
Let i(m) be the first derivative of m**5/10 - 7*m**4/8 - 17*m**3/6 - 9*m**2/4 + 182. Let i(q) = 0. Calculate q.
-1, 0, 9
Let z be ((306/(-117) - -12) + -11)*(-4)/14. Factor 0*l - z*l**3 + 2/13*l**5 + 0*l**4 - 4/13*l**2 + 0.
2*l**2*(l - 2)*(l + 1)**2/13
Let f(z) be the first derivative of 26 - 35/3*z**3 + 0*z + z**5 + 15*z**2 + 0*z**4. Factor f(u).
5*u*(u - 2)*(u - 1)*(u + 3)
Let u(d) be the third derivative of -1/70*d**5 + 0*d + 0 + 1/420*d**6 + 1/28*d**4 + 39*d**2 - 1/21*d**3. Factor u(f).
2*(f - 1)**3/7
Suppose -784 - 301 = 5*o. Let d = o + 1092/5. Suppose 0 + 4/5*s + s**4 - 8/5*s**2 - d*s**3 = 0. What is s?
-1, 0, 2/5, 2
Suppose 6 = -3*x, -j + 6*x - 7*x = 0. Let o(f) be the second derivative of -j*f + 0 + 1/36*f**3 - 1/72*f**4 + 0*f**2. What is w in o(w) = 0?
0, 1
Let a be (-8)/14 + (-1352)/(-504) - (-10)/(-90). Solve 4/5*z**5 + 0*z**a + 0 + 0*z**4 + 0*z - 4/5*z**3 = 0.
-1, 0, 1
Factor -45*f + 6*f**2 + 54 + 3*f**3 - 8*f**2 - 2*f**2 - 8*f**2 + 0*f**2.
3*(f - 6)*(f - 1)*(f + 3)
Let r be 1098/(-54) + 19 + (-26)/(-6). Let j(s) be the first derivative of 0*s - 7 - 3/4*s**2 - 1/6*s**r. Determine x, given that j(x) = 0.
-3, 0
Suppose b - 5*b = -36. Factor -b*m**3 + 36*m - 3*m**4 + 17 + 6 + 1 + 6*m**2.
-3*(m - 2)*(m + 1)*(m + 2)**2
Let s be (-349)/(-4) - 1*(-6)/8. Let l = 92 - s. Factor -1/5 - 2/5*v**3 + 1/5*v**l + 0*v**2 + 2/5*v.
(v - 1)**3*(v + 1)/5
Let w(h) be the first derivative of -h**6/120 - 13*h**3/3 - 21. Let s(f) be the third derivative of w(f). Determine u so that s(u) = 0.
0
Suppose 13/6*r**2 + 8/3*r**3 - 8/3*r - 2/3 - 3/2*r**4 = 0. Calculate r.
-1, -2/9, 1, 2
Suppose 47*d - 49*d - 136 = 0. Let n be (-8)/(-10) - d/(-170). Factor -4/5*q**2 + 6/5*q**4 - n + 4/5*q**3 - 6/5*q + 2/5*q**5.
2*(q - 1)*(q + 1)**4/5
Suppose 4*f + 0 = 12. Factor -16 + b**2 + 13*b**f - 17*b**3 - 2*b**2 + 28*b - 7*b**2.
-4*(b - 1)**2*(b + 4)
Let n(a) = a + 3. Let c be n(-3). Let x = 11932 + -59658/5. Let c + 0*k + x*k**3 - 2/5*k**2 = 0. What is k?
0, 1
Let m(a) be the first derivative of 0*a**4 + 0*a + 3/4*a**2 + 3/4*a**3 - 3/20*a**5 - 21. Factor m(i).
-3*i*(i - 2)*(i + 1)**2/4
Let -5*j**2 - 34/3*j + 0 + 1/3*j**3 = 0. What is j?
-2, 0, 17
Let b(o) be the second derivative of -o**8/4480 - o**7/240 - o**6/80 + 5*o**4/4 - 7*o. Let w(f) be the third derivative of b(f). Factor w(q).
-3*q*(q + 1)*(q + 6)/2
Let o(p) be the second derivative of p**7/42 + 4*p**6/15 + 9*p**5/10 + 4*p**4/3 + 5*p**3/6 + 4*p - 11. Suppose o(t) = 0. What is t?
-5, -1, 0
Let 2*w + 2*w**2 + 2/3 + 2/3*w**3 = 0. Calculate w.
-1
Let a(f) = -4*f**3 + 14*f**2 + 25*f - 29. Let m(k) = -17*k**3 + 59*k**2 + 99*k - 115. Let c(b) = -26*a(b) + 6*m(b). Suppose c(s) = 0. Calculate s.
-4, 1, 8
Factor 21*c + 20*c + 220 + 11*c - 4*c**2 - 76*c.
