
-1, 1
Let c(i) = -55*i**3 - 280*i**2 + 1575*i - 1260. Let g(u) = -8*u**3 - 40*u**2 + 225*u - 180. Let v(k) = -3*c(k) + 20*g(k). Factor v(r).
5*(r - 3)*(r - 1)*(r + 12)
Find i such that -344/5*i - 86/5*i**2 - 192/5 - 3/5*i**3 = 0.
-24, -4, -2/3
Let w(n) be the second derivative of 7*n**4/12 - 5*n**3/6 - 5*n**2/2 - 16*n. Let z(g) = -3*g**2 + 2*g + 2. Let f(o) = -2*w(o) - 5*z(o). What is k in f(k) = 0?
0
Let w = -4150 + 4151. Suppose -w + 1/6*a**2 - 1/6*a = 0. What is a?
-2, 3
Let i(g) = -6*g**5 + 2*g**4 + 6*g**3 + 22*g**2 + 8. Let m(t) = 2*t**5 - t**4 - 2*t**3 - 8*t**2 - 3. Let d(k) = 3*i(k) + 8*m(k). Find v, given that d(v) = 0.
-1, 0, 1
Let t(f) be the first derivative of f**4/10 + 392*f**3/15 + 9604*f**2/5 - 244. Determine w, given that t(w) = 0.
-98, 0
Find p such that 2/9*p**2 + 4*p + 130/9 = 0.
-13, -5
Suppose 4*j = 7*j - 9. Let r(o) be the second derivative of 0*o**4 - 1/20*o**5 + 0*o**2 - 1/42*o**7 + 0*o**j + o + 1/15*o**6 + 0. Factor r(l).
-l**3*(l - 1)**2
Let k(p) = p**3 + 53*p**2 + 100*p - 100. Let q be k(-51). Let -7/3*w**4 - 1/3*w**5 - 3*w**q - 5*w**3 + 0*w + 0 = 0. Calculate w.
-3, -1, 0
Suppose -5*x + 5*b + 35 = 0, -5*b - 11 = -x - 2*b. Let 3/2*q**3 + 1/2*q**x + 3/2*q**4 + 0*q + 1/2*q**2 + 0 = 0. What is q?
-1, 0
Factor 28/3*j + 26/3 + 2/3*j**2.
2*(j + 1)*(j + 13)/3
Factor 5970*r**5 + 14*r**4 + 16*r + 36*r**3 - 5968*r**5 + 0*r**3 + 40*r**2.
2*r*(r + 1)*(r + 2)**3
Let q = 143 - 143. Let h(g) be the second derivative of 0*g**3 + 0 - 3*g + q*g**4 + 3/100*g**5 + 0*g**2 + 1/50*g**6. Let h(d) = 0. Calculate d.
-1, 0
Suppose -10*a + 7*a = 0. Let l(h) be the second derivative of 0*h**3 + 1/30*h**6 + a + 0*h**2 - 1/20*h**5 + 0*h**4 - 9*h. Suppose l(d) = 0. What is d?
0, 1
Let z(c) = -9*c**3 + 12*c**2 - 21*c - 12. Let m(k) = -16*k**3 + 23*k**2 - 41*k - 25. Let v(q) = -6*m(q) + 11*z(q). Factor v(a).
-3*(a - 2)*(a + 1)*(a + 3)
Let k(p) be the second derivative of -11*p**4/60 + p**3/6 + 3*p**2/5 + 101*p. Factor k(t).
-(t - 1)*(11*t + 6)/5
Let c(p) = p**2 + 6*p - 14. Let a be c(2). Let q = 6 - 2. Factor -5/2*u**2 - a + q*u + 1/2*u**3.
(u - 2)**2*(u - 1)/2
Let r(y) = 3*y**3 - 127*y**2 - 576*y - 586. Let v(o) = 3*o**3 - 123*o**2 - 576*o - 585. Let t(s) = -3*r(s) + 2*v(s). Factor t(c).
-3*(c - 49)*(c + 2)**2
Let c(q) be the third derivative of -q**5/360 + q**4/9 + 21*q**2 - 8*q. Determine f, given that c(f) = 0.
0, 16
Let n = 94225/129514 + -3/11774. Find s such that -14/11*s**4 - n*s**2 - 32/11*s**3 + 0*s + 0 = 0.
-2, -2/7, 0
Let i(a) be the third derivative of -a**5/510 - a**4/51 - a**3/17 - 38*a**2. Solve i(k) = 0 for k.
-3, -1
Determine r, given that 24/5*r**2 - 2/5*r**5 - 24/5*r**4 - 26/5*r + 0 + 28/5*r**3 = 0.
-13, -1, 0, 1
Let t = 5/2319 - -2309/4638. Suppose 0*w = -4*w. Determine f so that w*f - 1/2*f**3 + 0 + 1/2*f**5 + t*f**2 - 1/2*f**4 = 0.
