. Factor g + 1/3*l - 1/3*l**2.
-l*(l - 1)/3
Let f(j) = j**3 + 9*j**2 + 8*j + 5. Let q be f(-8). Suppose -2*t + q*y = -t + 15, -2*y + 6 = -5*t. Solve -3/4*z**2 + t + 3/4*z**4 - 1/2*z**3 + 1/2*z = 0.
-1, 0, 2/3, 1
Let j be 1/7 - 40/(-14). Factor -1/6*c**j + 0 + 0*c**2 + 1/6*c.
-c*(c - 1)*(c + 1)/6
Solve 4/3*q**3 - 5/3*q**5 + 2*q**2 - 2*q**4 + 1/3*q + 0 = 0.
-1, -1/5, 0, 1
Suppose 2 = c + 4*j, 0 = 4*c + j - 7 - 1. Let v = c + 1. What is g in -g + 1/3*g**5 + 2/3*g**v - g**4 + 2/3*g**2 + 1/3 = 0?
-1, 1
Factor -8*t**2 - 6*t**2 + 10*t + 9*t**2 - 5*t**3.
-5*t*(t - 1)*(t + 2)
Let b(r) be the third derivative of r**6/540 - 4*r**5/135 + 5*r**4/36 - 9*r**2 - 2. Suppose b(a) = 0. What is a?
0, 3, 5
Let a = -1 + 4/3. Suppose 0*v + 2 = -v, 4*v = 2*t - 16. Determine u, given that a + 1/3*u**t + 0*u**3 - 2/3*u**2 + 0*u = 0.
-1, 1
Let x(c) be the third derivative of -c**6/30 + 8*c**5/15 - 13*c**4/6 + 4*c**3 + 4*c**2. Factor x(p).
-4*(p - 6)*(p - 1)**2
Let c(g) = -5*g**2 + 20*g - 21. Let k(m) = m**2 - 4*m + 4. Let w(i) = 2*c(i) + 11*k(i). Let z be w(4). Factor -2*r - 1/2*r**3 + 0 + z*r**2.
-r*(r - 2)**2/2
Let u(l) be the first derivative of l**4/16 - l**3/3 + 5*l**2/8 - l/2 + 7. Determine t so that u(t) = 0.
1, 2
Let k(r) be the second derivative of 0*r**3 + 1/10*r**5 + 0 + 3*r + 0*r**2 + 1/3*r**4 - 1/15*r**6. Factor k(n).
-2*n**2*(n - 2)*(n + 1)
Let n(v) be the first derivative of -5*v**3/3 + 20*v**2 - 80*v - 12. Determine j, given that n(j) = 0.
4
Let i(b) be the third derivative of 1/6*b**3 + 0 + 0*b + 3*b**2 + 1/40*b**5 + 5/48*b**4. Factor i(u).
(u + 1)*(3*u + 2)/2
Let q = 0 + 10. Let x be 0 - (26/q + -3). Suppose 0*h + 0 - 2/5*h**3 + 2/5*h**4 + x*h**5 - 2/5*h**2 = 0. What is h?
-1, 0, 1
Let x(w) be the third derivative of -w**5/180 + w**4/9 - 8*w**3/9 - 7*w**2. Factor x(o).
-(o - 4)**2/3
Let w(j) be the second derivative of j**6/10 + 3*j**5/20 - j**4/4 - j**3/2 + 3*j. Suppose w(n) = 0. What is n?
-1, 0, 1
Let d(w) be the second derivative of w**4/66 + 2*w**3/33 + w**2/11 + 10*w. Factor d(b).
2*(b + 1)**2/11
What is x in 4*x**3 - 8*x + x**2 + 5 - 2*x**4 - 13 + 5*x**2 = 0?
-1, 2
Let r = -647 + 12943/20. Let g(z) be the second derivative of 0 + 4*z**3 + 2*z - 6*z**2 + r*z**5 - 5/4*z**4. Determine h so that g(h) = 0.
1, 2
Let -2/11*w**2 + 0 - 4/11*w = 0. What is w?
-2, 0
Find c, given that 4/3*c**2 - 4/3*c + 0 + 26/3*c**4 + 9*c**3 + 7/3*c**5 = 0.
-2, -1, 0, 2/7
Suppose 3*f - 5*b = 65, -3*f = -f - b - 55. Let y be (8/f)/(1/6). Find p such that 2/5*p**3 - y*p**2 + 8/5*p + 0 = 0.
0, 2
Suppose 0 = -6*q + 24*q. Factor -2/9*v**4 + 0 + 0*v + q*v**3 + 2/9*v**2.
-2*v**2*(v - 1)*(v + 1)/9
Let z(w) be the third derivative of 2*w**7/735 + w**6/210 - w**5/105 - w**4/42 + 12*w**2. Factor z(t).
