Factor z(a).
2*a*(a + 1)*(a + 2)
Let u = -22141 + 22148. Factor -u*c**2 - 1/9 + 5/3*c + 49/9*c**3.
(c - 1)*(7*c - 1)**2/9
Find r, given that 20*r**3 + 16*r + 221*r**2 + 172*r**3 + 103*r**2 - 48 - 28*r**4 - 24*r**5 = 0.
-2, -1/2, 1/3, 3
Let h(o) be the first derivative of -o**5/20 + o**4/2 - 3*o**3/2 + 8*o**2 + 10. Let m(w) be the second derivative of h(w). Factor m(b).
-3*(b - 3)*(b - 1)
Let p(q) = -q**2 + 8*q + 11. Let u be p(9). Let x(n) = 2*n**2 - 3*n + 1. Let h be x(u). Factor c**2 - 1/2*c**h + 1/2*c - 1.
-(c - 2)*(c - 1)*(c + 1)/2
Let z be (-2)/(2 - 4)*1. Let m(n) = -n**3 - n**2 - n - 1. Let d(x) = -x**4 - 4*x**3 - 3*x**2 - x - 1. Let w(k) = z*d(k) - m(k). Factor w(c).
-c**2*(c + 1)*(c + 2)
Let v(s) be the second derivative of s**6/120 + s**5/30 + s**4/24 - 5*s**2/2 + 13*s. Let r(h) be the first derivative of v(h). Determine g so that r(g) = 0.
-1, 0
Suppose 7*v + 8*v + 2*v**2 - 42 - 24*v + v = 0. Calculate v.
-3, 7
Factor 0*y + 4/3*y**2 + 2/3*y**3 - 2*y**4 + 0.
-2*y**2*(y - 1)*(3*y + 2)/3
Suppose -9*u + 5 = 2*j - 4, -1 = -2*j - u. Let k(z) be the second derivative of j + 0*z**3 + 1/6*z**2 - 1/36*z**4 - 8*z. Let k(d) = 0. What is d?
-1, 1
Let v(a) be the third derivative of -1/540*a**6 + 0*a + 1/108*a**4 + 1/27*a**3 - 11*a**2 - 1/270*a**5 + 0. Solve v(o) = 0.
-1, 1
Determine z so that 19 + 14 + 44*z**2 + 48*z - 4*z**3 - 33 = 0.
-1, 0, 12
Let p be (-21931)/195 - 2/(-3). Let h = p - -113. Find b, given that 2/5*b + h*b**3 - 6/5*b**2 - 2/5*b**4 + 0 = 0.
0, 1
Let d(a) be the first derivative of a**7/2520 - a**6/540 - a**5/90 + a**4/9 + 4*a**3 + 12. Let i(w) be the third derivative of d(w). Factor i(c).
(c - 2)**2*(c + 2)/3
Let o(b) be the second derivative of -4*b**7/63 + 7*b**6/9 - 29*b**5/10 + 20*b**4/9 + 16*b**3/9 - 8*b. Solve o(a) = 0.
-1/4, 0, 1, 4
Let q = 8457/65 + -649/5. Factor -q - 6/13*o + 2/13*o**3 + 0*o**2.
2*(o - 2)*(o + 1)**2/13
Determine v so that -3*v**3 - 30*v**2 + 39*v - 22*v - 24 - 68*v = 0.
-8, -1
Let d(o) be the third derivative of o**9/3780 - o**8/1680 - 5*o**4/12 + 16*o**2. Let y(l) be the second derivative of d(l). Find m, given that y(m) = 0.
0, 1
Let f be ((-2)/3)/((-1)/(-6)). Let a = 1 - f. Find t, given that -2*t**2 + t**a + 0*t**5 - 12*t**3 - t + 2*t**4 + 12*t**3 = 0.
-1, 0, 1
Let a(j) = -j + 17. Let h be a(9). Let f be -11 + h - 14/(-2). Factor q - q - 14*q**3 + 5*q**5 + f*q**3 + 5*q.
5*q*(q - 1)**2*(q + 1)**2
Suppose 4*v + 4*v = 24. Let l be 1/((v/6)/(1 - 0)). Factor 0 + 2/5*o**l - 1/5*o**4 + 0*o - 1/5*o**3.
-o**2*(o - 1)*(o + 2)/5
Let h(y) = -7*y**4 + 51*y**3 + 16*y**2 - 699*y - 980. Let k(s) = -2*s**4 + s**3 + s**2 + s. Let d(z) = -h(z) + k(z). Factor d(a).
5*(a - 7)**2*(a + 2)**2
Let p(y) be the first derivative of -1/10*y**6 + 3/5*y**5 + 22 - 21/20*y**4 + 12/5*y**2 - 1/5*y**3 - 12/5*y. Solve p(b) = 0.
