1. Factor l(c).
-4*c*(c - 1)*(c + 1)*(c + 4)
Let l = -1194 - -15534/13. Factor l*z + 2/13*z**2 + 18/13.
2*(z + 3)**2/13
Suppose -4*i + 9*i = 2*i. Let 0 + i*x + 0*x**3 + 1/4*x**2 - 1/4*x**4 = 0. Calculate x.
-1, 0, 1
Let n = -1 + 6. Suppose 3*z + 5*y + 2 = 2*z, n*z - 20 = 5*y. Factor -i**z - i**3 - 4*i**2 + 4 + 2*i - 2 + 2*i**2.
-2*(i - 1)*(i + 1)**2
Suppose 75/4*c + 81/4*c**2 + 33/4*c**3 + 3/4*c**4 + 6 = 0. Calculate c.
-8, -1
Let b(s) be the third derivative of s**8/2184 - 4*s**7/1365 + s**6/130 - 2*s**5/195 + s**4/156 + 3*s**2. What is f in b(f) = 0?
0, 1
Let x(z) = -z**3 - z**2 - z - 1. Let h(v) = -12*v**3 - 21*v**2 - 24*v - 15. Let k(p) = -h(p) + 9*x(p). Let k(u) = 0. Calculate u.
-2, -1
Determine c so that 1/3*c**2 + 1/3*c**3 + 0 - 2/3*c = 0.
-2, 0, 1
Suppose 7 + 5 = 4*d. Let t(n) be the second derivative of 2*n**d - n + 3/2*n**4 + n**2 + 0 + 2/5*n**5. What is a in t(a) = 0?
-1, -1/4
Let z(h) be the third derivative of -7*h**9/540 - h**8/80 + 4*h**7/105 - h**6/45 + h**4/4 + 2*h**2. Let o(w) be the second derivative of z(w). Factor o(j).
-4*j*(j + 1)*(7*j - 2)**2
Let q(w) be the third derivative of 1/15*w**3 + 0 - 5*w**2 - 17/600*w**6 + 0*w + 2/525*w**7 - 13/120*w**4 + 2/25*w**5. Suppose q(z) = 0. What is z?
1/4, 1, 2
Let b = 161 - 161. Factor -4/3 + b*u + u**2 + 1/3*u**3.
(u - 1)*(u + 2)**2/3
Suppose 0 = a - 2*a + 4*l + 13, -a - 4*l = 19. Let t be 2*(0 + a)/(-30). Let -4/5*q**3 + 2/5*q**5 + 2/5*q**2 + 2/5*q - 1/5 - t*q**4 = 0. What is q?
-1, 1/2, 1
Factor -4/17 + 30/17*a - 32/17*a**3 - 48/17*a**2.
-2*(a + 2)*(4*a - 1)**2/17
Let f(y) be the third derivative of 0 + 6*y**2 + 0*y - 1/10*y**4 + 3/5*y**3 + 1/150*y**5. Determine h so that f(h) = 0.
3
Factor 0 - 1/5*m**2 + m.
-m*(m - 5)/5
Let y(d) be the second derivative of d**7/280 + d**6/120 + d**5/160 - d**3/3 + 2*d. Let g(q) be the second derivative of y(q). Let g(z) = 0. What is z?
-1/2, 0
Let q = -6 + 15. Let b = -92 - -101. Factor b - 2*m**4 - 2*m**3 - q.
-2*m**3*(m + 1)
Let z(s) be the second derivative of 1/20*s**5 - 1/6*s**3 + 0*s**2 + 0*s**4 + 3*s + 0. Factor z(q).
q*(q - 1)*(q + 1)
Let -33*h**2 + 2*h - 25*h**2 - 23*h**2 + 82*h**2 + 1 = 0. Calculate h.
-1
Let l(i) = -i**2 + 5*i - 2. Let d be l(3). Suppose 0 = k + d*k - 5. Factor -1 - k - 2*v**2 + 4.
-2*(v - 1)*(v + 1)
Suppose 5*w - 2 = 8. Suppose 10/7*f**4 + 0 + 2*f**w + 18/7*f**3 + 2/7*f**5 + 4/7*f = 0. Calculate f.
-2, -1, 0
Let l(g) = g - 1. Let k be l(4). Suppose -4*v - 2*s = -10, -v + 6 = -k*s - 0. Factor v*b**2 - b - 8*b**4 - 14*b**3 + 3*b - 7*b**2.
-2*b*(b + 1)**2*(4*b - 1)
Let p(b) be the first derivative of b**5/180 + b**4/48 + b**3/36 + 5*b**2/2 - 6. Let r(g) be the second derivative of p(g). Suppose r(t) = 0. What is t?