4*t*(t - 1)*(t + 1)**2/7
Let b(f) = -5*f**2 + 15*f - 5. Let l(k) = k**3 - 5*k**2 + 16*k - 6. Let c(a) = 6*b(a) - 5*l(a). Factor c(n).
-5*n*(n - 1)*(n + 2)
Let a(j) be the second derivative of -j**5/25 + 2*j**4/15 + 2*j**3/5 + 2*j. Let a(k) = 0. Calculate k.
-1, 0, 3
Suppose 0 = -4*d - g - 8, 6 = -5*d + 2*d - 3*g. Let n(z) = z**2 + 2*z - 3. Let t(v) = -2*v**2 - 5*v + 7. Let o(i) = d*t(i) - 5*n(i). Factor o(u).
-(u - 1)*(u + 1)
Suppose 4*c = 10 + 2. Let f(w) = w**2 + w - 1. Let a(n) = -5*n**2 - 3*n + 3. Let s(t) = c*f(t) + a(t). Determine y, given that s(y) = 0.
0
Factor 6/13 + 2/13*x**2 + 8/13*x.
2*(x + 1)*(x + 3)/13
Let l(s) = 6*s + 5. Let i be l(-4). Let m = i + 21. Let 22/7*q**m - 4/7 + 82/7*q**3 - 138/7*q**4 - 18/7*q + 8*q**5 = 0. What is q?
-2/7, -1/4, 1
Let k(s) = -s**2 + 8*s - 7. Let g be k(6). Determine q, given that q**3 - 3*q**4 - q**g + 2*q**4 + q**4 = 0.
-1, 0, 1
Suppose -5*f + 2*r + 1 = -r, 2*f = -5*r + 19. Let c = 0 + 0. Factor 2 - f*z**2 + 2*z**3 + 4*z - 6*z + c*z**3.
2*(z - 1)**2*(z + 1)
Let b(o) = -o**3 + 3*o. Let k be 10 + (0 + -2)/(-2). Let s(p) = -6*p**3 - p**2 + 16*p. Let m(y) = k*b(y) - 2*s(y). Factor m(l).
l*(l + 1)**2
Let n(b) = 3*b**2 - 5*b - 2. Let x be n(2). Let j(g) be the first derivative of 1/4*g**4 + 2/5*g**5 - 2 - 2/3*g**3 + x*g**2 - 1/6*g**6 + 0*g. Factor j(q).
-q**2*(q - 2)*(q - 1)*(q + 1)
Let x(a) be the second derivative of -a**6/15 + 3*a**5/10 - a**4/2 + a**3/3 + 13*a. Factor x(h).
-2*h*(h - 1)**3
Let j = 13 + -10. Suppose -4*v - r + 12 = 0, -7*v + j*r - 4 = -3*v. Suppose -5/3*b**v - 4/3 + 4*b = 0. Calculate b.
2/5, 2
Suppose -4*i + i - 4*d = -22, -26 = -5*i - 4*d. Determine v, given that 3 + v**3 + i*v + 2*v + 5*v + 5*v**2 - 2*v = 0.
-3, -1
Factor 75/4*q**3 + 0 + 5/4*q**5 + 0*q - 125/4*q**2 + 45/4*q**4.
5*q**2*(q - 1)*(q + 5)**2/4
Let i(v) = v**3 + 8*v**2 - 9*v + 3. Let r be i(-9). Suppose 4*z - 13 = -5*x + 3, -3*x - 16 = -4*z. What is q in -r*q**2 + 0 + z + 2*q**3 + q**3 - 4*q**3 = 0?
-2, 1
Let n(l) = l**4 + l**3 - 3*l**2 - 5*l + 2. Let f(i) = -15*i**4 - 15*i**3 + 48*i**2 + 81*i - 33. Let w(c) = 2*f(c) + 33*n(c). Let w(s) = 0. Calculate s.
-1, 0, 1
Let u = 1639/2 + -837. Let h = -17 - u. Find n such that 1/2*n**3 + n**2 - 1/4 - h*n - 3/4*n**4 = 0.
-1, -1/3, 1
Let r(t) be the third derivative of 9*t**8/196 - 17*t**7/490 + t**6/140 + 7*t**2. Factor r(g).
3*g**3*(4*g - 1)*(9*g - 2)/7
Let u be (-15)/((-675)/(-10))*-9. Factor -18/11*a**3 + 2/11*a**2 + 0 + 2/11*a - 8/11*a**5 + u*a**4.
-2*a*(a - 1)**3*(4*a + 1)/11
Let f(x) be the first derivative of -x**6/24 + x**5/10 - x**4/16 - 2. Suppose f(k) = 0. What is k?
0, 1
Factor 0 - 2/11*m**3 - 4/11*m + 6/11*m**2.
-2*m*(m - 2)*(m - 1)/11
Let d(b) be the second derivative of -b**6/150 + b**5/100 + b + 1. Factor d(g).
