1)/3
Let d be 0 + (-1 - -35)/1. Let r(u) = -u**3 + 6*u**2 - 5*u + 3. Let y(v) = 6*v**3 - 35*v**2 + 29*v - 17. Let a(c) = d*r(c) + 6*y(c). Let a(k) = 0. Calculate k.
0, 1, 2
Let w = 422 - 1252/3. Let x(k) = k**3 - 3*k**2 - k + 6. Let r be x(2). Factor w*j**3 + 0 + r*j - 4/3*j**2.
2*j**2*(7*j - 2)/3
Let m = 5 - 18. Let l be m/169*-3*4. Factor -16/13 - 2/13*a**3 - l*a**2 - 24/13*a.
-2*(a + 2)**3/13
Determine u, given that -4*u**4 + 14*u + 15*u**2 - 23*u**3 - 4 + 0 - 5*u**3 + 14*u**5 - 7*u**2 = 0.
-1, 2/7, 1
Let f(z) be the third derivative of -2/3*z**5 - 2/3*z**3 + 0 - 3*z**2 - 5/6*z**4 + 0*z - 2/21*z**7 - 1/3*z**6 - 1/84*z**8. What is i in f(i) = 0?
-1
Let p = -6/125 + 231/125. Factor p*w - 3*w**2 + 3/5*w**3 + 27/5.
3*(w - 3)**2*(w + 1)/5
Let n(v) = 3*v - 1. Let h be n(2). Suppose -15 = -h*m - 0*m. Factor y**3 + y - 3*y**2 + y**2 + 3*y - 3*y**m.
-2*y*(y - 1)*(y + 2)
Let h(l) be the third derivative of -4*l**2 + 0*l + 1/2*l**3 + 0 + 1/12*l**5 + 1/120*l**6 + 7/24*l**4. Factor h(b).
(b + 1)**2*(b + 3)
Let g(u) be the third derivative of u**7/168 - 7*u**6/480 - u**5/30 + u**4/24 - 3*u**2. Factor g(s).
s*(s - 2)*(s + 1)*(5*s - 2)/4
Let w(s) = -4*s**5 + 6*s**4 + 8*s**3 - 22*s**2 + 12*s - 2. Let q(g) = -g**5 + g**3 - 1. Let d(t) = 2*q(t) - w(t). Factor d(k).
2*k*(k - 3)*(k - 1)**2*(k + 2)
Let t(g) be the third derivative of -g**7/35 + g**6/30 + g**5/10 - g**4/6 - 8*g**2. Factor t(z).
-2*z*(z - 1)*(z + 1)*(3*z - 2)
Let v(j) be the third derivative of j**5/300 + j**4/60 + j**3/30 + 6*j**2. Determine s so that v(s) = 0.
-1
Let m(t) be the second derivative of -t**5/70 - t**4/21 - t**3/21 - 9*t. Factor m(c).
-2*c*(c + 1)**2/7
Let c(p) = -12*p**3 + 8*p**2 + 12*p. Let l(r) = -r**3 + r + 1. Let x(a) = -c(a) + 8*l(a). Determine b, given that x(b) = 0.
-1, 1, 2
Let j(t) be the first derivative of -t**8/4200 - t**7/3150 - 8*t**3/3 - 2. Let m(y) be the third derivative of j(y). Let m(p) = 0. Calculate p.
-2/3, 0
Let w(g) = 10*g**2. Let p(b) = 11*b**2 + 1. Let f(y) = -5*p(y) + 6*w(y). Factor f(t).
5*(t - 1)*(t + 1)
Let o(u) be the first derivative of -4*u**2 - 8*u + 2*u**3 + u**4 - 2/5*u**5 - 4. Factor o(a).
-2*(a - 2)**2*(a + 1)**2
Let i(f) be the third derivative of f**7/252 + f**6/144 - 5*f**5/72 + 5*f**4/48 - 16*f**2. Factor i(p).
5*p*(p - 1)**2*(p + 3)/6
Suppose -10 = 76*n - 81*n. Suppose 9/2 + 1/2*k**n + 3*k = 0. Calculate k.
-3
Let d(u) be the first derivative of 2*u**6/21 - u**5/5 + u**4/14 + u**3/21 - 10. Determine q so that d(q) = 0.
-1/4, 0, 1
Let r(w) be the first derivative of w**4/14 + 2*w**3/21 - 5*w**2/7 + 6*w/7 - 8. Factor r(n).
2*(n - 1)**2*(n + 3)/7
Let p(u) be the second derivative of 1/4*u**4 - 3*u**2 + 1/2*u**3 + 4*u + 0. Solve p(o) = 0 for o.
-2, 1
Let d(g) be the first derivative of g**6/255 + g**5/170 - g**4/102 - g**3/51 + 9*g + 4. Let w(b) be the first derivative of d(b). Solve w(r) = 0.
