1, 2
Let h(g) = 3*g**2 - 5*g + 2. Let q = -20 + 39. Let a(o) = 0 - 9 + 2*o + q*o - 37*o**2 + 24*o**2. Let f(p) = 4*a(p) + 18*h(p). Factor f(k).
2*k*(k - 3)
Factor 15/2*o**2 + 81/4*o + 3/4*o**3 + 27/2.
3*(o + 1)*(o + 3)*(o + 6)/4
Let j(x) = -2*x**3 - 10*x**2 + 3*x + 17. Let c be j(-5). Let l(o) be the first derivative of 7 - 4/3*o**3 - 8*o**c - 16*o. Find g such that l(g) = 0.
-2
Let u = -24 + 24. Factor 4*j + u*j + 30*j - 2*j - 16 - 20*j**2 + 4*j**3.
4*(j - 2)**2*(j - 1)
Let w(u) be the third derivative of -u**6/420 - 24*u**5/35 - 1775*u**4/28 - 10082*u**3/21 + 171*u**2 - u. Determine r, given that w(r) = 0.
-71, -2
Let v be ((-54)/(-7))/(30/140). Let o be 9*((-21)/v)/(-7). Factor 0*h - 3/2*h**3 + 0 - o*h**2.
-3*h**2*(2*h + 1)/4
Factor -2/11*n**2 + 6/11*n - 4/11.
-2*(n - 2)*(n - 1)/11
Let h be 12/78 - (204/(-26) + 3). Let d(t) be the first derivative of 1/7*t**3 + 0*t**2 + h - 3/7*t. Suppose d(z) = 0. What is z?
-1, 1
Let q(z) be the first derivative of 2 + 0*z + 2*z**3 + 2*z**2 - 6/5*z**5 - 1/3*z**6 - 1/2*z**4. Solve q(c) = 0.
-2, -1, 0, 1
Suppose 3*b = 5*u - 28, -3*u = 3*b + 15 - 51. Suppose 0 = -u*y + 7*y + 2. Factor -5*x - x**4 + 2*x**3 - 1 + y*x**2 - 2*x + 4*x + 2*x - x**5.
-(x - 1)**2*(x + 1)**3
Let l(y) = 17*y**3 - 5*y**2 - y. Suppose -3*x + 18 + 0 = 0. Let i(c) = 9*c**3 - 10599*c + 10599*c - 3*c**2. Let w(d) = x*l(d) - 11*i(d). Solve w(g) = 0 for g.
-2, 0, 1
Determine f, given that -26*f**3 - 14/5*f**4 - 246/5*f**2 - 28/5 - 158/5*f = 0.
-7, -1, -2/7
Suppose -11*h + 1336 = -3*h. Let i = h - 331/2. Factor i*b**2 + 1/2*b - 1.
(b + 1)*(3*b - 2)/2
Let m(w) be the first derivative of 1/4*w**3 + 0*w - 46 - 3/20*w**5 + 1/24*w**6 - 1/4*w**2 + 1/16*w**4. Determine z so that m(z) = 0.
-1, 0, 1, 2
Let u = 23 - 69. Let c be -1 + u/(-7) - 5. Factor -2*x + 4/7 + c*x**2 + 6/7*x**3.
2*(x - 1)*(x + 2)*(3*x - 1)/7
Solve -6*h**2 + 14*h**2 - 6*h**2 + 61 - 28*h - 7 + 42 = 0 for h.
6, 8
Suppose -5*g = -w - 10, 32 = 4*g + 8*w - 4*w. Suppose 109*v - g - v**2 - 103*v - 2*v**2 = 0. Calculate v.
1
Factor -k**3 + 589 + 3*k**3 + 104*k**2 - 489 + 202*k.
2*(k + 1)**2*(k + 50)
Let r be ((-2)/(-30))/(4/6*2). Let y(f) be the second derivative of -1/6*f**3 + 0 + f**2 - 5*f - 1/4*f**4 + 1/30*f**6 + r*f**5. Find k, given that y(k) = 0.
-2, -1, 1
Let u(g) be the second derivative of -g**6/320 + g**5/80 - g**4/64 - 2*g**2 + 7*g. Let h(m) be the first derivative of u(m). Factor h(w).
-3*w*(w - 1)**2/8
Let w(m) = 6*m - 58. Let s be w(10). Let o(p) be the second derivative of 0 - p + 6*p**2 + 1/4*p**4 - s*p**3. Factor o(k).
3*(k - 2)**2
Find g such that 8*g**2 - 21*g**4 - 11*g**4 + 12*g**3 + 45*g**5 - 33*g**5 = 0.
-1/3, 0, 1, 2
Factor 6 - 9/2*q**2 + 15/4*q**3 - 3/4*q**4 - 3*q.
