x(c) be the first derivative of m(c). Factor x(q).
-q*(q + 1)*(q + 2)/2
Suppose 16*z**2 + 1256*z - 124739 - 9*z**2 + 26143 - 11*z**2 = 0. Calculate z.
157
Let p(i) be the third derivative of -1/60*i**5 - 1/336*i**8 + 0*i**4 + 0*i**3 + 1/210*i**7 + 0*i - 16*i**2 + 1/120*i**6 + 0. Factor p(m).
-m**2*(m - 1)**2*(m + 1)
Let q(u) be the third derivative of -54*u**7/245 + 159*u**6/140 - 53*u**5/35 + u**4/7 + 8*u**3/7 - 175*u**2 - 2. Find a, given that q(a) = 0.
-2/9, 1/2, 2/3, 2
Let i(t) = 2*t**2 - 11*t + 18. Let f be i(5). Suppose -19 = -16*y + f. Factor 0 + 0*v + 1/3*v**4 + 0*v**y - 2/3*v**3.
v**3*(v - 2)/3
Let a(f) be the second derivative of f**6/10 - 57*f**5/10 + 429*f**4/4 - 646*f**3 + 1734*f**2 - 9*f + 3. Find k such that a(k) = 0.
2, 17
Let p(m) = -8*m**4 - 2*m**3 + 4*m**2 - 5*m - 3. Let o(f) = -f**4 - f**3 + f**2 - 1. Let k(t) = -21*o(t) + 3*p(t). Factor k(s).
-3*(s - 4)*(s - 1)**2*(s + 1)
Suppose 26 = 5*q + 6. Suppose -5*b - 3*l + 10 = 0, -3*l = -3*b - q*l + 6. Factor 10*x**b + 12*x - 8*x**3 + 0*x**3 + 4 - 12*x**4 - 2*x**2 - 4*x**5.
-4*(x - 1)*(x + 1)**4
Let f = -1178 - -1181. Suppose 10/7*b + 4/7 + 8/7*b**2 + 2/7*b**f = 0. Calculate b.
-2, -1
Let t(s) = -3*s**3 - 27*s**2 - 16*s + 2. Let m(p) = -p**3 + p**2 - 2*p - 1. Let o(j) = 2*m(j) + t(j). Factor o(v).
-5*v*(v + 1)*(v + 4)
Suppose -2*q + 10 = s - 0*q, 4*q - 8 = 4*s. Factor -5*x**2 + 8*x**3 + 7*x - 3*x + 2*x**4 + 3*x**s + 12*x**2.
2*x*(x + 1)**2*(x + 2)
Let i be 1*9*(-42)/(-6). Let -20 + 40*t**3 + 3*t**4 + i*t**2 + t**4 + 69*t**2 + 160*t + 84 = 0. Calculate t.
-4, -1
Factor 29/8*c + 9/8*c**2 + 3/4.
(c + 3)*(9*c + 2)/8
Suppose -4*m = -3*b + 3, 3*b + b - 4 = -m. Let r(o) be the second derivative of -1/54*o**4 - 2/27*o**3 + 0*o**2 + m - 4*o. Factor r(l).
-2*l*(l + 2)/9
Let c(b) be the first derivative of 0*b + 6/5*b**5 + 0*b**2 - 3/4*b**4 - 27 - 2*b**3 + 1/2*b**6. Factor c(p).
3*p**2*(p - 1)*(p + 1)*(p + 2)
Let l = -314 - -461. Solve 180*g + 315*g**3 + l*g**2 + 20 + 145*g**2 + 315*g**2 - 132*g**2 = 0.
-1, -2/7, -2/9
Let y(f) = 49*f + 245. Let b be y(-5). Let j be 3*(-10)/45*-2. Find u such that b*u + j*u**3 + 4/3*u**5 + 8/3*u**4 + 0 + 0*u**2 = 0.
-1, 0
Let w(h) = 9*h**2 - 56*h + 106. Let v(c) = 4*c**2 - 28*c + 52. Let d(b) = -5*v(b) + 2*w(b). Determine k so that d(k) = 0.
2, 12
Suppose -9*f + 12 = -7*f. Suppose -14*i**2 + f*i + 14*i - 6*i**2 + 5*i**3 = 0. What is i?
0, 2
Factor -4708*h**2 + 2355*h**2 + 2353*h**2 + 29*h**3 + h**4.
h**3*(h + 29)
Factor 0*r - 4*r - 12*r + 12 + 5*r - r**2.
-(r - 1)*(r + 12)
Let d(g) be the second derivative of 0 + 1/9*g**3 - 1/30*g**5 - 1/24*g**4 - 1/180*g**6 - 3*g + 1/3*g**2. Find u such that d(u) = 0.
-2, -1, 1
Let t be 72/168 + (-8)/(-14). Let b(u) be the first derivative of 1/4*u**4 - 4*u**3 + t + 24*u**2 - 64*u. Find a, given that b(a) = 0.
