. Let g(a) = 2*a - 5. Let w(b) = 11*g(b) - 6*y(b). Let n be w(-2). Determine p so that 8/9*p + 2/9*p**2 - 2/9 - 8/9*p**n = 0.
-1, 1/4, 1
Let c = 693 - 3447/5. Factor -c*h + 3/5*h**2 + 27/5.
3*(h - 3)**2/5
Let w(c) be the first derivative of -c**4/12 - c**3/3 - 48. Factor w(a).
-a**2*(a + 3)/3
Let f(i) be the first derivative of i**8/1680 + i**7/210 + i**6/72 + i**5/60 - 2*i**3 - 4. Let k(j) be the third derivative of f(j). Let k(h) = 0. Calculate h.
-2, -1, 0
Let p(s) = 8*s**5 - 12*s**4 + 10*s**3 + 6*s**2 + 6*s + 6. Let b(l) = -7*l**5 + 11*l**4 - 9*l**3 - 5*l**2 - 5*l - 5. Let v(z) = 6*b(z) + 5*p(z). Factor v(k).
-2*k**3*(k - 2)*(k - 1)
Let l(j) be the first derivative of 2*j**3/33 + 3*j**2/11 + 4*j/11 - 3. Factor l(m).
2*(m + 1)*(m + 2)/11
Let z(j) = 7*j - 42. Let f be z(6). Determine r, given that f + 2/5*r**2 - 4/5*r + 2/5*r**3 = 0.
-2, 0, 1
Let z(p) be the second derivative of p**5/5 - 4*p**4/3 + 10*p**3/3 - 4*p**2 - 10*p. Factor z(c).
4*(c - 2)*(c - 1)**2
Suppose -2*w = -0 - 4. Solve 5*x**4 + 3*x**5 - 3*x**2 + 4*x**w + 4*x**3 - x**5 = 0 for x.
-1, -1/2, 0
Let c be (0/(-1))/2 + 3. Let j be 65/(-39)*2/(-5). What is k in -2/3*k - 2*k**c - 2*k**2 + 0 - j*k**4 = 0?
-1, 0
Let h(b) be the second derivative of b**9/37800 + b**4/12 - 2*b. Let q(a) be the third derivative of h(a). Factor q(f).
2*f**4/5
Suppose 21 = 4*f - 3. Suppose 2*g - f = -0*g. Suppose 5*x**3 - g*x - 7*x**3 + 5*x = 0. Calculate x.
-1, 0, 1
Suppose 0 = 3*n - 5*n - 4*a + 20, 18 = 3*n + 3*a. Factor 1/4*i**4 + 0*i**n + 1/4*i**3 + 0*i + 0.
i**3*(i + 1)/4
Let g(i) be the first derivative of i**3/3 + 7*i**2/2 + 10*i - 42. Factor g(r).
(r + 2)*(r + 5)
Suppose 9*w - 9 = 6*w. Let -1/3*r**2 - 1/3*r + 0 + 1/3*r**4 + 1/3*r**w = 0. Calculate r.
-1, 0, 1
Let i(n) be the third derivative of -n**7/630 - n**6/360 + n**5/30 + n**4/18 - 4*n**3/9 + 17*n**2. Factor i(y).
-(y - 2)*(y - 1)*(y + 2)**2/3
Let n(w) be the first derivative of w**4/22 + 6*w**3/11 + 27*w**2/11 + 54*w/11 + 4. Find l such that n(l) = 0.
-3
Let g + 0 - g**3 + 1/2*g**2 - 1/2*g**4 = 0. Calculate g.
-2, -1, 0, 1
Let n(w) be the third derivative of w**7/105 - w**6/180 - w**5/30 + w**4/36 + 19*w**2. Solve n(j) = 0.
-1, 0, 1/3, 1
Let w(q) = -7*q**3 + 4*q**2 + 7*q - 4. Let b(f) = -4*f**3 + 2*f**2 + 4*f - 2. Let i(a) = -10*b(a) + 6*w(a). Factor i(r).
-2*(r - 2)*(r - 1)*(r + 1)
Let o be ((-116)/260)/(-1) + 4/26. Let l(v) be the first derivative of 0*v**3 - 1 + 0*v**2 + o*v**5 + 0*v - 1/3*v**6 - 1/4*v**4. Let l(m) = 0. Calculate m.
0, 1/2, 1
Let w(t) be the second derivative of -t**9/22680 + t**7/1890 - t**5/180 - t**4/2 - 3*t. Let s(r) be the third derivative of w(r). Factor s(v).
-2*(v - 1)**2*(v + 1)**2/3
Let m = 3 + -6. Let h(d) = d**3 + d + 1. Let l(z) = -6*z**2 - 3. Let f(v) = m*h(v) - l(v). Factor f(k).
