3*l + 1)
Let u(r) = -3*r**2 - 1. Let w(s) = 20*s**3 + 120*s**2 + 76*s + 40. Let c(j) = 16*u(j) + w(j). Factor c(q).
4*(q + 1)*(q + 2)*(5*q + 3)
Let g(o) be the first derivative of -2*o**3/21 + 32*o**2/7 - 512*o/7 + 95. Factor g(t).
-2*(t - 16)**2/7
Suppose 0 = -6*a + 79 + 245. Factor -180 + 163*w**2 - 6*w - 168*w**2 - a*w.
-5*(w + 6)**2
Factor 0*l**3 - 18*l**2 + 10*l**2 + 11*l**2 - 3*l**3 + 12*l - 12.
-3*(l - 2)*(l - 1)*(l + 2)
Determine c, given that 1/7*c**2 + 225/7 + 30/7*c = 0.
-15
Factor -11514*b**3 + 54*b**5 + 48*b**5 - 37635*b + 53*b**5 + 36858*b**2 - 206*b**5 + 48*b**5 - 381*b**4 + 12675.
-3*(b - 1)**3*(b + 65)**2
Factor -2178/7*g - 2/21*g**3 + 66/7*g**2 + 23958/7.
-2*(g - 33)**3/21
Let v = 46 - 64. Let m be ((-1)/(-6))/((84/v)/(-7)). Let m*z - 1/4*z**4 - 1/4*z**3 + 0 + 1/4*z**2 = 0. What is z?
-1, 0, 1
Let k(n) be the first derivative of -n**3 + 57*n**2/2 - 102*n + 116. Solve k(z) = 0.
2, 17
Let y(q) be the third derivative of -q**7/490 + 3*q**6/280 - q**5/70 + 53*q**2. Solve y(x) = 0.
0, 1, 2
Let y(f) = -13*f**3 + 42*f**2 - 77*f + 41. Let m(s) = -9*s**3 - 24*s + 29 - 2 - 27*s + 28*s**2. Let t(r) = 7*m(r) - 5*y(r). Factor t(g).
2*(g - 4)*(g - 2)*(g - 1)
Let u be -1 + -3 + 5 - (0 - 1). Let m be 0 + ((-2)/u - 7/(-4)). Factor -3/8*r**3 + 9/8*r + m + 0*r**2.
-3*(r - 2)*(r + 1)**2/8
Let g(x) be the first derivative of -4*x**5/5 + 2*x**4 + 4*x**3/3 - 4*x**2 - 62. Let g(y) = 0. Calculate y.
-1, 0, 1, 2
Suppose 2*r = -5*m + 17, -5*r = -4*m + 2 + 5. Suppose 0 = 2*a - m*a + 4. Find k such that -6 + 4*k - 2 - 2*k**2 - 8*k - a*k = 0.
-2
Let m = -45 + 31. Let u = 18 + m. Factor 6*l**3 - 4*l**2 - l**4 - 7*l**u + 6*l**4.
-2*l**2*(l - 2)*(l - 1)
Find v, given that 0*v**2 + 2/9*v**3 + 0*v + 0 = 0.
0
Find k such that -12/11 + 2*k - 8/11*k**2 - 2/11*k**3 = 0.
-6, 1
Let i(f) be the first derivative of 2*f**3/39 - 9*f**2/13 - 20*f/13 + 114. Factor i(p).
2*(p - 10)*(p + 1)/13
Suppose r - 9 = -0*t + t, -2*r + t + 14 = 0. Let z(u) = -6*u**3 - 6*u**2 + u - 4. Let l(o) = -7*o**3 - 7*o**2 + o - 5. Let d(w) = r*l(w) - 6*z(w). Factor d(f).
(f - 1)*(f + 1)**2
Let a(i) be the second derivative of -i**4/3 - 152*i**3 - 349*i. Factor a(x).
-4*x*(x + 228)
Factor -1176*d - 15*d**4 - 4116/5 - 3/5*d**5 - 141*d**3 - 609*d**2.
-3*(d + 2)**2*(d + 7)**3/5
Suppose -4*l + 3*q = -17, q = 2*l + 4*q + 5. Let y be l/56 + (-27)/(-108). Factor -y*h + 0 + 1/7*h**2.
h*(h - 2)/7
Let k(r) be the first derivative of -324*r**5/5 - 531*r**4 + 992*r**3/3 - 56*r**2 - 262. Solve k(f) = 0 for f.
-7, 0, 2/9
Suppose z - 2 - 3 = 0. Let n = z + -3. Suppose 3*h - 9*h**3 - 6*h**4 + 4*h**n - 4*h**2 = 0. What is h?
-1, 0, 1/2
Solve -1/2*z**2 - 20 + 11*z = 0 for z.
2, 20
What is l in -l**2 + 1718 + 14*l - 11*l**2 - 1598 + 0*l**3 - 2*l**3 = 0?