-1, 0, 1
Factor 2/5*r**2 - 12/5 - 2*r.
2*(r - 6)*(r + 1)/5
Let y(x) be the third derivative of x**8/336 - x**7/105 + x**5/30 - x**4/24 + 15*x**2. Let y(i) = 0. Calculate i.
-1, 0, 1
Suppose -2*f + 8 = 2*f. Let i be f + (-7)/(-5) + -3. Let i*y**3 - 1/5*y**2 + 0*y + 0 - 1/5*y**4 = 0. What is y?
0, 1
Let b(t) be the first derivative of 3*t**4/20 - 6*t**2/5 + 12. Factor b(h).
3*h*(h - 2)*(h + 2)/5
Let c(g) = -5*g**2 + g - 2. Let o be c(2). Let k be (-18)/15*o/6. Find p, given that -2*p - 4 + k + p**2 = 0.
0, 2
Let v(d) = -2*d**2 - 12*d - 21. Let z(l) = -1. Let h(n) = -2*v(n) + 22*z(n). What is c in h(c) = 0?
-5, -1
Let h(m) be the second derivative of -m**7/8820 - m**6/2520 + m**5/210 - m**4/4 + 2*m. Let q(u) be the third derivative of h(u). Factor q(p).
-2*(p - 1)*(p + 2)/7
Let u be 2371/9 - (-2 - -3). Let q = u + -262. Suppose 0 - 4/9*p**3 - 10/9*p**2 + 10/9*p**4 + q*p = 0. Calculate p.
-1, 0, 2/5, 1
Let u(w) be the first derivative of w**6/36 + w**5/30 - w**4/12 - w**3/9 + w**2/12 + w/6 + 4. Suppose u(c) = 0. What is c?
-1, 1
Let i(o) be the third derivative of 5*o**8/336 - o**7/42 - o**6/24 + o**5/12 + 29*o**2. Find n, given that i(n) = 0.
-1, 0, 1
Let w(x) be the second derivative of -1/10*x**5 - 2/3*x**4 - 4/3*x**3 + 0 - 2*x + 0*x**2. Factor w(d).
-2*d*(d + 2)**2
Let k(w) be the first derivative of -w**6/90 - w**5/120 + 4*w**3/3 - 2. Let n(a) be the third derivative of k(a). Factor n(c).
-c*(4*c + 1)
Let y(z) be the first derivative of -3*z**4/8 + z**3 + 5. Factor y(w).
-3*w**2*(w - 2)/2
Let r = 5/4 - 1. Factor -1/4*f - r*f**2 + 1/2.
-(f - 1)*(f + 2)/4
Let g be (29/174)/((-2 - -1)/(-3)). Factor g*b**3 + 0 - 1/2*b**5 + 1/2*b**4 - 1/2*b**2 + 0*b.
-b**2*(b - 1)**2*(b + 1)/2
Let m(r) = 2*r**3 + r**2 + 4*r + 2. Let o = -3 + 9. Let p = o - 3. Let l(j) = 3*j**3 + j**2 + 7*j + 4. Let b(y) = p*l(y) - 5*m(y). Factor b(n).
-(n - 1)*(n + 1)*(n + 2)
Let s(i) = 3*i**2 - 7*i - 3. Let n be s(12). Let b = n - 3097/9. Determine q so that b*q - 4/3*q**2 - 2/9*q**4 - 2/9 + 8/9*q**3 = 0.
1
Suppose 3*j - 40 = j. Suppose 3*t - 2*r = j, 0 = 4*t + 6*r - 2*r. Factor 0 - 1/3*o + 1/3*o**3 - 1/3*o**t + 1/3*o**2.
-o*(o - 1)**2*(o + 1)/3
Let u be -3 + 0 + 7 + -5. Let m = 3 + u. Factor 4 - v**2 - m*v - 5 + 0.
-(v + 1)**2
Let a be ((-2)/3)/(14/(-189)). Let k = a + -7. Factor 0*r + 2/3 + 0*r**3 - 4/3*r**k + 2/3*r**4.
2*(r - 1)**2*(r + 1)**2/3
Let b(t) be the second derivative of 1/3*t**3 - 1/6*t**4 + 0 + t**2 - 1/10*t**5 + 7*t. Factor b(o).
-2*(o - 1)*(o + 1)**2
Let p(d) be the first derivative of 0*d**3 + 1/12*d**4 - 1 - 1/2*d**2 + 2*d. Let r(x) be the first derivative of p(x). Find q such that r(q) = 0.
-1, 1
Let y(z) = z + 3*z**4 + z - 4*z**3 - 2*z - 1 - 2*z**2. Let w(u) = -5*u**4 + 7*u**3 + 3*u**2 + 2. Let a(h) = -4*w(h) - 7*y(h). Factor a(b).