-3*k*(k - 1)**2
Let j(o) be the first derivative of -1/5*o**2 + 0*o - 2/5*o**3 - 2 - 1/5*o**4. Solve j(c) = 0.
-1, -1/2, 0
Let k = 25 + -10. Suppose -4*x + k = x. Determine v so that -2/3*v - 3*v**2 - 7/3*v**x + 0 = 0.
-1, -2/7, 0
Factor -5*u**3 + 10*u - 2*u**3 + 3*u**3 - 4 - 6*u**3 + 4*u**2.
-2*(u - 1)*(u + 1)*(5*u - 2)
Suppose -s = -l, -2*s + 4*l = l + 3. Let o(m) be the first derivative of -1/6*m**s - 1/8*m**4 + 3 + 1/2*m + 1/4*m**2. Suppose o(i) = 0. What is i?
-1, 1
Suppose 9 + 3 = 3*u. Let a(o) be the first derivative of 8/3*o**3 - 2 + 7*o**2 - u*o. Find w, given that a(w) = 0.
-2, 1/4
Let f(l) be the first derivative of -l**3/6 + 19*l**2/2 - 361*l/2 - 73. Factor f(p).
-(p - 19)**2/2
Factor 4/7 - 2/7*x**2 + 2/7*x.
-2*(x - 2)*(x + 1)/7
Let w(q) be the third derivative of -1/32*q**6 - 9/32*q**4 - 3*q**2 + 0*q + 1/4*q**3 + 3/20*q**5 + 0. Factor w(u).
-3*(u - 1)**2*(5*u - 2)/4
Let a(i) be the third derivative of 1/1680*i**8 - 1/24*i**4 + 2*i**2 - 1/15*i**3 + 2/525*i**7 + 0 - 1/150*i**5 + 1/150*i**6 + 0*i. Factor a(c).
(c - 1)*(c + 1)**3*(c + 2)/5
Let w(b) = b - 5. Let c be w(9). Factor -t**3 + 7*t**3 - 5*t**3 - t**c.
-t**3*(t - 1)
Let m = 1/36 + 2/9. Let k(i) be the second derivative of 3/20*i**5 + 1/6*i**3 - i + 1/30*i**6 + m*i**4 + 0*i**2 + 0. Factor k(y).
y*(y + 1)**3
Let i(a) be the third derivative of a**7/420 + a**6/240 - a**5/40 - a**4/48 + a**3/6 + 17*a**2. Factor i(l).
(l - 1)**2*(l + 1)*(l + 2)/2
Let k(x) be the third derivative of -1/1155*x**7 + 0*x**6 + 0 + 0*x**4 + 0*x + 1/330*x**5 + 0*x**3 + 3*x**2. Determine o, given that k(o) = 0.
-1, 0, 1
Let z be (-4 + (-224)/(-72))*6/(-4). Factor z*n - n**3 - 1/3*n**4 + 0*n**2 + 0.
-n*(n - 1)*(n + 2)**2/3
Solve -2/19*k**2 + 8/19*k + 0 = 0 for k.
0, 4
Suppose 0 = -3*r - 1 - 2. Let x(f) = f**4 + f**2 - f + 1. Let i(g) = -4*g**4 - 4*g**3 - 6*g**2 + 7*g + 1. Let j(s) = r*i(s) - 3*x(s). Find n such that j(n) = 0.
-2, -1, 1
Let g(v) = -17*v**2 + 3*v - 5 + 16*v**2 - 11*v. Let l be g(-7). Solve -2 - 1/2*i**3 + 3/2*i**l + 0*i = 0.
-1, 2
Let t(s) be the first derivative of 0*s + 0*s**3 - 1 + 1/4*s**4 + 0*s**2 + 1/5*s**5. Determine g, given that t(g) = 0.
-1, 0
Let s = 222 - 1996/9. Let i(g) be the first derivative of 1/9*g**6 + 0*g - 1 - 1/6*g**4 - 2/15*g**5 + 0*g**2 + s*g**3. Find w, given that i(w) = 0.
-1, 0, 1
Let s(w) be the third derivative of 0*w + 0 + 0*w**4 + 1/840*w**7 + 0*w**6 + 1/24*w**3 - w**2 - 1/120*w**5. Factor s(p).
(p - 1)**2*(p + 1)**2/4
Let n be 6850/(-1781) + 4 + 0. Factor -2/13*w**5 + n*w**2 - 16/13*w + 10/13*w**3 - 2/13*w**4 + 8/13.
-2*(w - 1)**3*(w + 2)**2/13
Let x = -8 - -10. Factor 2/9 + 0*m - 2/9*m**x.
-2*(m - 1)*(m + 1)/9
Factor 5*o**2 + 13*o**3 + 0*o**2 + 13*o**3 - 8*o - 27*o**3 + 4.
