h that 6*u**5 + 32*u - 56*u**2 + 128*u**2 - 36*u**4 - 4*u**3 - u**5 + 3*u**5 = 0.
-1, -1/2, 0, 2, 4
Let g(r) = -2*r**2 - 51*r + 32. Let b be g(-26). Suppose 0 = -d + 2, b*d = -i + d + 19. Factor 3/2*n**2 + 27/2 - i*n.
3*(n - 3)**2/2
Determine h so that -451*h**3 - 20*h**2 + 16*h + 892*h**3 - 445*h**3 + 80 = 0.
-5, -2, 2
Let n(v) be the third derivative of 11*v**7/14 + 133*v**6/24 + 34*v**5/3 + 5*v**4/6 - 2*v**2 - 205. Suppose n(z) = 0. What is z?
-2, -1/33, 0
Let a be (-111)/(-132) + -5 + (-231)/(-44). Factor -2/11*b**2 + a*b + 14/11.
-2*(b - 7)*(b + 1)/11
Let r(o) be the second derivative of -3*o**5/20 + 11*o**4/4 + o**3/2 - 33*o**2/2 - 2*o + 39. Factor r(s).
-3*(s - 11)*(s - 1)*(s + 1)
Suppose -16*h**3 + 9075 + 13*h**3 + 3037*h - 11782*h - 327*h**2 = 0. What is h?
-55, 1
Let k = 412 - 260. Factor 77*t**3 + 74*t**3 + 3*t - k*t**3 + 2.
-(t - 2)*(t + 1)**2
Suppose 3*k - 4 - 8 = 0. Factor 4*l**2 - l**2 - k*l - 4*l**2 + 2*l**2.
l*(l - 4)
Let f(i) = -13*i**5 + 5*i**4 + 6*i**2 - 20*i. Let y(w) = -7*w**5 + 3*w**4 - w**3 + 3*w**2 - 10*w. Let p(t) = -6*f(t) + 11*y(t). Find k, given that p(k) = 0.
-5, -1, 0, 1, 2
Factor 42 + 35*o + 19 - 13 + 4*o**2 - 87*o.
4*(o - 12)*(o - 1)
Suppose 67*c = 2*g + 68*c - 4, -4*g - 5*c + 20 = 0. Factor 0 + 2/7*p**3 + g*p - 2/7*p**2.
2*p**2*(p - 1)/7
Let a(g) be the second derivative of -2*g**6/5 + 101*g**5/5 - 385*g**4 + 3146*g**3 - 5324*g**2 - 36*g - 4. Factor a(q).
-4*(q - 11)**3*(3*q - 2)
Let u = -61 + 58. Let k be 2/u*(-18)/4. Factor 0*t**k - 3/4*t**4 + 0*t - 3/4 + 3/2*t**2.
-3*(t - 1)**2*(t + 1)**2/4
Factor -4*c - 16*c**2 + 36*c**3 - 16*c**4 - 60*c**3 - 9*c**5 + 5*c**5.
-4*c*(c + 1)**4
Let u(h) be the first derivative of -h**5/150 + h**3/15 + h**2 - 9. Let i(x) be the second derivative of u(x). Determine o, given that i(o) = 0.
-1, 1
Suppose l - 4*o = 13, 2*l + 29 = -4*o + 7. Let b be l/5 - (-266)/10. Solve -b*t**4 - 4 + 36*t**2 + 11*t - 18*t**5 + 8*t**3 - t - 6*t**4 = 0.
-1, 2/9, 1
Suppose -9 = -5*s + 6. Let i(h) = -2*h**2 + 6*h + 3. Let k be i(s). What is w in -5/2*w**4 + 0 + 1/2*w**k + 2*w**5 + 0*w + 0*w**2 = 0?
0, 1/4, 1
Factor 0 + 4*y**2 + 4/5*y.
4*y*(5*y + 1)/5
Let n(j) = 2*j**2 - j. Suppose -3*g - 2 = -g. Let x(i) = -4*i**2 - 8*i. Let o(c) = g*x(c) - 4*n(c). Factor o(m).
-4*m*(m - 3)
Let g(v) be the second derivative of -v**4 + 1/5*v**5 - 2*v**2 + 0 + 25*v + 2*v**3. Solve g(h) = 0 for h.
1
Factor -a**3 - 10*a**2 + a**3 - 11*a**4 + 13*a**4 - 6*a - 2*a**3.
2*a*(a - 3)*(a + 1)**2
Let b(x) be the first derivative of -x**6/2340 - x**5/130 - 5*x**4/156 + 10*x**3/3 - 4. Let j(c) be the third derivative of b(c). Factor j(y).
-2*(y + 1)*(y + 5)/13
Suppose s - 36 = -s. Let x = s + -14. Factor -27*a**3 + 24*a**2 + 21*a**x - 5*a**3 - 4 - 9*a**4.