-1, 1, 2
Factor 75/4*o**2 + 5/2 - 85/4*o.
5*(o - 1)*(15*o - 2)/4
Suppose 0 = u - 5*n + 2 + 1, 0 = -4*u + n + 7. Factor 294*h**4 + 0*h**2 - 293*h**4 + 2*h - h**u - 2*h**3.
h*(h - 2)*(h - 1)*(h + 1)
Let z(m) be the first derivative of 1/9*m**4 + 2 + 1/90*m**5 - m**2 + 4/9*m**3 + 0*m. Let f(x) be the second derivative of z(x). Suppose f(s) = 0. Calculate s.
-2
Solve -9/2 - 19/2*w**2 - 23/2*w - 5/2*w**3 = 0 for w.
-9/5, -1
Factor -1/7*h**4 - 24/7*h - 22/7*h**2 - 9/7 - 8/7*h**3.
-(h + 1)**2*(h + 3)**2/7
Let d(m) = -2*m**2 - 20*m - 14. Let x(w) = -w. Let f(p) = d(p) - 4*x(p). Let u(b) = -4*b**2 - 33*b - 29. Let z(n) = 13*f(n) - 6*u(n). Factor z(o).
-2*(o + 1)*(o + 4)
Let a = 126 + -76. Factor -q**4 + a - 2*q**3 - 50 - q**2.
-q**2*(q + 1)**2
Let j(n) be the third derivative of -n**5/240 + n**4/32 + n**3/6 + 4*n**2 - 7*n. Suppose j(w) = 0. Calculate w.
-1, 4
Let a(t) be the third derivative of -t**5/20 + 21*t**4/8 + 36*t**3 + 34*t**2 + 3*t. What is i in a(i) = 0?
-3, 24
Suppose -17*k + 9*k = -40. Let g(y) be the third derivative of 1/315*y**7 + 0 + 0*y**4 + 0*y**k + 0*y**3 - 8*y**2 - 1/90*y**6 + 0*y + 1/168*y**8. Factor g(j).
2*j**3*(j + 1)*(3*j - 2)/3
Let q(n) be the second derivative of n**6/15 + 2*n**5 + 13*n**4 - 220*n**3/3 + 121*n**2 + 286*n. Determine b so that q(b) = 0.
-11, 1
Determine y, given that -21/8 + 1/8*y**2 - 1/2*y = 0.
-3, 7
Let g(s) = -s**2 + 2*s + 401. Let j be g(21). Factor 0 + 2/5*q**j - 2/5*q**4 + 3/5*q + 1/5*q**5 - 4/5*q**3.
q*(q - 3)*(q - 1)*(q + 1)**2/5
Suppose -5*d + 5 = 0, -4*s + 2*d = d - 43. Let i(g) be the second derivative of 3/100*g**5 - 6/5*g**2 - s*g + 0*g**3 + 0 + 3/20*g**4. Factor i(l).
3*(l - 1)*(l + 2)**2/5
Suppose 0 = -3*a - 2*a + 45. Suppose -1 - a = -5*o. Factor -8*i - 5*i**o - 11*i**3 + 33*i**2 - 5*i**3 - 4.
-4*(i - 1)**2*(4*i + 1)
Let r be ((-12)/(-78))/(3/45*10/4). Factor -r*l + 2/13*l**2 + 18/13.
2*(l - 3)**2/13
Let z(n) be the second derivative of 0 + 1/2*n**2 - 1/120*n**6 + 1/24*n**4 + 0*n**3 + 0*n**5 + 7*n. Let v(q) be the first derivative of z(q). Factor v(p).
-p*(p - 1)*(p + 1)
Suppose -36*g**2 - 6*g**2 - 14*g**4 - 52*g**3 + 32 - 12*g**2 - 8*g - 24 = 0. Calculate g.
-2, -1, 2/7
Suppose -4*s = -n + 9, -8 = 3*n - 5*s - 35. Let q = -6 + n. Factor q*b**4 + 0*b**3 - 3*b**3 + 2*b**4 - 2*b**4.
3*b**3*(b - 1)
Let r(c) be the first derivative of -c**5 + 15*c**4 - 110*c**3/3 - 210*c**2 - 245*c - 145. Factor r(m).
-5*(m - 7)**2*(m + 1)**2
Let p(c) be the first derivative of -4*c**3/3 - 48*c**2 + 208*c + 529. Let p(l) = 0. What is l?
-26, 2
Suppose 3*u - 15 - 9 = 0. Determine c so that 2*c - 5*c + u*c + 3*c**2 + 13*c + 27 = 0.