4
Let w = 16 - 44/3. Suppose 0 = 4*f + 3 - 11. Suppose -w - 1/3*t**f - 4/3*t = 0. Calculate t.
-2
Suppose -4*u - 3251 = -5*m, 3*u - 4074 = 8*u + 4*m. Let g = -4042/5 - u. Solve 7*f**4 - 59/5*f**3 - 4/5*f + g*f**2 + 0 = 0.
0, 2/7, 2/5, 1
Suppose -v = -6*s + 3*s + 21, 3*s = 5*v + 21. Factor s*g + 6*g + 2*g + 5*g**2 - 20.
5*(g - 1)*(g + 4)
Let y(f) = -4*f**3 + 3*f**2 - 2*f. Let l be y(1). Let u(a) = -2*a - 4. Let k be u(l). Factor 4/5*z**k + 0 - 8/5*z.
4*z*(z - 2)/5
Let j = -4 - -6. Factor 20*p**3 + 7*p - 32*p**j - 4*p + 9*p - 4*p**4 + 4*p.
-4*p*(p - 2)**2*(p - 1)
Suppose -2*y = -2*f + 110, -2 = 3*y - 2*y. Let h = 56 - f. What is q in 5/3*q**h + 2/3 + 7/3*q**4 - 5/3*q - 3*q**2 = 0?
-1, 2/7, 1
Factor -30*i**2 + 33/2*i**3 + 0 + 0*i - 3/4*i**4.
-3*i**2*(i - 20)*(i - 2)/4
Let o(q) = 60*q - 237. Let l be o(4). Suppose 0*p + 2/7*p**5 + 0 + 0*p**2 + 2/7*p**l - 4/7*p**4 = 0. What is p?
0, 1
Let j = -1578 - -1580. Factor -3/4*h**3 + 0 + 3/4*h**j + 0*h.
-3*h**2*(h - 1)/4
Let p(q) be the third derivative of -q**8/1176 + q**7/735 + q**6/420 - q**5/210 - q**2 - 32. Let p(h) = 0. Calculate h.
-1, 0, 1
Let d = 104/7 - 1559/105. Let h(z) be the third derivative of 4/3*z**3 + 13/30*z**5 + 0 - z**4 + d*z**7 + 0*z - 4*z**2 - 1/10*z**6. Factor h(k).
2*(k - 2)**2*(k - 1)**2
Suppose 3*t = 7*s - 1, -34*t - 4*s + 14 = -29*t. Factor 27/4*p - 9/4*p**t + 1/4*p**3 - 27/4.
(p - 3)**3/4
Let f(m) be the first derivative of m**3/3 + 7*m**2 - 58. Determine o so that f(o) = 0.
-14, 0
Let k(q) be the third derivative of q**6/240 + 11*q**5/60 + 25*q**4/16 + 9*q**3/2 + 2*q**2 + 7. Let k(a) = 0. Calculate a.
-18, -3, -1
Let m(a) be the third derivative of -a**8/90720 - 3*a**5/20 + 11*a**2. Let z(t) be the third derivative of m(t). Factor z(b).
-2*b**2/9
Let d(n) be the first derivative of -n**6/1080 - n**5/120 - 38*n**3/3 - 19. Let v(g) be the third derivative of d(g). Factor v(u).
-u*(u + 3)/3
Suppose 9*q - 25 = 4*q. What is c in c**4 + 15*c**3 - 20*c**5 + 8*c**4 - 8*c**2 + c + 4*c**q - c**4 = 0?
-1, 0, 1/4, 1
Suppose -20*y + 19*y + 54 = 0. Suppose y = 6*m + 36. Factor 0 - 1/3*g**4 - 1/3*g**m + 1/3*g**2 + 1/3*g**5 + 0*g.
g**2*(g - 1)**2*(g + 1)/3
Suppose a + 23 = 3*r, -a - 30 = -4*r - 0*a. Suppose m**5 + m**4 - m**2 + 6*m**3 - r*m**3 - 4*m**5 + 4*m**5 = 0. Calculate m.
-1, 0, 1
Let u be 190/(-600) - (1 - 0)/(-3). Let k(r) be the third derivative of 2*r**2 - 1/12*r**4 - u*r**5 + 0*r + 0 + 0*r**3. What is a in k(a) = 0?
-2, 0
Let o(v) be the third derivative of 0*v**4 + 1/40*v**6 - 24*v**2 + 0*v + 0*v**3 + 0*v**7 + 0 - 1/336*v**8 - 1/30*v**5. Factor o(w).
-w**2*(w - 1)**2*(w + 2)
Let p be (-16)/48 - (-22)/30. Suppose -p*j**2 - 2/5*j**4 + 0*j + 4/5*j**3 + 0 = 0. Calculate j.
