 - 1. Let z(g) = 18*a(g) + 4*d(g). Factor z(k).
2*(k - 1)*(k + 1)*(k + 3)
Let k(m) = m**5 - m**4 - m**2 + m. Let t(a) = 4*a**5 - 6*a**4 + a**3 - 4*a**2 + 5*a. Let l(q) = -5*k(q) + t(q). Factor l(o).
-o**2*(o - 1)*(o + 1)**2
Let z(w) = w**4 + 35*w**3 + 23*w**2 - 11*w. Let n(a) = 12*a**3 + 8*a**2 - 4*a. Let s(y) = -11*n(y) + 4*z(y). Factor s(p).
4*p**2*(p + 1)**2
Suppose 4*f + 5*l - 82 = 3*l, -2*f + 2*l = -26. Let u = f - 6. Suppose 3 + 6*d**2 + u*d + 5 + d**3 + 0 = 0. What is d?
-2
Let j(m) be the third derivative of -1/660*m**6 + 0*m + 0*m**3 - 1/330*m**5 + 0*m**4 + 0 + 5*m**2. Let j(z) = 0. Calculate z.
-1, 0
Let f(l) = l**4 - l**3 - 1. Let w(c) = -10*c**4 + 13*c**3 + c**2 + 11. Let b(z) = 22*f(z) + 2*w(z). Find h such that b(h) = 0.
-1, 0
Let a(q) = 3*q**4 - 6*q**3 + 3*q**2 - 6. Let u(x) = -3*x**4 + 5*x**3 - 2*x**2 + 5. Let i(r) = 5*a(r) + 6*u(r). Factor i(c).
-3*c**2*(c - 1)*(c + 1)
Suppose -4*q + 20 = 2*o, -16 = -3*q - 2*o - 0*o. Suppose -j + q = 2. Factor -3*d**2 - 4*d**3 - 2*d**2 - 2*d**4 + 3*d**j.
-2*d**2*(d + 1)**2
Let c be (1 - (-12)/(-9))*-18. Suppose 11 = -c*a + 3*a + 4*z, 0 = -4*a + 2*z + 2. Suppose -2/7*n**a + 0*n**2 + 0*n + 4/7*n**4 - 2/7*n**5 + 0 = 0. What is n?
0, 1
Solve -9*w**2 - 3*w**3 + 17*w**5 + 9*w**4 - 8*w**5 - 6*w**5 = 0 for w.
-3, -1, 0, 1
Determine s, given that 6/5*s - 1/5*s**2 - 9/5 = 0.
3
Let h(t) be the third derivative of -t**2 + 1/300*t**6 + 0*t**3 + 0*t**4 + 0*t + 0 + 1/150*t**5. Factor h(v).
2*v**2*(v + 1)/5
Let f(j) be the second derivative of 1/15*j**3 + 0 - 3/50*j**5 + 2/5*j**2 + 2*j - 2/15*j**4. Factor f(i).
-2*(i + 1)**2*(3*i - 2)/5
Suppose -d - 10 = -5*v + 9, -4*d = 3*v - 16. Factor -12*b**2 + 4*b + v*b**4 - 3*b**4 + b**4 + 8*b**3 + 22*b**2.
2*b*(b + 1)**2*(b + 2)
Let v(q) = -6*q**5 - 4*q**4 + 10*q**3 + 4*q**2 - 4*q - 7. Let z(u) = -u**5 + u**3 - 1. Let s(h) = 3*v(h) - 21*z(h). Factor s(b).
3*b*(b - 2)**2*(b - 1)*(b + 1)
Let c = 173/86772 + 2/5165. Let j(k) be the third derivative of 0 + 0*k**3 + c*k**6 + 0*k**5 - 1/735*k**7 + 0*k**4 + 0*k - k**2. Suppose j(t) = 0. What is t?
0, 1
Suppose -a = -1 + 2. Let y be ((a + 2)*2)/1. Determine m so that 76*m**y + 14*m + 32*m + 16 - 200*m**4 + 250*m**5 + 42*m - 173*m**3 - 57*m**3 = 0.
-2/5, 1
Let o(j) be the first derivative of 169*j**4/16 + 13*j**3/2 + 3*j**2/2 + 3*j - 3. Let q(m) be the first derivative of o(m). Factor q(w).
3*(13*w + 2)**2/4
Find m, given that 1/4*m**3 + 1/2 - 3*m**2 + 5/4*m + m**4 = 0.
-2, -1/4, 1
Factor -1 + n**3 + 12*n - 3 - 3*n**4 + 2 + 11*n**2 + 6 - n**5.
-(n - 2)*(n + 1)**3*(n + 2)
Suppose 2*r + 6 = -2*l, 21 = 4*r - 5*l - 12. Factor 8*m + 0 + 1 + 2*m**r + 7 + 0.