-3*(q - 2)**3*(q + 1)/4
Suppose 3*d - 5 = 7. Factor 88*r - 8*r + 33 - 16*r**2 + d*r**2 - 5.
-4*(r - 7)*(3*r + 1)
Let v(n) be the second derivative of 2*n**7/105 - n**6/10 + n**5/5 - n**4/6 + 3*n**2 + 7*n. Let f(m) be the first derivative of v(m). What is h in f(h) = 0?
0, 1
Let r(h) be the first derivative of h**7/14 - h**6 + 99*h**5/20 - 10*h**4 + 8*h**3 + 3*h - 15. Let d(b) be the first derivative of r(b). Factor d(p).
3*p*(p - 4)**2*(p - 1)**2
Let h(s) = 3*s**3 - s**2 - 3*s + 1. Let l = 2 - -5. Let v(q) = -q**2 + q - l + 6 + 2*q**2 - q**3. Let w(b) = -2*h(b) - 4*v(b). Factor w(p).
-2*(p - 1)*(p + 1)**2
Suppose 3*l = 12 - 0. Suppose j = -3*z + 37, 4*z - 53 = -l*j - 9. Solve -z*c**5 - 6*c**2 + 15*c**3 + 6*c**4 - 8*c**5 + 6*c**3 = 0 for c.
-1, 0, 2/7, 1
Let g(o) be the first derivative of 0*o - 1/13*o**4 + 31 - 4/13*o**2 + 6/13*o**3. Solve g(y) = 0.
0, 1/2, 4
Let w be 2/12 + -200*(-16)/8448. Suppose -8/11*y + 2/11*y**2 + w = 0. Calculate y.
1, 3
Let f(n) be the third derivative of -n**6/2160 + n**4/36 + n**3 - 14*n**2. Let w(z) be the first derivative of f(z). Factor w(t).
-(t - 2)*(t + 2)/6
Let i(u) be the second derivative of 3/10*u**2 + 0 + 3/25*u**5 + 3/20*u**4 - 2/5*u**3 + 6*u - 2/25*u**6. Solve i(s) = 0 for s.
-1, 1/2, 1
Let b(o) = -o + 4*o - 4*o**2 + 3 + 3*o**2. Let s(z) = -z**2 + 4*z + 4. Let u be 3/((-3)/6 + 2/(-4)). Let h(p) = u*s(p) + 4*b(p). Factor h(l).
-l**2
Let o be (-12)/(-14)*70/15. Let b be 38/9 + o/(-18). Factor 5*m**2 - 28*m**3 + b*m**5 - 2*m**2 - 20*m**4 - 15*m**2 - 8*m**5.
-4*m**2*(m + 1)**2*(m + 3)
Suppose g - 17 = 5*j - 0*j, -5*g + 19 = -3*j. Suppose 2*u + 4 = -2*c, 2*c + 2*c + g*u = -4. Suppose c*o + 0 + 1/2*o**2 = 0. Calculate o.
0
Factor 9/4*r**2 - 9/4 + 3/4*r - 3/4*r**3.
-3*(r - 3)*(r - 1)*(r + 1)/4
Factor -28/9 + 4/9*x**2 - 1/9*x**3 + 25/9*x.
-(x - 7)*(x - 1)*(x + 4)/9
Let g(c) = c**2 - 7*c + 2. Suppose 0*a - 4*a + 32 = 2*y, -4*a = -3*y - 22. Let f be g(a). Factor 3*k + 9*k**f + 3*k - 12*k.
3*k*(3*k - 2)
Let d(c) be the first derivative of c**4/38 - 14*c**3/19 - 153*c**2/19 - 486*c/19 + 697. Suppose d(y) = 0. What is y?
-3, 27
Let a(f) be the first derivative of f**7/105 - f**6/30 + 5*f**2 - 17. Let k(t) be the second derivative of a(t). Find p such that k(p) = 0.
0, 2
Let t = -128/77 + 18/7. Factor -t*n - 8/11 - 2/11*n**2.
-2*(n + 1)*(n + 4)/11
Solve 1298 - 107*o - 5*o + 290 - 20 + 2*o**2 = 0.
28
Let g(y) = 9*y**4 - 53*y**3 + 18*y**2 + 19*y - 10. Let k(o) = 3*o**4 - 18*o**3 + 6*o**2 + 6*o - 3. Let m = -71 + 65. Let j(l) = m*g(l) + 17*k(l). Factor j(b).
-3*(b - 3)*(b - 1)**2*(b + 1)
Let u = 471 + -267. Let d = u - 607/3. Determine a so that -1/3 + a**5 - 1/3*a - d*a**4 - 2/3*a**3 + 2*a**2 = 0.
-1, -1/3, 1
Let p(c) be the second derivative of c**4/24 - 5*c**3/2 - 31*c**2/4 - 72*c + 2. Factor p(s).
