1
Let b(v) = v**2 - v. Let l(f) = 12*f**2 - 24*f. Let m(s) = 15*b(s) - l(s). Factor m(u).
3*u*(u + 3)
Let s(l) = -l + 13. Let u be s(9). Let j(i) be the first derivative of -1/4*i**u + 1/2*i**2 - 1/3*i**3 + i - 3. Factor j(x).
-(x - 1)*(x + 1)**2
Let 2/3*o**4 + 8/3*o**3 - 32/3 + 0*o**2 - 32/3*o = 0. What is o?
-2, 2
Suppose -5*w + 10 = -0. Let h = w - 0. Determine o, given that 3*o**2 + 7*o - 3*o + 10*o**3 + 11*o**h = 0.
-1, -2/5, 0
Let t be (-55)/18 - -3 - (-1)/2. Suppose -2/9*l**4 + t*l + 4/9*l**5 - 8/9*l**3 - 2/9 + 4/9*l**2 = 0. What is l?
-1, 1/2, 1
Let v(r) be the second derivative of 0*r**2 - 2/3*r**3 + 0 - 3*r - 1/3*r**4 - 1/20*r**5. Suppose v(d) = 0. Calculate d.
-2, 0
Factor -4 + 4 - 4*k + 4*k**2 - 13 + 5.
4*(k - 2)*(k + 1)
Let v(s) = s + 4. Let l be v(-3). Let x(r) = 3*r**3 - r. Let m be x(l). Solve -g + 2*g**m + g = 0.
0
Let n(z) be the second derivative of -z**5/20 + z**4/4 + z**3/6 - 3*z**2/2 + 4*z. Factor n(a).
-(a - 3)*(a - 1)*(a + 1)
Let k(c) = -14*c**3 - 40*c**2 + 14*c + 2. Let f(n) = -n**2 + n + 1. Let o(a) = 2*f(a) - k(a). Find w, given that o(w) = 0.
-3, 0, 2/7
Let w be 8 + 8*(-9)/9. Factor w + 0*r + 2/3*r**2.
2*r**2/3
Factor 0 - 3/5*h**2 + 0*h + 0*h**3 + 3/5*h**4.
3*h**2*(h - 1)*(h + 1)/5
Let k be ((-329)/(-70) - 5)*-2. Factor -k + 0*q + 3/5*q**2.
3*(q - 1)*(q + 1)/5
Let f(j) be the second derivative of -j**7/2016 + 7*j**6/2880 - j**5/240 - j**4/4 + 3*j. Let a(o) be the third derivative of f(o). Let a(d) = 0. What is d?
2/5, 1
Let x = -7 - -12. Let o(n) be the third derivative of 0*n**3 + 1/270*n**x + 0 + 1/108*n**4 - n**2 + 0*n. Factor o(b).
2*b*(b + 1)/9
Let c(j) be the first derivative of 3*j**5/20 - j**4/3 + j**3/6 - j - 3. Let q(x) be the first derivative of c(x). Let q(y) = 0. Calculate y.
0, 1/3, 1
Let s(u) = u**5 - u**4 - u**3 - u**2 - u - 1. Let z(a) = 7*a**5 - 5*a**4 - 11*a**3 - 7*a**2 + 2*a - 10. Let v(w) = -6*s(w) + z(w). Find r, given that v(r) = 0.
-2, 1
Suppose g - 3 = 2. Let d = 8 - g. Determine j so that -5*j**4 + d*j**4 + 4*j + j**4 + 4*j**3 - 6*j**2 - 1 = 0.
1
Let b be (-1)/1 + -7*(-10)/14. Find f, given that 1/6*f**b - 1/3*f**2 + 0*f**3 + 1/6 + 0*f = 0.
-1, 1
Let m(s) be the third derivative of 3*s**7/350 - s**6/40 + s**5/50 - 20*s**2. Solve m(l) = 0.
0, 2/3, 1
Let n be (-3)/2*(-32)/24. Let u be 1/(-2) + n/2. Factor r - 1/2 - u*r**2.
-(r - 1)**2/2
Let a(j) = -7 - 6*j + 2*j + 4*j + j. Let s be a(7). Let 0 + 1/4*k**2 + s*k = 0. What is k?
0
Suppose 24 - 8 = 8*o. Let d(x) be the first derivative of -4/3*x**4 + 1/3*x**o + 2 - 12/5*x**5 + 4/9*x**3 - x**6 + 0*x. Solve d(f) = 0.
-1, -1/3, 0, 1/3
Let w(s) be the first derivative of 0*s**2 - 1/3*s**6 + 1/2*s**4 - 3 + 0*s + 2/3*s**3 - 2/5*s**5. Determine r so that w(r) = 0.
-1, 0, 1
Let w = 21/10 - 43/30. Factor 4/3*l - w*l**3 - 2/3*l**2 + 0.