-g**3*(g - 1)/5
Let q(j) be the first derivative of -j**6/3 + 8*j**5/5 - 3*j**4 + 8*j**3/3 - j**2 + 4. Factor q(w).
-2*w*(w - 1)**4
Factor -6*n - 24*n**3 + 28*n**3 - 2*n + 4*n**2.
4*n*(n - 1)*(n + 2)
Suppose 7*s = 2*s + 10. Factor 0 + 1/2*h - 1/2*h**s.
-h*(h - 1)/2
Suppose -17*n - 36 = -70. Let -9/4*b - 7/2*b**3 + 4*b**n + 1/2 - 1/4*b**5 + 3/2*b**4 = 0. Calculate b.
1, 2
Find m, given that -3*m + 51*m - 10 - 2 + 9*m**3 - 39*m**2 = 0.
1/3, 2
Let g(o) be the first derivative of -4 + 1/15*o**5 + 0*o**3 - 1/3*o + 1/3*o**2 - 1/6*o**4. Let g(a) = 0. What is a?
-1, 1
Find u, given that 0*u + 0 + 1/4*u**3 + 3/4*u**4 - 1/2*u**2 = 0.
-1, 0, 2/3
Let j(b) = 4*b**4 - 6*b**3 + 7*b**2 + 21*b - 32. Let s(g) = g**4 + g**2 - g. Let o(x) = 2*j(x) - 6*s(x). Solve o(k) = 0.
-2, 2, 4
Let w(i) be the third derivative of -i**7/1260 + i**6/180 - i**5/120 + 5*i**2. Factor w(t).
-t**2*(t - 3)*(t - 1)/6
Let h be (12/(-15))/((-4)/(-30)). Let t be ((-32)/(-264))/((-2)/h). Factor 0*m**2 - t*m**3 + 2/11 - 2/11*m**4 + 4/11*m.
-2*(m - 1)*(m + 1)**3/11
Let i(d) = 2*d**2 + 2*d. Let w be i(-2). Let n be 6 + w/6*-3. Factor -c - c + 2*c**2 - 2 - n*c**2 + 2*c**3 + 4.
2*(c - 1)**2*(c + 1)
Let k(c) be the first derivative of c**6/50 + 3*c**5/50 - c**4/20 - c**3/5 + 5*c + 7. Let u(i) be the first derivative of k(i). Find f, given that u(f) = 0.
-2, -1, 0, 1
Solve 0 + 6/5*k**3 - 3/5*k**4 - 6/5*k + 3/5*k**2 = 0 for k.
-1, 0, 1, 2
Let i(o) be the second derivative of o**6/10 + 3*o**5/4 + 9*o**4/4 + 7*o**3/2 + 3*o**2 + 14*o. Factor i(v).
3*(v + 1)**3*(v + 2)
Factor 12*k**2 + 16 - 23*k**2 + 5*k**2 + 20*k + 10*k**2.
4*(k + 1)*(k + 4)
Let b be (1/(-3))/(1/3). Let f be (-6)/3 - b*2. Find u, given that 0 + f*u**2 - 1/4*u**3 + 0*u - 1/4*u**5 + 1/2*u**4 = 0.
0, 1
Let f = 1/89 - 183/445. Let x = f - -9/10. Factor r**3 + r**2 - x*r**5 - 1/2 - 1/2*r**4 - 1/2*r.
-(r - 1)**2*(r + 1)**3/2
Suppose -3*s + 5 = -2*s. Suppose -2*g + 2 = 2*x, g - 7 = -3*x - 0. Let 1/2*a**s - 1/2*a**x + 0*a - 1/2*a**2 + 1/2*a**4 + 0 = 0. What is a?
-1, 0, 1
Suppose 5*y + 5*q = 35, -3*q + 9 = -y - 0*q. Factor -5*r - 2 - 4*r**2 + 0 + 0*r**2 - 4*r**3 + y*r**3.
-(r + 1)**2*(r + 2)
Let z(u) = 4*u**2 + 12*u + 2. Let g(i) = i**2 + i + 1. Let r(j) = -6*g(j) + z(j). Find a such that r(a) = 0.
1, 2
Let t(o) be the second derivative of 1/2*o**2 + 1/48*o**4 + 0 - o - 1/24*o**3 - 1/240*o**5. Let k(w) be the first derivative of t(w). Solve k(m) = 0.
1
Let k(q) be the third derivative of 0*q + 1/4*q**5 + 0 - 7/8*q**4 + q**2 + 1/10*q**6 - q**3. Factor k(m).
3*(m - 1)*(m + 2)*(4*m + 1)
Let s be (-1 + 0 - 5)*(-44)/110. Determine y, given that 0 + 3/5*y**3 + 12/5*y**4 - s*y**2 - 3/5*y = 0.
-1, -1/4, 0, 1
Solve -2/5*z**4 + 8/5*z**2 + 0 - 2/5*z**3 + 8/5*z = 0 for z.
-2, -1, 0, 2
Let m(p) be the fi