2*(m + 2)**2
Let q(z) be the first derivative of -z**5/20 - z**4/8 + z**3 + z**2 - 1. Let x(k) be the second derivative of q(k). Let x(a) = 0. What is a?
-2, 1
Let o = 32/29 - 172/261. Suppose 4/9*j**2 + 14/9*j**4 - 16/9*j**3 - 2/9 - o*j**5 + 4/9*j = 0. Calculate j.
-1/2, 1
Let v(o) = -o. Let a be v(-2). Factor 3 + a*b - 3 + b**4 - b**2 - b - b**3.
b*(b - 1)**2*(b + 1)
Let j(z) be the third derivative of z**8/10080 - z**6/360 + 7*z**5/60 + 2*z**2. Let g(s) be the third derivative of j(s). Factor g(t).
2*(t - 1)*(t + 1)
Let g = -4 + 24/5. Let p(c) = c + 4. Let u be p(-4). Determine m so that 2/5*m + u - g*m**3 + 2/5*m**5 + 0*m**4 + 0*m**2 = 0.
-1, 0, 1
Let o(i) be the first derivative of -4/9*i**3 - 1/3*i**2 + 1 + 0*i - 1/6*i**4. Find m such that o(m) = 0.
-1, 0
Let a(s) be the third derivative of 0*s**5 + 0 + 1/735*s**7 + 0*s**3 + 0*s + 1/210*s**6 + 0*s**4 - 6*s**2. Factor a(y).
2*y**3*(y + 2)/7
Find j such that -j**2 + 7*j - 2*j**2 - j**2 + 17*j - 32 = 0.
2, 4
Let y = 875 + -875. Let 0*h + y + 2/17*h**2 = 0. What is h?
0
Let v(r) be the second derivative of -r**7/3780 - r**4/4 - 2*r. Let l(q) be the third derivative of v(q). Factor l(k).
-2*k**2/3
Let z(t) = 4*t + 3. Let x be z(1). Factor 0*y**2 + 27*y - x*y - y**2 + 16 + 5*y**2.
4*(y + 1)*(y + 4)
Let v be (-1)/(-2) - 74/48. Let b = v + 11/8. Factor 0 + 1/3*k - 1/3*k**4 + b*k**2 - 1/3*k**3.
-k*(k - 1)*(k + 1)**2/3
Suppose 3*c = 5*c - 6. Suppose 0 = -3*p + 2*s + s, -3*p - c*s = -12. Let -l**5 + 0*l**4 + 0*l - p*l**4 + 0*l**4 + l + 2*l**2 = 0. What is l?
-1, 0, 1
Let t be (-1)/(-1)*(-3 - 0). Let w be (-11)/t + (-8)/12. Factor -3*v**2 - 4*v - v**4 + 4*v - 3*v**w - v.
-v*(v + 1)**3
Determine i so that -2/7 - i**2 + 9/7*i = 0.
2/7, 1
Let p(d) = 54*d**2 - 113*d - 41. Let y(i) = 9*i**2 - 19*i - 7. Let n(q) = 6*p(q) - 34*y(q). Solve n(m) = 0.
-2/9, 2
Suppose 13 = 5*n - 12. Determine f so that -3*f**4 + f**3 + 3*f**2 + 0*f**5 - 9*f**5 + 3*f**5 + n*f**3 = 0.
-1, -1/2, 0, 1
Suppose -2*a + 0*a = 0. Let p(o) be the first derivative of 2 + 2/21*o**3 + a*o - 1/7*o**2 + 22/35*o**5 + 9/14*o**4 + 4/21*o**6. Factor p(d).
2*d*(d + 1)**3*(4*d - 1)/7
Let j(r) = -19*r - 3*r**3 - 1 + 2*r**3 + 20*r. Let h(q) = -2*q**4 - 14*q**3 - 54*q**2 - 58*q + 4. Let l(p) = h(p) + 4*j(p). Factor l(w).
-2*w*(w + 3)**3
Let x(j) be the second derivative of -j**6/1800 + j**5/200 - j**4/60 - 3*j**3/2 - 3*j. Let m(l) be the second derivative of x(l). Factor m(c).
-(c - 2)*(c - 1)/5
Let p be 1*(-6)/2*-1. Determine c, given that 11*c**2 - 3*c + 2*c - 4*c**2 + p*c = 0.
-2/7, 0
Suppose 10 = 5*s, i + 2*s - s = 2. Determine f so that -4*f**2 + 2 + 0*f**3 - 2*f**5 - 2*f + i*f**3 + 2*f**4 + 4*f**3 = 0.
-1, 1
Let x(l) be the third derivative of -2*l**8/441 + 8*l**7/441 - 5*l**6/252 - l**5/126 + 5*l**4/252 + l**3/63 - 13*l**2. Factor x(z).
-2*(z - 1)**3*(4*z + 1)**2/21
Find b such that 34*b**2 + 27*b**2 - 64*b**2 + 3 = 0.