4*(a - 1)**3*(3*a + 1)
Let r(n) be the first derivative of 4*n**3/3 + 92*n**2 + 2116*n - 45. Factor r(w).
4*(w + 23)**2
Let q(y) be the third derivative of y**5/60 + y**4/6 + 2*y**2 - 245*y. Factor q(r).
r*(r + 4)
Let b = -703 + 703. Suppose -8/5 + 6/5*o**2 - 2/5*o**3 + b*o = 0. Calculate o.
-1, 2
Let q(x) be the third derivative of -x**8/168 + 4*x**7/105 + x**6/20 - 11*x**5/15 + x**4/3 + 8*x**3 + 259*x**2. Determine u, given that q(u) = 0.
-2, -1, 2, 3
Let c = 628/11 + -5597/99. Let -4/9*m**2 - c*m - 1/9*m**3 - 2/9 = 0. What is m?
-2, -1
Let h = -56338/1857 - -3/619. Let d = -29 - h. Let -2 + d*f - 2/9*f**2 = 0. Calculate f.
3
Let j be 3*1 - (-2 + -1 + 702/130). Factor -2/5 + 1/5*v + j*v**2 - 1/5*v**4 - 1/5*v**3.
-(v - 1)**2*(v + 1)*(v + 2)/5
Suppose 7 + 5 = -3*u, -3033 = 5*g + 2*u. Let v = g - -9079/15. What is k in 2/5*k**3 + 0*k + 0 + 2/15*k**4 + v*k**2 = 0?
-2, -1, 0
Let b(i) be the second derivative of i**7/147 + 4*i**6/35 - 9*i**5/35 - 164*i**4/21 + 219*i**3/7 - 324*i**2/7 + 305*i. Suppose b(q) = 0. Calculate q.
-9, 1, 4
Let u(m) = m**3 - m**2 + m - 1. Suppose 3*z = -3 - 12. Let r(p) = 4*p**3 - 8*p**2 + 2*p - 6. Let n(x) = z*u(x) + r(x). Factor n(q).
-(q + 1)**3
Let h be 1*2*9*(-3)/(-18). Let 3*c**3 + 78*c + 61*c**h - 223*c - 43*c - 352*c**2 - 24 = 0. Calculate c.
-1/4, 6
Suppose 0*p + 34*p = 68. Factor 0*g - 1/2*g**4 + 1/2*g**p - 1/2*g**5 + 0 + 1/2*g**3.
-g**2*(g - 1)*(g + 1)**2/2
Let j(g) be the first derivative of g**3/15 + 37*g**2/5 + 1369*g/5 - 142. Find l such that j(l) = 0.
-37
Let y(n) be the first derivative of n**6/15 + 2*n**5/25 - n**4/5 - 4*n**3/15 + n**2/5 + 2*n/5 - 367. Determine f so that y(f) = 0.
-1, 1
Let a be 19/(-2) + (-3)/(-6). Let n be (3/14)/(a/(-12)). Factor n + 2/7*l**3 - 2/7*l - 2/7*l**2.
2*(l - 1)**2*(l + 1)/7
Let f(w) be the third derivative of -5/4*w**4 + 24*w**2 + 0 - 1/60*w**6 + 7/3*w**3 + 0*w + 3/10*w**5. Factor f(c).
-2*(c - 7)*(c - 1)**2
Find d such that -9/4*d**3 + d**4 - 9/4*d**2 + 4*d + 3 = 0.
-1, -3/4, 2
Let h(x) be the first derivative of -x**5/20 - x**4/48 - 6*x**2 + 21. Let t(o) be the second derivative of h(o). Determine y, given that t(y) = 0.
-1/6, 0
Let k(m) be the first derivative of m**4/18 - 14*m**3/27 + 4*m**2/3 - 75. What is a in k(a) = 0?
0, 3, 4
Factor 6 - 7/3*m - 10/3*m**2 - 1/3*m**3.
-(m - 1)*(m + 2)*(m + 9)/3
Let o(y) be the second derivative of y - 1/5*y**5 + 48*y**2 + 0 - 56/3*y**3 + 10/3*y**4. Factor o(q).
-4*(q - 6)*(q - 2)**2
Find n, given that -10*n**2 - 5/3*n**4 + 140/3*n**3 - 13300/3*n - 45125/3 = 0.
-5, 19
Let t(x) = x**2 - 7*x + 14. Let s be t(4). Factor -16*r**4 + 2*r**s + 4*r + 18*r**4 - 4*r**2 + 2*r**5 - 6*r**3.
2*r*(r - 1)**2*(r + 1)*(r + 2)
Let q be (-132)/154*(-14)/2. Let y(w) be the first derivative of 4*w**3 - 12 + 6/5*w**q + 33/5*w**4 + 0*w + 4/5*w**2 + 116/25*w**5. Factor y(z).