-5, -4, 3
Suppose -24*x**3 + 8*x**4 - 80 - 76*x - 55*x**2 - 25*x**2 + 4*x**5 + 56 = 0. Calculate x.
-2, -1, 3
Let g be (-10 - 890/(-90))*6/(-10). Let x(w) be the second derivative of -5*w + 2/5*w**2 + 1/50*w**5 - 1/15*w**3 - g*w**4 + 0. Factor x(h).
2*(h - 2)*(h - 1)*(h + 1)/5
Let f = -792 + 792. Let c(z) be the second derivative of 10/9*z**3 - 5/9*z**4 + 1/12*z**5 - 11*z + 0*z**2 + f. Let c(t) = 0. What is t?
0, 2
Suppose d - 30 = 5*r - 7, -41 = -4*d + 3*r. Factor -6*c - d*c**2 - 4*c**5 - 20*c**2 - 36*c**3 - 20*c**4 - 2*c.
-4*c*(c + 1)**3*(c + 2)
Let l(s) be the third derivative of -s**7/630 - s**6/90 + s**5/10 - 11*s**4/6 + 13*s**2 - 3*s. Let g(o) be the second derivative of l(o). Factor g(p).
-4*(p - 1)*(p + 3)
Suppose -5*y + x = -y - 8, -5*x = y - 23. Let z(i) = -12*i**2 + 2*i. Let s be z(0). Factor 1/4*p**y + 1/4*p + 1/2*p**2 + s.
p*(p + 1)**2/4
Let z = 12 + -9. Let t be z/((-6)/4) - 0. Let k(c) = -6*c. Let m(g) = g**2 + 7*g + 1. Let f(o) = t*m(o) - 3*k(o). Factor f(s).
-2*(s - 1)**2
Suppose -8*q + 16*q + 9*q = 3*q. Find c, given that -10/3*c - 2/3*c**3 - 4*c**2 + q = 0.
-5, -1, 0
Let l(q) = -q**2 - 5*q + 17. Let d(b) = 2*b**2 + 9*b - 33. Let i(t) = -3*d(t) - 7*l(t). Suppose i(m) = 0. Calculate m.
-10, 2
Let d(p) be the third derivative of -6*p**2 + 0*p - 5/8*p**4 - 1/840*p**7 + 0 - 3/2*p**3 - 1/48*p**6 - 37/240*p**5. Factor d(i).
-(i + 2)**2*(i + 3)**2/4
Let j(x) = x**3 - x. Let f(s) = -s**3 - 5*s. Let z = -7 + 10. Let o(n) = z*j(n) + f(n). Factor o(c).
2*c*(c - 2)*(c + 2)
Let d(r) be the second derivative of r**4/54 + 2*r**3/27 + r**2/9 - r + 8. Factor d(i).
2*(i + 1)**2/9
Let a(o) = o**2 - 4*o. Let x be (1 - 1)*(-3)/9*-3. Let v be a(x). Determine d so that 1/8*d**2 - 1/4*d**5 + 0 + 5/8*d**4 - 1/2*d**3 + v*d = 0.
0, 1/2, 1
Let q(v) = 27*v**3 + 35*v**2 - 51*v - 11. Let z(g) = 176*g**3 + 228*g**2 - 332*g - 72. Let p(l) = 32*q(l) - 5*z(l). Factor p(a).
-4*(a - 1)*(a + 2)*(4*a + 1)
Suppose -212*v - 5*v**2 + 8374 + 9*v**2 - 2756 - 2*v**2 + 0*v**2 = 0. What is v?
53
Let j(i) = -i**3 - 13*i**2 + 69*i + 21. Let n be j(-17). Factor 0*t + 0*t**2 + 0 - 1/4*t**n + 1/2*t**3.
-t**3*(t - 2)/4
Let z(d) be the third derivative of d**6/40 + d**5/8 - d**4/4 - 3*d**3/4 + 2*d**2 - 52*d. Factor z(j).
3*(j - 1)*(j + 3)*(2*j + 1)/2
Factor -2/7*v**4 - 256/7*v**3 - 262144/7*v - 12288/7*v**2 - 2097152/7.
-2*(v + 32)**4/7
Factor -29*f**2 - 48*f**2 + 77*f**2 - 34*f**5 + 4*f**4.
-2*f**4*(17*f - 2)
Suppose -15*v = -29*v + 70. Let f(g) be the first derivative of -2/7*g**2 + 2/21*g**3 + v + 2/7*g. Factor f(s).
2*(s - 1)**2/7
Let w(q) be the first derivative of 0*q - 4/15*q**3 + 0*q**2 - 12/25*q**5 + 2/15*q**6 + 3/5*q**4 - 10. Find s, given that w(s) = 0.