(s - 31)*(s + 1)/2
Let w(m) be the third derivative of -m**5/60 + m**4/6 + 2*m**3 + 20*m**2. Factor w(b).
-(b - 6)*(b + 2)
Factor -14045/3 - 5/3*t**2 - 530/3*t.
-5*(t + 53)**2/3
Let t(q) = -70*q - 2657. Let y be t(-38). Factor 5/6*u**2 - 4/3*u + 2/3 - 1/6*u**y.
-(u - 2)**2*(u - 1)/6
Let d be (2/10*-3)/(2905/(-4150)). Determine m, given that 0 + 2/7*m + 6/7*m**2 + 2/7*m**4 + d*m**3 = 0.
-1, 0
Solve -8/7 - 6/7*a**3 + a**2 + 6/7*a + 1/7*a**4 = 0.
-1, 1, 2, 4
Let x be 11 + (-16 - 54)/10. Solve -36/7*j**2 + 3/7*j**x - 12/7*j**3 + 96/7*j + 192/7 = 0.
-2, 4
Solve -52/7*i**2 + 4/7*i**3 + 96/7 + 40/7*i = 0 for i.
-1, 2, 12
Let j(g) be the third derivative of 1/1008*g**8 + 1/8*g**4 - 1/180*g**6 + 0 + 0*g + 21*g**2 - 2/315*g**7 + 0*g**3 + 1/15*g**5. Factor j(d).
d*(d - 3)**2*(d + 1)**2/3
Let z(o) be the first derivative of 0*o - 1/3*o**4 - 4/9*o**3 + 0*o**2 - 9. Factor z(p).
-4*p**2*(p + 1)/3
Let c = 672 - 672. Let x(w) be the second derivative of -3*w - 1/54*w**4 + 0*w**2 + c*w**3 + 0 + 1/135*w**6 + 0*w**5. Find g, given that x(g) = 0.
-1, 0, 1
Suppose 2*r - 5*f - 12 = 16, -3*f = -3*r + 24. Factor 121*b**r - 63*b**4 - 68*b**4 + 0*b - 32*b**2 - 34*b**3 - 8*b.
-2*b*(b + 1)*(b + 2)*(5*b + 2)
Let h(s) be the second derivative of 1/10*s**3 + 0 - 1/10*s**4 + 1/50*s**6 + 1/70*s**7 - 3/50*s**5 + 3/10*s**2 + 30*s. What is u in h(u) = 0?
-1, 1
Let z = -10 - -4. Let d be 0 - (3/90)/(z/24). Find n such that -2/3*n - 8/15 - d*n**2 = 0.
-4, -1
Suppose -5*x = -6*q - 2, -x + 4*q - 20 = -3*x. Let 28/11*f**x + 62/11*f**3 + 8/11 - 6/11*f**2 - 32/11*f = 0. What is f?
-2, -1, 2/7, 1/2
Let f be (1 + 0)*(-9 - 414/(-45)). Let r(a) be the second derivative of 9*a - 1/20*a**4 - f*a**2 + 1/6*a**3 + 0. Factor r(h).
-(h - 1)*(3*h - 2)/5
Let z be (-154)/(-8) - 4/16. Let t = z + -19. Factor t*k + 0 + 2/7*k**3 + 0*k**2 + 0*k**4 - 2/7*k**5.
-2*k**3*(k - 1)*(k + 1)/7
Let a(k) be the second derivative of -2*k**7/105 + 7*k**6/150 - 2*k**5/75 - 7*k**2 - 6*k. Let p(x) be the first derivative of a(x). Find t, given that p(t) = 0.
0, 2/5, 1
Let n(l) = -l**4 + 7*l**3 + 3*l**2 - 3*l - 3. Let h = 19 + -24. Let i(j) = j**4 - 13*j**3 - 5*j**2 + 5*j + 5. Let t(x) = h*n(x) - 3*i(x). Factor t(s).
2*s**3*(s + 2)
Let b(c) = -6*c - 64. Let t be b(-12). Let o be t/(-18)*(-27 + 21). Determine g so that 0 + 0*g - 4/3*g**3 - o*g**2 = 0.
-2, 0
Solve -2*g**5 + 32*g**4 + g + 0*g - 38*g**4 + 6*g**2 + 3*g - 2*g**3 = 0 for g.
-2, -1, 0, 1
Let a(r) be the first derivative of -2*r**2 + 1/90*r**5 + 0*r + 3 - 1/36*r**4 + 0*r**3. Let v(y) be the second derivative of a(y). Factor v(j).
2*j*(j - 1)/3
Suppose 0 = -f - 2*d - 2, 79*d - 14 = -5*f + 81*d. Factor f*s**2 - 2/3*s + 0.
2*s*(3*s - 1)/3
Let t(h) = -h**4 - 1. Let z = -143 - -144. Let j(c) = 3*c**5 - 3