-4*(c - 5)*(c + 11)
Suppose 0*q + 4*f - 1656 = -4*q, -2*q + 4*f = -822. Find k, given that 24*k**3 + 0*k + 0*k + 401*k**4 - q*k**4 + 2*k**5 - 16*k**2 = 0.
0, 2
Let m be ((-4)/12*-9)/(-1). Let n be 16/6 + m*4/6. Find z, given that -n - 2/3*z**2 - z**3 + 7/3*z = 0.
-2, 1/3, 1
Find p such that -10/3*p**3 + 10/3*p + 0*p**2 + p**4 - 1 = 0.
-1, 1/3, 1, 3
Let v(g) = g - 3. Let i be v(8). Suppose -5*h = i - 15. Determine y, given that -h*y**2 - 6*y**3 + 2*y**4 + 7*y**3 - 2*y + y = 0.
-1, -1/2, 0, 1
Factor -520 - 11360*c**3 + 11355*c**3 + 500*c - 18*c**2 - 92*c**2.
-5*(c - 2)**2*(c + 26)
Let z(b) be the second derivative of b**5/330 + b**4/44 + 2*b**3/33 + 9*b**2 - 10*b. Let g(i) be the first derivative of z(i). Factor g(x).
2*(x + 1)*(x + 2)/11
Factor -149*q - 225 - q**3 + 10*q**2 - 46*q + 19*q**2 + 0*q**2.
-(q - 15)**2*(q + 1)
Let i(n) = 8*n**4 + 22*n**3 - 71*n**2 + 23*n + 103. Let m(o) = 3*o**4 + 11*o**3 - 35*o**2 + 11*o + 52. Let k(g) = -2*i(g) + 5*m(g). Factor k(w).
-(w - 6)*(w - 3)**2*(w + 1)
Let t(b) = -10*b**3 - 321*b**2 - 2442*b + 1024. Let q(f) = -5*f**3 - 161*f**2 - 1222*f + 512. Let k(o) = -5*q(o) + 3*t(o). Let k(a) = 0. What is a?
-16, 2/5
Let f(i) = -24*i**4 + 8*i**3 + 36*i**2 - 72*i. Let h(o) = -o**4 + o**2 - 2*o. Let l(d) = -f(d) + 20*h(d). Let l(u) = 0. Calculate u.
-2, 0, 2
Let z(g) be the third derivative of g**6/480 + g**5/80 + g**4/48 + 83*g**2. Determine b so that z(b) = 0.
-2, -1, 0
Let b(w) = -2*w**3 + 7*w**2 - 7*w - 16. Let v(i) = i**3 - 3*i**2 + 3*i + 7. Let u(a) = -4*b(a) - 9*v(a). Factor u(r).
-(r - 1)*(r + 1)**2
Let h = 52323/61019 + -3/8717. Factor -2/7*m**3 + 2/7*m + 4/7 + 2/7*m**4 - h*m**2.
2*(m - 2)*(m - 1)*(m + 1)**2/7
Let c be ((8/(-32))/(9/8))/((-32)/18816). Let -c - 164/3*q**3 + 4*q**4 + 524/3*q**2 + 308/3*q = 0. What is q?
-1, 2/3, 7
Let i(x) be the third derivative of x**6/540 + 8*x**5/135 + 41*x**4/108 + 26*x**3/27 - x**2 - 38*x. Determine p so that i(p) = 0.
-13, -2, -1
Let d(i) = 5*i**2 - 20*i - 23. Let n(u) = 1. Let s(p) = -d(p) + 2*n(p). What is t in s(t) = 0?
-1, 5
Let s(n) be the first derivative of -2*n**3/33 + 2*n**2/11 + 30*n/11 + 36. Factor s(j).
-2*(j - 5)*(j + 3)/11
Let -1/10*m**3 + 1/5*m**2 + 0 - 1/10*m = 0. Calculate m.
0, 1
Let h(s) = 237*s**2 - 261*s + 24. Let i(d) = -592*d**2 + 652*d - 60. Let f(w) = -12*h(w) - 5*i(w). Factor f(a).
4*(a - 1)*(29*a - 3)
Suppose -2*u - 5*h + 1 = 5, -5*h - 10 = 0. Factor -40 + u*c + 0*c**2 - 5*c**2 - 33*c.
-5*(c + 2)*(c + 4)
Let c(a) be the second derivative of -a**5/12 + 25*a**4/12 - 125*a**3/6 - 8*a**2 - 22*a. Let u(l) be the first derivative of c(l). Solve u(b) = 0.
5
Let i(j) = -j**3 + j**2 - 2*j + 2. Let h be i(0). Let c(d) be the first derivative of -2 - 1/2*d**4 + 0*d + 0*d**3 + d**h. Factor c(b).