-1, 0, 1
Let t = 2178/7 - 311. Factor 0 - 1/7*a**2 + t*a.
-a*(a - 1)/7
Find g such that -10 + 5*g**3 - 10*g**2 + 20*g**4 - 25*g + 5*g**5 + 22*g**3 - 7*g**3 = 0.
-2, -1, 1
Suppose -y + 24 = 2*f, 3*f = 3*y - 0*f - 27. Let -12*o**3 + 7*o**3 - 17*o - 8*o - 20*o**2 + 4 - y = 0. Calculate o.
-2, -1
Suppose 2*d + 151 = 3*v, -277 = 4*d - 0*d - v. Let q(l) = -3684*l**2 - 1178*l - 54. Let w(f) = 335*f**2 + 107*f + 5. Let b(z) = d*w(z) - 6*q(z). Factor b(j).
-4*(13*j + 2)**2
Factor -81/5*d + 3/5*d**3 - 36/5*d**2 - 42/5.
3*(d - 14)*(d + 1)**2/5
Let b(w) be the first derivative of 4*w**3/3 - 82*w**2 + 160*w - 426. Factor b(s).
4*(s - 40)*(s - 1)
Suppose -3*a - 2*s = -4, -4*a + 8 = -2*s + 6*s. Let n(x) be the second derivative of a*x**2 - 1/30*x**6 + 0*x**3 + 0 + x + 0*x**5 + 1/12*x**4. Solve n(w) = 0.
-1, 0, 1
Suppose 0 = -8*m + 16*m + 13 - 29. Factor l**3 + 7/2*l - l**4 + 1 + 4*l**m - 1/2*l**5.
-(l - 2)*(l + 1)**4/2
Let s = 58304/9 + -6476. What is u in -14/9*u - s - 2/9*u**2 = 0?
-5, -2
Suppose -43/4*u**2 + 9/2*u + 0 - 5/4*u**3 = 0. What is u?
-9, 0, 2/5
Find l, given that 53/3*l + 361/6*l**2 + 0 - 35/6*l**3 = 0.
-2/7, 0, 53/5
Let f(d) = -d**3 - 31*d**2 + 35*d - 39. Let m be f(-32). Let g be ((-6)/m - 0)*(40 - 5). Find v such that -2*v + 0 + 2/9*v**4 + 10/3*v**2 - g*v**3 = 0.
0, 1, 3
Let m(k) be the first derivative of k**3/9 - 146*k**2/3 + 21316*k/3 - 210. Factor m(h).
(h - 146)**2/3
Suppose -a + 100 = 97. Let s(c) be the third derivative of -3*c**2 + 0*c + 0 + 1/360*c**6 - 1/72*c**4 - 1/180*c**5 + 1/18*c**a. Factor s(w).
(w - 1)**2*(w + 1)/3
Let l(z) be the first derivative of -1/12*z**3 + 0*z + 0*z**2 + 1 - 1/16*z**4. Factor l(d).
-d**2*(d + 1)/4
Let s be -2 + ((-18)/216 - 25/(-12)). Let a(x) be the second derivative of 0 + 2/21*x**7 - 5*x + 0*x**2 + s*x**4 + 0*x**3 + 1/5*x**5 + 4/15*x**6. Factor a(u).
4*u**3*(u + 1)**2
Suppose o = 4*g - 2*o - 255, 192 = 3*g - 3*o. Factor 36*w**2 - 21*w**4 - 12*w + 29 + 34 + 27*w**3 - g.
-3*w*(w - 2)*(w + 1)*(7*w - 2)
Suppose -3*r - 116 = -101. Let b be 4/r - (6 + -8). Factor -b*l + 0*l**2 + 4/5 + 2/5*l**3.
2*(l - 1)**2*(l + 2)/5
Let u = -115 + 137. Let t be 2/3*6/u. Determine f so that t*f**2 - 2/11*f**3 + 0 + 0*f = 0.
0, 1
Factor 9 + 5*j + 1/4*j**2.
(j + 2)*(j + 18)/4
Factor 21780 + 239*q**2 + 4420*q + 5*q**3 + 118*q**2 - 77*q**2 - 8260.
5*(q + 4)*(q + 26)**2
Let h(d) be the second derivative of -1/3*d**4 + 0 + 0*d**2 + 1/3*d**3 + 13*d + 1/10*d**5. Suppose h(y) = 0. What is y?
0, 1
Let h(b) be the first derivative of b**6/90 - b**4/18 + b**2/6 + 9*b - 9. Let m(v) be the first derivative of h(v). Factor m(g).
(g - 1)**2*(g + 1)**2/3
Let s = 1819/2280 - -1/456. Let f(c) be the first derivative of -1/2*c**4 - s*c**3 - 3/5*c**2 - 3/25*c**5 - 1/5*c - 5. Let f(t) = 0. What is t?