-1, -1/2
Let x(v) be the third derivative of v**5/390 + v**4/78 + v**3/39 + 7*v**2. Suppose x(m) = 0. What is m?
-1
Let f(s) = 2*s**2. Let p be (3 + (-2 - 0))*1. Let c be f(p). Suppose 0 - 5/2*u**3 - 4*u**c - 2*u - 1/2*u**4 = 0. Calculate u.
-2, -1, 0
Suppose 6*c = -3*c - 3*c. Determine t so that c*t + 0 + 1/3*t**5 - 1/3*t**2 + 1/3*t**4 - 1/3*t**3 = 0.
-1, 0, 1
Let o = 9 - 6. Factor -2*n**2 + 3*n + n - o*n + 4 + n.
-2*(n - 2)*(n + 1)
Let h(q) be the third derivative of 0*q + 0*q**3 - 1/42*q**5 - 1/735*q**7 + 6*q**2 + 1/42*q**4 + 0 + 1/105*q**6. Solve h(t) = 0 for t.
0, 1, 2
Let y(d) = 2*d**4 + 10*d**3 + 8*d**2 - 36. Let s(w) = -w**3 + 2. Let p(j) = -36*s(j) - 2*y(j). Suppose p(v) = 0. What is v?
0, 2
Suppose 0 = n - 3*n + 4. Let j(q) be the second derivative of -2*q + 0*q**n + 0 - 1/12*q**4 + 0*q**3. Factor j(m).
-m**2
Let s(p) be the third derivative of -1/56*p**8 + 0*p + 0*p**3 + 0 - 6*p**2 - 9/40*p**6 + 1/10*p**7 + 1/4*p**5 - 1/8*p**4. Factor s(c).
-3*c*(c - 1)**3*(2*c - 1)
What is q in 9*q**2 - 22*q - 4 - 17*q**2 + 4*q = 0?
-2, -1/4
Let r(o) be the first derivative of o**4/18 - 2*o**3/9 + o**2/3 + 4*o - 5. Let j(k) be the first derivative of r(k). Determine a so that j(a) = 0.
1
Let y(f) be the second derivative of -5*f**4/36 + 5*f**3/9 + 5*f. Factor y(s).
-5*s*(s - 2)/3
What is m in 2/5*m**2 + 4/5*m + 0 = 0?
-2, 0
Let z = -2/229 + 237/916. Factor -1/2 + 15/4*f**2 - z*f - 19/4*f**3 + 7/4*f**4.
(f - 1)**3*(7*f + 2)/4
Let a = 8 + -8. Let y(m) be the first derivative of -1/3*m**3 + 3/2*m**4 + 0*m - 2 + a*m**2 + 2/3*m**6 - 9/5*m**5. Factor y(j).
j**2*(j - 1)**2*(4*j - 1)
Let d be (-2 + (3 - 0))*4. Solve -24*n**5 + 11*n**4 + 12*n**3 - n**4 + 2*n**2 - n**d + n**4 = 0 for n.
-1/3, -1/4, 0, 1
Let f(q) be the second derivative of 1/84*q**7 - 1/20*q**5 + 5*q - 1/12*q**4 + 1/60*q**6 + 1/4*q**2 + 0 + 1/12*q**3. Suppose f(p) = 0. What is p?
-1, 1
Let t(d) be the first derivative of -3*d**5/5 - 3*d**4/4 + 3*d**3 + 3*d**2/2 - 6*d + 2. Factor t(v).
-3*(v - 1)**2*(v + 1)*(v + 2)
Let u(w) = -2*w**3 + 15*w**2 - 7*w + 2. Let q be u(7). Find o, given that 0 + 0*o + 1/2*o**3 + o**q - 3/2*o**4 = 0.
-2/3, 0, 1
Let c be 68/24 - 3/(-18). Let a(i) be the first derivative of 0*i**4 + 1/11*i**2 - 1/33*i**6 + 4/33*i**c + 0*i - 4/55*i**5 - 3. Factor a(y).
-2*y*(y - 1)*(y + 1)**3/11
Let u(j) be the second derivative of -j**6/6 + j**5 - 5*j**4/4 + 19*j. Factor u(l).
-5*l**2*(l - 3)*(l - 1)
Let n = -10 - -10. Suppose 2*c - 3*c = n. Factor 25/2*z**3 + c + 1/2*z - 5*z**2.
z*(5*z - 1)**2/2
Let a = 8 + -3. Let h(u) be the second derivative of 0*u**2 - u + 0 - 1/40*u**a + 1/24*u**4 + 0*u**3. Find f such that h(f) = 0.
0, 1
Let d(a) = 3*a**3 - 19*a**2 + 19*a + 7. Let y(i) = i**3 - 6*i**2 + 6*i + 2. Suppose 6*h - 56 = 2*h. Let m(v) = h*y(v) - 4*d(v). Find c, given that m(c) = 0.