-2*b*(b - 1)*(b + 1)
Let o be ((-110)/495)/(2 - (-19)/(-9)). Let n(m) be the first derivative of 2/3*m**3 + 0*m + 5 - 2*m**o. Factor n(r).
2*r*(r - 2)
Let l(h) be the second derivative of h**5/30 - 2*h**4 + 47*h + 1. Suppose l(m) = 0. What is m?
0, 36
Let o(m) = m**2 + 5*m + 6. Let r be 0 + -6 + 3 + -1. Let z be o(r). Factor -4 + s**3 - 4*s**2 + 0*s**2 + 8*s - s**z.
(s - 2)**2*(s - 1)
Suppose -2*v + 3*a + 4 = 0, 32*v - 34*v + 2*a = -4. Let c(d) be the third derivative of -1/2*d**4 + 1/20*d**5 + 0 + 3/2*d**3 + v*d**2 + 0*d. Factor c(u).
3*(u - 3)*(u - 1)
Factor 2*n**4 + 3*n**4 - n + 0*n + 25*n**3 + 21*n + 40*n**2.
5*n*(n + 1)*(n + 2)**2
Let u = -1061 + 1061. Let z(j) be the second derivative of 1/105*j**6 - 1/42*j**4 + 0*j**2 + 2/21*j**3 + u - 1/35*j**5 + 2*j. Factor z(t).
2*t*(t - 2)*(t - 1)*(t + 1)/7
Suppose y - 2*y = 10. Let g(q) = -q - 4. Let h be g(y). Factor -j**2 - h - 4 - 3*j**2 + 15*j - j**2.
-5*(j - 2)*(j - 1)
Suppose a - 44 = -a. Determine y, given that y - 22 + a + 4*y**2 - 3*y**2 = 0.
-1, 0
Factor -55/3*d - 2/3*d**2 + 1/3*d**3 + 200/3.
(d - 5)**2*(d + 8)/3
Suppose 18*z - 48*z + 90 = 0. Let a(v) be the first derivative of 2*v**z + 7 - 3*v + 1/2*v**6 - 3/5*v**5 + 3/2*v**2 - 3/2*v**4. Suppose a(b) = 0. What is b?
-1, 1
Suppose -l = 4*x - 2, 10 = l + 15*x - 19*x. Let w(t) be the third derivative of 0*t + 0*t**3 - 1/4*t**4 + l*t**2 + 0 - 1/20*t**5. Factor w(q).
-3*q*(q + 2)
Suppose -2*x + 2 = 3*o - 7*o, 4*o - 18 = -2*x. What is m in 13*m - 12 + 4*m**4 + 11*m**5 - 24*m**3 + 7*m + 8*m**o - 7*m**5 = 0?
-3, -1, 1
Let y = 270 + -265. Suppose y*k - 8 = -2*h, -5*k + h + 15 = 4. Determine s so that 0*s + 4/9*s**3 + 0*s**k - 2/9*s**4 + 0 = 0.
0, 2
Let k(i) be the third derivative of -i**5/540 - i**4/216 + 2*i**3/9 + 85*i**2 - 2*i. Factor k(p).
-(p - 3)*(p + 4)/9
Let s be -4 - (-25)/5 - (-357)/(-360). Let t(o) be the third derivative of 4*o**2 + 1/8*o**4 + 0*o**5 + 1/3*o**3 + 0*o + 0 - s*o**6. Factor t(p).
-(p - 2)*(p + 1)**2
Suppose 0 = r - 5*f - 16 - 3, -3*r = 2*f - 6. Factor 2/13*b**5 + 2/13*b + 0*b**2 + 0 - 4/13*b**3 + 0*b**r.
2*b*(b - 1)**2*(b + 1)**2/13
Suppose 0*w**2 - 2*w**2 - 27*w - 18*w - 241 + 317 + 11*w = 0. Calculate w.
-19, 2
Let d(g) be the first derivative of g**4/4 - g**3 + 7*g**2 + 25*g + 17. Let s(p) = 3*p**2 - 15*p - 24. Let j(q) = -6*d(q) - 7*s(q). Factor j(o).
-3*(o - 2)*(o + 1)*(2*o + 3)
Let g(v) be the second derivative of -10*v - 1/12*v**4 + 1/12*v**6 + 0*v**2 + 0 + 7/40*v**5 + 0*v**3 - 1/21*v**7. Solve g(b) = 0.
-1, 0, 1/4, 2
Solve -2/11*y**3 + 192/11 + 58/11*y**2 - 248/11*y = 0.
1, 4, 24
Let x = -3117 + 3119. Factor 1/5*y**4 + 1/5*y**x + 3/5*y - 2/5 - 3/5*y**3.
(y - 2)*(y - 1)**2*(y + 1)/5
Let v(o) be the first derivative of -o**6/12 + 2*o**5 - 145*o**4/8 + 75*o**3 - 1