0, 1
Factor -13*t**3 - 92*t + 5*t**4 - 40*t**4 - 54*t**2 + 34*t**4 - 56.
-(t + 2)**3*(t + 7)
Let v(h) = h**4 + h**2 + 1. Let u(n) = -9*n**4 + 4*n**3 + 5*n**2 - 5*n. Let o = 36 + -40. Let g(k) = o*u(k) - 4*v(k). What is l in g(l) = 0?
-1, 1/2
Suppose 9 + 3000*c**3 + 810*c + 2700*c**2 - 63 + 135 = 0. Calculate c.
-3/10
Factor 3/2*a**3 + 969/2*a + 105/2*a**2 + 867/2.
3*(a + 1)*(a + 17)**2/2
Let s = 9 - 6. Determine z, given that 3*z**2 + 3*z**s - 27 - z**4 - 4*z + 8 + 15 - z**3 = 0.
-1, 2
Let z be 20/520 - 2/52. Factor 0 + z*t - 2/9*t**2.
-2*t**2/9
Let r = 26 - 20. Factor r + 66*g**2 - 31*g**3 - 20*g - 4 - 41*g**3.
-2*(3*g - 1)**2*(4*g - 1)
Let d(k) be the third derivative of -k**5/105 - 8*k**4/21 + 24*k**3/7 - 117*k**2 - 2*k. Factor d(p).
-4*(p - 2)*(p + 18)/7
What is w in 2/3 - 1/3*w**2 + 1/3*w = 0?
-1, 2
Let h(b) = 16*b - 478. Let q be h(30). Let d(n) be the second derivative of -q*n**3 + 6*n**2 + 0 - 1/4*n**4 + 3/20*n**5 - 8*n. Factor d(g).
3*(g - 2)*(g - 1)*(g + 2)
Suppose 176 = 4*i - 0*i. Solve 6*v**2 - 15*v**2 - 242 + i*v + 7*v**2 = 0.
11
Let x = -6702 + 6704. Factor 3/2 - 2*f + 1/2*f**x.
(f - 3)*(f - 1)/2
Let h = 27 + -21. Let o(y) be the second derivative of 64*y**2 + 7*y + 4/15*y**h - 16/3*y**4 + 2/21*y**7 + 0 - 8/5*y**5 + 32/3*y**3. Factor o(l).
4*(l - 2)**2*(l + 2)**3
Let v(n) be the first derivative of 3/2*n**4 + 12 + 2/3*n**3 + 0*n + 0*n**2 + 1/3*n**6 + 6/5*n**5. Suppose v(h) = 0. Calculate h.
-1, 0
Suppose -10*y = -13*y + 60. Suppose 3*c + 5*h = -y, -2*c = -c - 5*h - 20. Factor c - 2/9*b**2 + 0*b.
-2*b**2/9
Let z(t) be the first derivative of -t**5 + 25*t**4/4 - 10*t**3 - 10*t**2 + 40*t - 237. Solve z(a) = 0.
-1, 2
Let i = 22 - 17. Suppose 0 = j - i*j + 8. Factor -j*g**2 + 5*g + 6*g - 2*g - g.
-2*g*(g - 4)
Let w = 1154/91 + -163/13. Determine l, given that -w*l**2 + 8/7*l - 16/7 = 0.
4
Let z(j) be the first derivative of -5*j**6/6 - 11*j**5 - 195*j**4/4 - 185*j**3/3 + 100*j**2 + 240*j + 216. Solve z(p) = 0.
-4, -3, -1, 1
Let t(n) be the first derivative of -26 + 3/25*n**5 + 3/10*n**2 + 0*n + 9/20*n**4 + 3/5*n**3. Factor t(a).
3*a*(a + 1)**3/5
Let y(c) be the first derivative of -15*c**4/4 + 37*c**3 - 66*c**2 + 36*c - 210. Factor y(j).
-3*(j - 6)*(j - 1)*(5*j - 2)
Let j(s) be the first derivative of 4*s**5/25 - 18*s**4/5 + 16*s**3 - 112*s**2/5 + 90. Factor j(h).
4*h*(h - 14)*(h - 2)**2/5
Let v(l) = -4*l**2 + l + 3. Let h = 36 - 33. Let b(o) = -44*o**2 + 12*o + 32. Let r(i) = h*b(i) - 32*v(i). Factor r(t).
-4*t*(t - 1)
Let -33*b - 27*b**2 + b**2 - 18 - 3*b**3 + 8*b**2 = 0. What is b?
-3, -2, -1
Let m(q) be the second derivative of 5*q + 5/2*q**2 - 1/60*q**4 - 1/25*q**5 + 0*q**3 + 0. Let l(v) be the first derivative of m(v). Factor l(b).
-2*b*(6*b + 1)/5
Let o be 1/4 - 27/108.