-2*l*(l - 1)*(l + 2)/3
Let p(x) be the second derivative of 9*x + 0 + 1/3*x**2 - 1/3*x**3 - 5/18*x**4 + 4/45*x**6 + 1/10*x**5. Let p(u) = 0. What is u?
-1, 1/4, 1
Let a(c) be the third derivative of 0*c**3 + 0 + 7/360*c**6 + 0*c + c**2 + 0*c**4 + 1/90*c**5. Factor a(g).
g**2*(7*g + 2)/3
Let w(z) be the third derivative of 0*z - 4*z**2 + 0 + 0*z**4 + 1/480*z**6 - 1/240*z**5 + 0*z**3. Determine h, given that w(h) = 0.
0, 1
Let y(j) = j**2 - j - 2. Let c(s) = -4*s**2 + 3*s + 7. Let m(n) = 6*c(n) + 22*y(n). Factor m(l).
-2*(l + 1)**2
Suppose -3*a + 31 = 5*d - a, 5*d - a - 22 = 0. Suppose -q = -0*q - d*o + 18, 4*o - 16 = 0. Factor -2*h + 2*h**3 + 4*h**3 + 9*h**2 + 0*h**q + 5*h.
3*h*(h + 1)*(2*h + 1)
Let d(f) = -2*f - 12. Let s be (3 - -2)*12/(-10). Let r be d(s). Factor -z**3 + r*z**2 + z + 1/2 - 1/2*z**4.
-(z - 1)*(z + 1)**3/2
Let s be (-202)/(-60) - 3/18. Let a = s + -134/45. Factor -2/3*w**3 + 0 + 2/3*w**4 + 2/9*w**2 + 0*w - a*w**5.
-2*w**2*(w - 1)**3/9
Let p = -43/45 - -14/9. What is q in 0*q**2 + 0 + 3/5*q - p*q**3 = 0?
-1, 0, 1
Suppose 0*z + 172 = -4*z. Let p = z - -131/3. Factor p*s + 0 - 2/3*s**2.
-2*s*(s - 1)/3
Let m(p) be the first derivative of 3*p**4/20 - p**3/5 - 3*p**2/2 - 9*p/5 - 26. Factor m(q).
3*(q - 3)*(q + 1)**2/5
Let h = 6 - 4. Factor -2*g**3 - 15 + 15 - 2*g + 2*g**2 + h*g**2.
-2*g*(g - 1)**2
Determine o, given that -18 - 142*o**4 - 230*o**2 + 11*o**3 + 38*o**5 + 247*o**3 - 6*o**5 - 2*o**4 + 102*o = 0.
3/4, 1
Let c = 2 - 2. Suppose -5 = -3*q + 1. Factor y**q + y + c*y + 2*y + 2.
(y + 1)*(y + 2)
Let j = -356 - -1433/4. Suppose 9*x + 6 - 9/2*x**2 + j*x**4 - 21/4*x**3 = 0. What is x?
-1, -2/3, 2
Suppose 3*i - 2*g + 4 = 0, -1 = 2*i - 5*i + g. Factor -1/2*r + 1/4*r**3 + 0 - 1/4*r**i.
r*(r - 2)*(r + 1)/4
Factor f + 1/4 + 1/2*f**3 + 5/4*f**2.
(f + 1)**2*(2*f + 1)/4
Let r = -2833 - -351277/124. Let p = 4/31 - r. What is q in 0*q**2 - p*q**3 + 0 + 0*q = 0?
0
Let t be ((-2)/(-3))/(3/27). Let o(d) be the second derivative of -7/120*d**t + d - 9/16*d**4 - 1/4*d**2 + 0 + 13/24*d**3 + 23/80*d**5. Solve o(z) = 0.
2/7, 1
Let b(n) be the second derivative of -n**4/4 - 2*n**3 - 6*n**2 + 2*n. Find z, given that b(z) = 0.
-2
Solve 0*f + 0 - 2/7*f**4 + 0*f**3 + 2/7*f**2 = 0 for f.
-1, 0, 1
Let n(t) be the first derivative of -3*t**5/20 + 3*t**4/8 + 3*t**3/4 - 3*t**2/2 - 3*t - 14. Factor n(d).
-3*(d - 2)**2*(d + 1)**2/4
Suppose -13 = -4*z - g, -2*z - 3*g + 4 = -5*g. Let v(l) be the first derivative of 0*l + 2/27*l**3 - z + 1/9*l**2. Find h, given that v(h) = 0.
-1, 0
Let c be 3*(0 + (-4)/(-6)). Factor 4/7*b**3 - 2/7*b**4 + 0 - 20/7*b**5 + 0*b + 0*b**c.
-2*b**3*(2*b + 1)*(5*b - 2)/7
Let t(b) be the first derivative of b**6/180 - b**5/60 - 4*b**3/3 + 2. Let y(q) be the third derivative of t(q). Factor y(o).