-(b - 1)**2*(b + 1)**2
Let g(v) be the second derivative of -v**7/28 + v**6/20 + 3*v**5/20 - v**4/4 - v**3/4 + 3*v**2/4 - 10*v. Factor g(t).
-3*(t - 1)**3*(t + 1)**2/2
Let g(q) be the second derivative of q**6/135 - q**5/90 - q**4/54 + q**3/27 + 2*q. Factor g(z).
2*z*(z - 1)**2*(z + 1)/9
Let f(p) be the first derivative of -p**6/18 + p**4/6 - p**2/6 - 3. Factor f(w).
-w*(w - 1)**2*(w + 1)**2/3
Let n(d) be the first derivative of -1/24*d**6 + 0*d - 1/20*d**5 + 0*d**2 + 1 + 1/12*d**3 + 1/16*d**4. Solve n(z) = 0 for z.
-1, 0, 1
Let p(m) be the first derivative of -7*m**4/24 + 5*m**3/12 + m**2/2 + 4*m - 4. Let j(s) be the first derivative of p(s). Suppose j(v) = 0. Calculate v.
-2/7, 1
Let b = -7 - -10. Suppose 22 = 30*t - 19*t. Factor -1/5*n**t + 1/5 + 4/5*n - 4/5*n**b.
-(n - 1)*(n + 1)*(4*n + 1)/5
Let d(f) be the second derivative of 1/6*f**3 - 1/12*f**4 + 0 + 7*f + 0*f**2. Suppose d(o) = 0. Calculate o.
0, 1
Factor -p**3 + 2*p**2 - 6*p + 2 - p**3 + 6*p**2 - 2*p**2.
-2*(p - 1)**3
Let m = 82 + -77. Let c(v) be the third derivative of -1/20*v**m + 0 - 1/2*v**3 + 2*v**2 - 1/4*v**4 + 0*v. Factor c(o).
-3*(o + 1)**2
Solve -10/11*x**2 - 2/11*x**4 + 0 - 8/11*x**3 - 4/11*x = 0.
-2, -1, 0
Suppose 15 = -z + 4*m, m - 3 = 3*z + 9. Let c be ((-24)/18)/(2/z). Factor -3*l - c*l**3 + 3*l - l**3.
-3*l**3
Let q = 64/17 - 303/85. What is v in 0 + 3/5*v**2 - 1/5*v**3 - q*v**5 + 2/5*v - 3/5*v**4 = 0?
-2, -1, 0, 1
Factor -6/11*k - 2/11*k**3 - 2/11 - 6/11*k**2.
-2*(k + 1)**3/11
Let r(u) = -u + 0 + 2 + u**2 + 3*u. Let l be r(-2). Suppose 2/7*d**3 + 0*d**l + 0*d + 0 = 0. Calculate d.
0
Factor 2*f**4 + 2/5*f**5 + 0*f**2 + 0 + 0*f + 12/5*f**3.
2*f**3*(f + 2)*(f + 3)/5
Let z(n) be the first derivative of 2*n**5/5 + 5*n**4/2 + 6*n**3 + 7*n**2 + 4*n + 8. Factor z(p).
2*(p + 1)**3*(p + 2)
Let w(k) = k**3 - 3*k**2 + 4*k - 3. Let b be w(2). Determine m, given that 1 - 4*m - b - 4 + m**2 - 2*m**2 = 0.
-2
Let s = 15 - 10. Suppose s*l + 5*t = -20, 4*t - 1 = -5*l - 17. Solve 1/4*x**5 + 1/4*x**3 - 1/2*x**4 + l + 0*x + 0*x**2 = 0.
0, 1
Let w(n) = n**2 - 6*n + 4. Let o be w(6). Suppose -2*c**3 - c + 2*c**5 + 4*c**4 + o*c**2 - 4*c**3 - 3*c**5 = 0. What is c?
0, 1
Let j(x) be the first derivative of -3*x**4/4 + x**3 + 3*x**2 + 4. Factor j(i).
-3*i*(i - 2)*(i + 1)
Suppose -5*i - 14 - 1 = 0. Let f be (1/i)/((-2)/18). Find m such that 77/3*m**2 + 49/3*m**f + 32/3*m + 4/3 = 0.
-1, -2/7
Suppose 2*g + 1 = 7. Let m = -5/2 + g. Let 0 - m*s**5 + 0*s**2 - 1/2*s**4 + 0*s**3 + 0*s = 0. What is s?
-1, 0
Let o be 9/6 - (-3)/2. Let 10*n**5 + 24*n**2 - 22*n**4 - 34*n**5 + 28*n**o - 4*n - 6 + 0*n 