7 - 324. Determine t so that m(t) = 0.
-16