-3
Let b(s) be the first derivative of s**5/5 - 3*s**4/2 + 3*s**3 - 2*s**2 + 73. Factor b(w).
w*(w - 4)*(w - 1)**2
Suppose 4*m - 3464 = -3*j, -2*j + 4572 = 2*j - 4*m. Solve -2*q**2 - 2*q**3 - q**2 + j*q - 1146*q = 0.
-2, 0, 1/2
Let m(y) be the second derivative of -y**7/21 - 2*y**6/15 + y**4/3 + y**3/3 + y + 36. Find q such that m(q) = 0.
-1, 0, 1
Let c(i) be the second derivative of -i**4/8 - 67*i**3/2 - 13467*i**2/4 + 16*i. Suppose c(q) = 0. What is q?
-67
Let b(s) be the third derivative of -s**7/1995 + s**6/228 - 101*s**2. Factor b(a).
-2*a**3*(a - 5)/19
Let a(f) = f**4 + f**3 - 4*f**2 + 4*f. Let g(b) = -b - 3*b**2 + 675*b**3 - 676*b**3 + 3*b**2. Let o(y) = -a(y) - 4*g(y). Factor o(x).
-x**2*(x - 4)*(x + 1)
Let a be (198/(-77))/(8/(-14)). Factor a + 3*j - 3/2*j**2.
-3*(j - 3)*(j + 1)/2
Suppose -2*r - 2 + 10 = 2*o, -4*o + 20 = 5*r. Factor -17*v**4 - 12*v**2 + 23*v**4 - 10*v**r + 4*v + 12*v**3.
-4*v*(v - 1)**3
Let s(a) be the first derivative of -3*a**4/4 - a**3 + 21. Solve s(l) = 0 for l.
-1, 0
Solve 50*l - 30*l - 20*l**2 + 5*l**5 - 20*l**4 - 15*l**3 + 30*l**4 = 0.
-2, 0, 1
Suppose 3*d - 8 = -4*b - d, -3*d = -b + 2. Let i(m) be the first derivative of 1/30*m**4 + 2/15*m**3 + 2/15*m**b + 0*m - 4. Let i(u) = 0. Calculate u.
-2, -1, 0
Let y be (4/(-13))/2 + -105*(-18)/3159. Solve 4/9*a**2 + 0 - 4/3*a**3 + 4/9*a**5 + 8/9*a - y*a**4 = 0.
-1, 0, 1, 2
Let c(w) = 56*w**3 - 66*w**2 - 10*w - 1. Let k = -74 - -67. Let y(h) = -37*h**3 + 44*h**2 + 7*h + 1. Let n(s) = k*y(s) - 5*c(s). Factor n(q).
-(q - 1)*(3*q - 1)*(7*q + 2)
Let i = 16 + -12. Find q, given that i*q**3 + 2*q + 12*q**4 - 5*q**2 + 10*q**4 - 23*q**4 = 0.
0, 1, 2
Let y = 6887/38060 - -3/3460. Factor 8/11 - 6/11*x - y*x**2.
-2*(x - 1)*(x + 4)/11
Suppose 0 = -6*o - 1000 - 404. Let c be (-6)/14 + o/(-105). Let -6/5 - 3/5*a**3 + 0*a**2 + c*a = 0. What is a?
-2, 1
Let q(j) be the first derivative of -2*j**3 + 0*j + 4 + 5/4*j**4 + 3/2*j**2. Let m(n) = n**4 + n**3 - n**2 + n. Let l(z) = 3*m(z) - 3*q(z). Factor l(u).
3*u*(u - 2)*(u - 1)**2
Let i(m) = m**3 + 100*m**2 + 26*m + 2602. Let o be i(-100). Determine b so that 8/3 - 20/3*b**o - 4/3*b - 8/3*b**3 = 0.
-2, -1, 1/2
Let z(p) be the second derivative of p**7/105 - 2*p**6/75 - 6*p**5/25 + 19*p**4/15 - 37*p**3/15 + 12*p**2/5 + 219*p. Let z(n) = 0. What is n?
-4, 1, 3
Solve -194*w**2 - 32 + 19*w**4 + 4*w**4 + 3*w**4 - 4*w**3 + 176*w + 20*w**4 + 8*w**5 = 0 for w.
-4, 1/4, 1
Let a(l) be the third derivative of l**5/30 - 7*l**4/2 + 147*l**3 - 123*l**2 - 2*l. Factor a(x).
2*(x - 21)**2
Determine n so that -7/9*n**3 + 79/9*n - 2 - 6*n**2 = 0.
-9, 2/7, 1
Let k = -4186 - -167449/40. Let d(u) be the second derivative of -k*u**5 + 0 + 7/8*u**4 + 0*u**3 + 2*u - 3*u**2. Factor d(n).
-3*(n - 2)*(n - 1)*(3*n + 2)/2
Let r be -3 + (3 - 2) - -3. Suppose -4*x + m + 3 + r = 0, 