2*o*(o - 1)
Let u(c) be the first derivative of -c**6/18 + 2*c**5/5 - c**4 + 10*c**3/9 - c**2/2 + 8. Factor u(n).
-n*(n - 3)*(n - 1)**3/3
Let 8/3*j**2 + 8*j**4 - 1/3*j + 0 - 3*j**5 - 22/3*j**3 = 0. What is j?
0, 1/3, 1
Let k(y) be the second derivative of 0 - 7/10*y**5 + 6*y - 5/2*y**4 - 3*y**3 + 0*y**2 - 1/15*y**6. Factor k(w).
-2*w*(w + 1)*(w + 3)**2
Let p(q) be the second derivative of 0*q**2 + 1/126*q**7 - 1/45*q**6 + 1/60*q**5 + 0*q**3 - q + 0 + 0*q**4. Factor p(m).
m**3*(m - 1)**2/3
Solve 533 + 4*k**2 - 533 + 4*k**3 = 0 for k.
-1, 0
Let o be (4/84)/((-48)/(-56)). Let b(c) be the first derivative of -4 - 2/9*c**3 - 1/6*c**4 - 1/3*c - o*c**6 + 1/5*c**5 + 1/2*c**2. Factor b(z).
-(z - 1)**4*(z + 1)/3
Let u(x) be the first derivative of 2*x**5/15 - x**4/6 - 2*x**3/9 + x**2/3 + 19. Suppose u(c) = 0. Calculate c.
-1, 0, 1
Let j(f) be the second derivative of 0*f**2 - 1/2*f**4 - f + 1/2*f**3 + 0 + 3/20*f**5. Find u, given that j(u) = 0.
0, 1
Let n = -1264/117 + 126/13. Let s = -14/45 - n. Factor 4/5 + 2/5*g**3 - s*g**2 - 2/5*g.
2*(g - 2)*(g - 1)*(g + 1)/5
Let z = 1183/12 - 381/4. Factor z*s - 2*s**2 + 2/3*s**4 - 2/3*s**3 - 4/3.
2*(s - 1)**3*(s + 2)/3
Let o(n) = 31*n**3 - 71*n**2 - 42*n + 73. Let m(b) = -15*b**3 + 36*b**2 + 21*b - 36. Let t(f) = -13*m(f) - 6*o(f). Factor t(z).
3*(z - 5)*(z + 1)*(3*z - 2)
Let d(o) be the first derivative of 5*o**4 - 16*o**3 + 8*o**2 - 7. Factor d(g).
4*g*(g - 2)*(5*g - 2)
Let c(p) be the second derivative of -p**5/20 + p**4/6 - p**3/6 + 8*p. Factor c(n).
-n*(n - 1)**2
Let v(a) be the second derivative of a**5/20 + a**4/4 + a**3/2 + a**2/2 + 11*a. Solve v(c) = 0.
-1
Let i(y) be the third derivative of -2*y**7/735 - y**6/420 - 6*y**2. Factor i(h).
-2*h**3*(2*h + 1)/7
Find x, given that 7/4*x**3 + 0 - 9/4*x**2 + 1/2*x = 0.
0, 2/7, 1
Suppose -6 = -2*r - r. Suppose -3*k = r*k. Factor 0 - 6/7*f**3 - 2/7*f**5 + k*f + 6/7*f**4 + 2/7*f**2.
-2*f**2*(f - 1)**3/7
Let j(k) = -k**3 + 2*k**2 + 4*k + 1. Let d(l) = -l**2 - 5*l - 3. Let m be d(-2). Let g be j(m). Factor y**3 + 5/2*y**g - 2 - 15/2*y**2 - 8*y.
(y - 2)*(y + 1)**2*(5*y + 2)/2
Let g(o) = 7*o**2. Let v be g(-1). Let m(j) = -j + 7. Let b be m(v). Factor 4/3*p**4 + b*p**3 + 0 - 2/3*p + 2/3*p**5 - 4/3*p**2.
2*p*(p - 1)*(p + 1)**3/3
Solve 3/8*j**2 - 1/4 + 1/8*j - 1/8*j**3 - 1/8*j**4 = 0 for j.
-2, -1, 1
Let h(p) = p - 2. Let d be h(4). Factor 12*n - 8*n**2 - 27 + 24*n - 4*n**d.
-3*(2*n - 3)**2
Suppose -9 + 4 = -t. Let a = t - 2. Determine v so that -5*v**3 - v - v**4 + 2*v**a - 4*v**2 + v**2 = 0.
-1, 0
Let j(q) be the third derivative of -2/3*q**3 - 1/60*q**5 + 1/6*q**4 + 0*q + 0 - 3*q**2. Factor j(d).
-(d - 2)**2
Let c be (-32)/(-15) - (-20)/(-150). Facto