0, 1
Let u(s) = 8*s**2 + 5*s + 7. Let q(d) = -7*d**2 - 4*d - 6. Let i(b) = -7*q(b) - 6*u(b). Find r such that i(r) = 0.
0, 2
Let u(r) be the second derivative of r**6/75 - r**5/50 - 7*r**4/30 + r**3/15 + 6*r**2/5 + 19*r. Find k such that u(k) = 0.
-2, -1, 1, 3
Suppose -2*o + 8 = 4*v, -3*v = 4*o - v - 28. Determine z, given that 8 - 8*z - o*z - 8 - 4*z**2 = 0.
-4, 0
Let m(n) be the third derivative of -n**8/33600 + n**6/3600 + n**4/4 + 2*n**2. Let h(j) be the second derivative of m(j). Factor h(f).
-f*(f - 1)*(f + 1)/5
Let v(w) = 0 + 9 + 4*w**2 + 19*w - 51*w - 6. Let u be v(8). Factor 3*m**5 - 3/2*m**2 - 15/2*m**4 + 0*m + 6*m**u + 0.
3*m**2*(m - 1)**2*(2*m - 1)/2
Factor -1/3*r**2 + 0 + 17/3*r.
-r*(r - 17)/3
Find v such that -84*v**2 - 14 + 3 + 22 - 4*v**3 + 6*v**4 + 21 - 8*v + 12*v**5 + 46*v**4 = 0.
-4, -1, 2/3, 1
Let y(j) = 2*j + 43. Let o be y(-21). Let m be (3*o/(-8))/(30/(-40)). Factor b + 1/2 + m*b**2.
(b + 1)**2/2
Let g be 4 - 1/((-65)/(-250)). Let h(t) be the first derivative of 2/39*t**3 - 3 + 1/26*t**4 - 1/13*t**2 - g*t. Let h(k) = 0. What is k?
-1, 1
Factor h**2 + 45 - 20*h**2 + 43*h**2 - 3*h**3 - 93*h + 27*h**2.
-3*(h - 15)*(h - 1)**2
Solve -3*n**2 + 0*n + 1/4*n**4 + 0 + 2*n**3 - 1/4*n**5 = 0 for n.
-3, 0, 2
Let a(j) = j**2 - 4*j + 9. Let s be a(4). What is y in 12*y**5 + 31*y**3 + s*y**2 - 9*y**4 + 0 - 46*y**3 + 3*y + 0 = 0?
-1, -1/4, 0, 1
Let h(k) be the third derivative of -1/56*k**8 + 0 + 0*k**3 + 1/15*k**7 + 0*k - 2/9*k**5 + 2/9*k**4 + 1/90*k**6 + 12*k**2. Let h(o) = 0. What is o?
-1, 0, 2/3, 2
Factor 2210 + 104*h + 33*h**2 + 11*h**2 - 2146 + 4*h**3.
4*(h + 1)*(h + 2)*(h + 8)
Let o be 115/(-115)*(5/(-25) + 1/5). Factor -t**2 + 0 - 2/3*t + 1/3*t**4 + o*t**3.
t*(t - 2)*(t + 1)**2/3
Let l be 6/226*22/33. Let i = l - -107/339. Find s, given that 0*s**2 - 1/3*s**3 + 0 + i*s = 0.
-1, 0, 1
Let x(i) = 2*i**3 - i**2 - i. Let f(o) = -o**3 + 2*o**2 - 25*o. Let u(k) = f(k) + 2*x(k). Factor u(g).
3*g*(g - 3)*(g + 3)
Let g(h) be the third derivative of -5*h**6/36 - 47*h**5/9 - 91*h**4/9 - 8*h**3 + 22*h**2. What is p in g(p) = 0?
-18, -2/5
Factor -98 + 1/2*a**2 + 195/2*a.
(a - 1)*(a + 196)/2
Let q(u) be the second derivative of u**5/4 - 20*u**4/3 + 105*u**3/2 - 4*u + 136. Let q(j) = 0. Calculate j.
0, 7, 9
Let j(i) = -i**2 + 7*i - 9. Let h be j(4). Factor -285 - 89 + 36*y + 30*y - h*y**2 + 11.
-3*(y - 11)**2
Let d(z) = -7*z**3 - 374*z**2 - 4832*z - 1360. Let b(u) = -7*u**3 - 372*u**2 - 4833*u - 1358. Let y(v) = -4*b(v) + 3*d(v). Factor y(r).
(r + 26)**2*(7*r + 2)
Factor n**2 + 2*n**2 + 45*n + 89*n + 11907 + 4*n + 240*n.
3*(n + 63)**2
Let o(x) be the first derivative of 2*x**3/39 - 8*x/13 - 171. Factor o(i).
2*(i - 2)*(i + 2)/13
Factor 9*x + 12 - 3/2*x**3 - 9/2*x**2.
-3*(x - 2)*(x + 1)*(x + 4)/2
Let p(x) be the first derivative of -1371