-1, -1/3
Suppose 2*k - 4*k = -10. Factor 2*q**2 + 20*q - 2*q**2 + 0*q**2 - k*q**2 - 15.
-5*(q - 3)*(q - 1)
Let k(i) be the first derivative of -7*i**6/120 - i**5/5 - i**4/12 - 8*i + 15. Let a(x) be the first derivative of k(x). Factor a(j).
-j**2*(j + 2)*(7*j + 2)/4
What is k in 6*k**2 - 5*k**2 - 11*k**2 + 0*k**2 + 15*k**3 - 5*k**4 = 0?
0, 1, 2
Let s(k) be the third derivative of -k**7/189 + 7*k**6/270 - 4*k**5/135 - 170*k**2 - 1. Factor s(o).
-2*o**2*(o - 2)*(5*o - 4)/9
Suppose 2*v = 4*g + 22, 4*v - 4*g - 20 = 12. Let y = v - 4. Let 6 + y - 3*z**2 + 3 + 3*z - 4 = 0. Calculate z.
-1, 2
Determine y, given that 3/4*y**5 + 0 + 0*y + 21/2*y**4 + 0*y**3 + 0*y**2 = 0.
-14, 0
Suppose -h = 5*c - 15 - 28, 0 = -c - h + 7. Suppose -9 = 6*w - 3*w - 3*o, 3*o - c = 4*w. Suppose w + 2/11*k + 2/11*k**2 = 0. Calculate k.
-1, 0
Let h(y) be the third derivative of 0 + 1/200*y**6 + 0*y - 8*y**2 - 1/40*y**4 + 0*y**3 - 1/350*y**7 + 1/100*y**5. Determine u, given that h(u) = 0.
-1, 0, 1
Let y(i) be the third derivative of i**5/180 - i**4/12 - 8*i**3/9 - 644*i**2. Factor y(b).
(b - 8)*(b + 2)/3
Let g be ((-5)/1)/20*0. Let l(i) be the second derivative of 1/10*i**5 + 3*i**2 + g + 5/6*i**4 + 7/3*i**3 + 5*i. Determine b so that l(b) = 0.
-3, -1
What is b in 11 - 4*b**4 + 29*b**2 + b**3 - b**4 - b**5 + 12*b + 0*b**4 - 47 = 0?
-3, -2, 1, 2
Suppose -7*b = -3*b + 4*i - 8, -3*i = -2*b + 4. Let o = 1 + b. Find a, given that -2*a**3 + 0*a**3 + 7*a - 6*a - 4*a**2 - o*a = 0.
-1, 0
Suppose -799*h + 19*h**3 + 227*h - 73*h**2 + 27*h**2 - 20*h**3 - 968 = 0. Calculate h.
-22, -2
Let v(t) be the third derivative of -1/6*t**3 - 1/60*t**5 + 0*t - 1/9*t**4 + 0 + 30*t**2 + 1/180*t**6. Solve v(m) = 0 for m.
-1, -1/2, 3
Suppose -3*j + 1496*v - 1499*v + 12 = 0, -3*j = 2*v - 11. Factor 3/5*y**j - 12/5 - 18/5*y**2 + 27/5*y.
3*(y - 4)*(y - 1)**2/5
Let y(r) be the second derivative of r**4/60 - 11*r**3/10 - 17*r**2/5 - 3*r - 16. Solve y(z) = 0.
-1, 34
Let p(b) be the third derivative of b**6/780 - b**5/78 + b**4/26 + b**2 - 9*b. Solve p(s) = 0 for s.
0, 2, 3
Suppose -2*a + 5*y = -167, 0*a + 2*y + 278 = 3*a. Let d = a - 93. Find v, given that 0*v + 0*v**2 - 3/4*v**d + 0 = 0.
0
Factor -1/4*q - 25/2*q**2 + 1/4*q**3 + 25/2.
(q - 50)*(q - 1)*(q + 1)/4
Suppose 3*a = -5*j + 23, 3*j - 3 = -4*a + 2. Factor -j*m**3 - 3*m**5 - 4*m**5 + 11*m**4 + 2*m**5 + 2*m**2 - m**2.
-m**2*(m - 1)**2*(5*m - 1)
Let b = -119 + 119. Let x(w) be the first derivative of 2/21*w**3 - 2/35*w**5 + b*w + 0*w**4 + 0*w**2 - 2. Factor x(r).
-2*r**2*(r - 1)*(r + 1)/7
Let a be (-12)/20 + (-72)/(-20). Factor 288*n + a - 290*n - 2*n**2 + 1.
-2*(n - 1)*(n + 2)
Suppose 68*w = 4*y + 67*w + 4, -4