0, 2
Let z = 29 - 11. Let d(g) = -g**3 + g**2 + g. Let l(k) = -k**3 - 12*k - 8 + 33*k + 3*k**2 - 7*k**3. Let y(o) = z*d(o) - 2*l(o). Find x, given that y(x) = 0.
2
Let l(t) = 4*t - 12. Let r be l(4). Let z(j) be the second derivative of -1/30*j**6 - 5/12*j**4 + 0 - 1/5*j**5 + 0*j**2 - 1/3*j**3 - r*j. What is f in z(f) = 0?
-2, -1, 0
Let q(r) be the first derivative of -1/18*r**4 - r + 0*r**2 - 1/9*r**3 + 1/45*r**6 - 1 + 1/30*r**5. Let g(x) be the first derivative of q(x). Solve g(k) = 0.
-1, 0, 1
Suppose -82*z = -79*z. Factor 1/2*p**2 - 3/2*p + z.
p*(p - 3)/2
Let s(i) be the second derivative of i**6/60 - i**5/10 + i**4/8 + i**3/3 - i**2 + 14*i. Factor s(d).
(d - 2)**2*(d - 1)*(d + 1)/2
Let y(g) be the first derivative of -1/3*g**3 + 2*g + 1/30*g**5 - 2/3*g**2 + 0*g**4 + 1. Let b(f) be the first derivative of y(f). Factor b(s).
2*(s - 2)*(s + 1)**2/3
Let u = 117 + -111. Let x(q) = -q**3 + 3*q**2 - q. Let f be x(2). Factor 3*k**f - 4 + 3*k + 2 - u + 2.
3*(k - 1)*(k + 2)
Let v = 89 + -87. Find s, given that 0 + 8/3*s**2 + 16/3*s**3 + v*s**4 + 0*s = 0.
-2, -2/3, 0
Let p(u) = 3*u**2 - 12*u + 47. Let g(d) = 10*d**2 - 35*d + 140. Let i(x) = 6*g(x) - 21*p(x). Factor i(n).
-3*(n - 7)**2
Let w(s) = s**3 - 12*s**2 - 12*s - 7. Let h be w(13). Let b be 2/8 + h + -6. Solve -b*v**3 - 1/2*v**2 - 1/4*v + 0 = 0 for v.
-1, 0
Suppose 5*t**2 + 0*t**2 - 15*t**3 + 15*t**4 + 35*t**3 = 0. What is t?
-1, -1/3, 0
Let s(u) = -u**2 + 8*u - 5. Let t be s(7). Let d be 3*((-14)/(-12))/7. Find l such that 5/4*l - 3/4*l**t - d = 0.
2/3, 1
Suppose 22*x - 20 = 18*x. Let s(i) be the second derivative of 1/80*i**x + 9/8*i**3 + 3/16*i**4 + 0 - 4*i + 27/8*i**2. Suppose s(j) = 0. What is j?
-3
Factor 3*k**2 - 3*k - 2 + 8*k**3 + 2 - 3*k**4 - 5*k**3.
-3*k*(k - 1)**2*(k + 1)
Suppose -5*b - u + 26 = -3*u, -4*b + 19 = -u. Factor 0*d**3 - 4 + 2*d + 6*d**2 - 2*d**3 + 0 + 43*d**b - 45*d**4.
-2*(d - 1)**2*(d + 1)*(d + 2)
Let g(j) = -2*j**2 - 2*j + 5. Let r(x) = -x**2 - 16*x + 3. Let u be r(-16). Let o(v) = v**2 + v - 3. Let i(s) = u*g(s) + 5*o(s). Factor i(c).
-c*(c + 1)
Let k be (162/297)/(2/(-4) + 2). Factor -2/11*n**5 + 2/11*n - 4/11*n**2 + 0*n**3 + 0 + k*n**4.
-2*n*(n - 1)**3*(n + 1)/11
Let j(a) = 2*a. Let r be j(1). Let y(n) be the third derivative of 0*n - 1/840*n**8 + 0 + 0*n**5 + 1/300*n**6 + 0*n**7 + 0*n**3 + 0*n**4 + n**r. Factor y(w).
-2*w**3*(w - 1)*(w + 1)/5
Let n(w) be the first derivative of w**8/280 - w**7/210 - w**6/60 + w**5/30 - w**3/3 + 2. Let k(y) be the third derivative of n(y). Factor k(u).
2*u*(u - 1)*(u + 1)*(3*u - 2)
Let i(h) be the second derivative of h**4/24 + h**3/6 + h**2/4 + 10*h. Determine w, given that i(w) = 0.
-1
Determine u, given that -10/3*u + 14/3*u**2 + 2/3 - 16/3*u**4 + 2