4*z*(z + 1)**3*(9*z + 2)/5
Let z(y) be the second derivative of -y**5/15 + y**4/12 + 2*y**3/9 - y**2/2 - 34*y. Factor z(q).
-(q - 1)*(q + 1)*(4*q - 3)/3
Suppose -202 - 38 = 12*q. Let b be ((-2)/(-4))/(q/(-48)). Factor -b*f**2 + 2/5 + 4/5*f.
-2*(f - 1)*(3*f + 1)/5
Suppose y + 0 = 7. Factor 3*k - 4*k**2 + y*k**2 + 6*k.
3*k*(k + 3)
Suppose 4*l - 1 - 11 = 0. Factor 11 + 0*z**2 - 8 - 12*z**l - 18*z + 27*z**2.
-3*(z - 1)**2*(4*z - 1)
Let q = -2110 - -2118. Let m(f) be the third derivative of 0 + 0*f**3 + 1/12*f**6 - 1/12*f**5 + 0*f**4 + 5/84*f**q + 0*f - 6*f**2 + 1/6*f**7. Factor m(j).
5*j**2*(j + 1)**2*(4*j - 1)
Let p be 15/(-6) + 3 + 78/(-252). Let r(v) be the second derivative of 2/147*v**7 + 0*v**2 - 6*v + p*v**4 + 2/21*v**3 + 0 + 8/105*v**6 + 6/35*v**5. Factor r(y).
4*y*(y + 1)**4/7
Let p(c) be the second derivative of 28*c + 1/40*c**5 - 1/12*c**3 + 0 + 1/6*c**4 - c**2. Factor p(b).
(b - 1)*(b + 1)*(b + 4)/2
Suppose -5*m - v + 5*v + 36 = 0, -3*m - 4*v = 4. Find c, given that -m*c**4 + 42*c**4 - 8*c**3 - 14*c**5 - 8*c**3 - 8*c**2 = 0.
-2/7, 0, 1, 2
Let q = -16141 - -64575/4. Factor 1/8*o**2 + 121/8 - q*o.
(o - 11)**2/8
Determine c so that 0 + 48/11*c**4 + 16/11*c + 6/11*c**2 - 5/11*c**5 - 65/11*c**3 = 0.
-2/5, 0, 1, 8
Let i(l) be the first derivative of l**6/21 - 2*l**5/35 - 5*l**4/14 - 2*l**3/7 + 14. Determine v so that i(v) = 0.
-1, 0, 3
Let r(u) be the third derivative of 0*u**4 - 1/735*u**7 - 1/420*u**6 + 0*u + 0*u**5 + 0*u**3 + 0 + 16*u**2. Determine b so that r(b) = 0.
-1, 0
Let r(z) be the second derivative of z**7/280 - z**6/60 - 11*z**3/6 - 19*z. Let j(v) be the second derivative of r(v). Factor j(m).
3*m**2*(m - 2)
Let g(f) = -3*f + 83. Let a be (-3800)/(-140) - (-2 - 30/(-14)). Let q be g(a). Find x, given that -8/9 + 0*x + 2/9*x**q = 0.
-2, 2
What is w in 72*w**3 - 754 - 30*w + 754 - 38*w**3 - 25*w**2 - 29*w**3 = 0?
-1, 0, 6
Let p(j) = -j - 3. Let q be p(-5). Let d be 2/(2/(-1 - (-2 + -1))). Factor 0 + b**2 + q - 3*b**d.
-2*(b - 1)*(b + 1)
Let h(d) = 5*d**3 + 9*d**2 + 16*d. Let q(r) be the third derivative of r**6/6 + 7*r**5/12 + 65*r**4/24 + 29*r**2. Let l(g) = -25*h(g) + 6*q(g). Factor l(i).
-5*i*(i + 1)*(i + 2)
Let g(i) be the third derivative of -i**6/120 + 4*i**5/15 - 41*i**4/24 + 13*i**3/3 - 346*i**2. Solve g(p) = 0 for p.
1, 2, 13
Let s(a) be the second derivative of 0*a**3 + 6*a + 0*a**5 + 0 - 1/11*a**2 + 1/33*a**4 - 1/165*a**6. Factor s(x).
-2*(x - 1)**2*(x + 1)**2/11
Let k = -16 + 18. What is g in 15 - 3*g + 5*g**3 + 3*g - 5*g**2 - 10*g**k - 5*g = 0?
-1, 1, 3
Suppose 65/6 + 125/6*t - 5/3*t**2 = 0. Calculate t.
-1/2, 13
Let h(t) be the first derivative of t - 1/5*t**5 + 0*t**3 - 3 - t**2 + 1/2*t**4. Fac