-1, 1
Suppose -3 = w - 5. Let n be w + 2 + (-15)/6. Suppose -3/2*t**3 - 3/2*t**2 + 7/2*t**4 - n*t**5 + t + 0 = 0. What is t?
-2/3, 0, 1
Let p(j) = -j**2 + 5*j + 5. Let m(f) = f + 1. Let s be (-23)/(-5) - (-6)/15. Let c(o) = s*m(o) - p(o). Factor c(i).
i**2
Let h be -16 + 19 + (-22)/4 - -3. Let 1/4*z**2 + 0 - h*z = 0. Calculate z.
0, 2
Let p = 23797/30 - 793. Let a(j) be the second derivative of 2*j + 1/14*j**7 + 1/10*j**5 - p*j**6 - 5/6*j**3 + 0 + 1/2*j**2 + 1/2*j**4. Factor a(s).
(s - 1)**3*(s + 1)*(3*s - 1)
Suppose -4*y = 3*j - 11, -j + 0*j + 21 = -3*y. Suppose -2 - 11*f**2 - 27*f**5 - 44*f**2 + 26*f**3 - j*f**5 + 19*f + 3*f**3 + 69*f**4 = 0. Calculate f.
-1, 1/4, 1/3, 2
Suppose -2*n - 5 = j + n, -2*n = -j + 5. Let g be (-1 + j)*(-3)/(-3). Factor -2/9*h**2 + g + 2/9*h.
-2*h*(h - 1)/9
Let c = -1382/5 + 278. Factor -2/5*f + 6/5*f**3 - c*f**2 + 4/5.
2*(f - 1)**2*(3*f + 2)/5
Let i(q) = q**5 - 8*q**4 - q**2 - 5*q - 5. Let n = -7 - -12. Let a(l) = l**5 - 7*l**4 - 4*l - 4. Let j(c) = n*a(c) - 4*i(c). Let j(p) = 0. What is p?
-1, 0, 2
Let o(h) be the third derivative of 0*h - 5*h**2 + 0 - 1/40*h**6 + 1/4*h**5 - 9/2*h**3 - 3/8*h**4. Let o(l) = 0. Calculate l.
-1, 3
Suppose -9*i + 12 = -3*i. Let u(f) be the second derivative of -f + 0*f**i + 1/50*f**5 - 1/30*f**4 - 1/15*f**3 + 0 + 1/75*f**6. Factor u(l).
2*l*(l - 1)*(l + 1)**2/5
Let o(g) = g**3 - 2*g**2 - 6*g - 6. Let y be o(4). Factor 1/2*w**y + 0*w - 1/2*w**5 - 3/2*w**3 + 3/2*w**4 + 0.
-w**2*(w - 1)**3/2
Let z(k) = -3*k - 1. Let s be z(-1). Suppose 0 = t - s*t. Factor -4/3*c + t - 1/3*c**3 - 4/3*c**2.
-c*(c + 2)**2/3
Let v = -7/65 + 4/13. Factor 1/5*l**4 + 0 - v*l**3 + 0*l - 1/5*l**2 + 1/5*l**5.
l**2*(l - 1)*(l + 1)**2/5
Suppose y = 2, -4*y - 8 = -4*t + 8. Let k(z) = 4*z**3 + 16*z**2 - 22*z + 2. Let n(w) = 9*w**3 + 33*w**2 - 45*w + 3. Let v(i) = t*n(i) - 13*k(i). Factor v(f).
2*(f - 2)**2*(f - 1)
Let z(a) be the third derivative of -a**8/1176 + a**7/735 + a**6/420 - a**5/210 - 4*a**2. Solve z(x) = 0 for x.
-1, 0, 1
Suppose 3*j - 3*r + 10 = 22, -4*j + 3*r = -15. Let k be (6/4)/((-2)/(-4)). Factor -2*a**2 + a**j - 2*a**3 - 4*a + k*a.
-a*(a + 1)**2
Let t(v) be the second derivative of -v**4/12 - 5*v**3/6 - v**2 + 4*v. Let y(l) = 5*l**2 + 26*l + 10. Let f(j) = 11*t(j) + 2*y(j). Factor f(b).
-(b + 1)*(b + 2)
Factor -2/17*n**5 + 2/17*n**3 + 0*n**2 + 0*n**4 + 0*n + 0.
-2*n**3*(n - 1)*(n + 1)/17
Suppose -3*d = 3*q + 6, q + 5*d - 6 = 4. Let h be 0 + (13/q - -3). Find a, given that 2/5 - 4/5*a + h*a**2 = 0.
1
Let l be 1/(-3) + 95/15. Suppose o = l*o. Factor o - 1/4*w + 1/4*w**2.
w*(w - 1)/4
Factor 2/11*c**2 + 2/11*c**3 + 0 - 4/11*c.
2*c*(c - 1)*(c + 2)/11
Let g(i) be the third derivative of i**7/840 - i**6/480 + 11*i**2. Deter