-(o - 2)**2*(o - 1)
Let s be 24/16 + 4*1 + 1. Factor 2*q + 6*q**2 + 3*q**4 + 0 + 1/2*q**5 + s*q**3.
q*(q + 1)**2*(q + 2)**2/2
Let g(a) = -19*a**3 + 20*a**2 + 81*a + 20. Let v(l) = -4*l**3 + 4*l**2 + 16*l + 4. Let j(k) = -2*g(k) + 11*v(k). Factor j(p).
-2*(p - 2)*(p + 1)*(3*p + 1)
Let d(a) be the first derivative of 0*a**2 + 12/7*a**5 - 2*a**4 + 16/21*a**3 + 3 - 3/7*a**6 + 0*a. Factor d(r).
-2*r**2*(r - 2)*(3*r - 2)**2/7
Find i, given that 0 - 5*i**3 + 5/4*i**5 - 5*i**2 + 5/4*i**4 + 0*i = 0.
-2, -1, 0, 2
Find c such that 2/7*c + 12/7 + 2/7*c**3 - 8/7*c**2 = 0.
-1, 2, 3
What is b in 0*b + 0*b**3 + 0 - 2/11*b**4 + 2/11*b**2 = 0?
-1, 0, 1
Let v(x) = -25*x**2 + 24*x - 17. Suppose -2*w + 161 = 3*l - 4*w, 4*l + 5*w = 184. Let o(u) = -3*u**2 + 3*u - 2. Let f(j) = l*o(j) - 6*v(j). Factor f(a).
-3*a*(a - 3)
Suppose -3*z + 9*z - 24 = 0. Find q, given that 3/4 + 3/2*q**3 - 3/4*q**5 - 3/4*q - 3/2*q**2 + 3/4*q**z = 0.
-1, 1
Let k(z) be the third derivative of -z**7/42 - z**6/8 - z**5/4 - 5*z**4/24 + 14*z**2. Factor k(c).
-5*c*(c + 1)**3
Let a(k) = k**5 - 10*k**4 + 18*k**3 - 10*k**2 + 5*k + 2. Let x(f) = -f**5 + f**4 + f**2 + f + 1. Let i(r) = a(r) - 2*x(r). Factor i(v).
3*v*(v - 1)**4
Let a(w) = -w**2 - 4*w - 3. Let f = 134 + -95. Let u(x) = -6*x**2 - 25*x - 19. Let z(d) = f*a(d) - 6*u(d). Determine i so that z(i) = 0.
-1
Let o(a) be the second derivative of -a**7/420 - a**3/3 + 4*a. Let j(f) be the second derivative of o(f). Let j(r) = 0. Calculate r.
0
Suppose -20*k - 12 = -23*k. Let b(y) be the second derivative of k*y + 1/3*y**2 - 1/10*y**5 - 1/9*y**3 + 0 - 5/18*y**4. Factor b(d).
-2*(d + 1)**2*(3*d - 1)/3
Factor -2/7 + 0*n + 2/7*n**2.
2*(n - 1)*(n + 1)/7
Suppose 3*j - j = 0. Suppose j*n = 3*n - 6. Factor -3*b**2 + 5*b**4 - 2*b**4 + 0*b**n.
3*b**2*(b - 1)*(b + 1)
Let c(m) be the third derivative of -25*m**9/6048 - m**8/672 + m**7/105 - m**6/180 - m**3/6 + 2*m**2. Let f(v) be the first derivative of c(v). Factor f(s).
-s**2*(s + 1)*(5*s - 2)**2/2
Let b(z) be the third derivative of z**6/10 - 7*z**5/15 + 5*z**4/6 - 2*z**3/3 - 3*z**2. Factor b(n).
4*(n - 1)**2*(3*n - 1)
Let t be (88/(-12) - -6) + (-36)/(-26). Let l(m) be the first derivative of 3/13*m**2 + 1 - t*m**3 - 4/13*m. Let l(y) = 0. Calculate y.
1, 2
Let m(k) = 4*k - 6. Let u be m(2). Let s(p) be the first derivative of 8/3*p**3 - u*p - 3*p**2 - 1. Factor s(x).
2*(x - 1)*(4*x + 1)
Suppose 1 = -3*x - 11, 3*x + 28 = 4*v. Solve 0 + 0*w - 1/4*w**3 - 1/4*w**2 + 1/4*w**5 + 1/4*w**v = 0.
-1, 0, 1
Suppose 6*c - 15*c + 18 = 0. Factor 0 + 1/2*l + 1/2*l**c.
l*(l + 1)/2
Let j(v) be the second derivative of -v**5/20 + 5*v**4/12 + v**3 + v**2 + 3*v. Let s be j(6). Factor -k + k - k**s - 3 + 2*k + 2.
-(k - 1)**2
Let h = -4 - -2. Let j be -3*1/2*