7). Factor -5/7*l**2 + 0 - l**t + 2/7*l.
-l*(l + 1)*(7*l - 2)/7
Let d(b) = b**3 - 5*b**2 + 6*b - 5. Let x be d(4). Suppose -3*y = -5*k, -y = -k + x*k - 11. Solve 0*v + 0*v**k + v**2 - 1/2*v**4 - 1/2 = 0 for v.
-1, 1
Let n(c) = -2*c**2 + 79*c + 125. Let w be n(41). Find d such that 8/5 + 1/10*d**w + 4/5*d = 0.
-4
Let l = 2 - 1. Suppose -3*j - 2*f = -11 + l, j + 4*f = 0. Suppose -42/5*m**5 - 6*m**3 + 68/5*m**j + 4/5*m**2 + 0 + 0*m = 0. What is m?
0, 2/7, 1/3, 1
Let r(a) be the second derivative of a**7/210 + a**6/24 + a**5/15 - a**4/8 + 2*a**3/3 + 2*a. Let b(j) be the second derivative of r(j). Solve b(q) = 0.
-3, -1, 1/4
Let n = 32 + -95/3. Factor -1/3*r + 0*r**2 + 1/6*r**4 - 1/6 + n*r**3.
(r - 1)*(r + 1)**3/6
Let c(i) be the second derivative of -13*i**7/70 - 3*i**6/10 + 33*i**5/100 + 3*i**4/4 + i**3/5 - i - 20. Let c(x) = 0. Calculate x.
-1, -2/13, 0, 1
Let p(q) be the second derivative of -q**4/12 - 4*q**3/3 - 7*q**2/2 - 5*q. Let f be p(-7). Solve 3/5*y**4 + 0 + 0*y**3 + 0*y**2 + f*y = 0.
0
Suppose 24/7 + 3/7*k**2 - 18/7*k = 0. Calculate k.
2, 4
Factor -4*t - 37*t**2 - 4*t - 5*t**4 + 25*t**3 - 3*t**2 + 28*t.
-5*t*(t - 2)**2*(t - 1)
Factor 2/7*a**3 - 4/7*a**2 - 2/7*a + 4/7.
2*(a - 2)*(a - 1)*(a + 1)/7
Let v(y) be the third derivative of -2*y**2 - 1/80*y**6 + 1/420*y**7 - 1/48*y**4 + 1/40*y**5 + 0*y + 0*y**3 + 0. What is l in v(l) = 0?
0, 1
Solve 2*c**2 + 4/3*c**3 - 5/3 - 4/3*c - 1/3*c**4 = 0.
-1, 1, 5
Let i(u) be the first derivative of -u**5/20 - 3*u**4/8 - 13*u**3/12 - 3*u**2/2 - u - 2. Find n, given that i(n) = 0.
-2, -1
Solve 8/7 + 0*i - 2/7*i**2 = 0 for i.
-2, 2
Let z(y) = -1 + 2 - y + 3*y**2 + 2 + 0*y**2. Let b(d) = 2*d**2 + 2. Let x(v) = -5*b(v) + 4*z(v). Solve x(s) = 0.
1
Let h(g) be the second derivative of 5*g**4/48 - 25*g**3/24 + 5*g**2/2 + g. Solve h(y) = 0.
1, 4
Let s(x) = 2*x**4 + 5*x**3 + 18*x**2 + 9*x + 4. Let t(z) = 2*z**4 + 6*z**3 + 18*z**2 + 10*z + 4. Let b(w) = -4*s(w) + 5*t(w). Solve b(i) = 0.
-2, -1
Suppose -4*b - 2 = -3*h + 9, 6 = b + h. Let p be 0/(-3)*(0 - b). Factor p - 4/3*k + 8*k**3 + 14/3*k**4 + 2*k**2.
2*k*(k + 1)**2*(7*k - 2)/3
Let l(t) be the first derivative of t**7/1050 - t**6/150 + t**5/75 + 3*t**2/2 + 3. Let j(h) be the second derivative of l(h). Factor j(a).
a**2*(a - 2)**2/5
Let m = 12 - 6. Suppose -4*x = -4*p - 0*p, p - 3*x = -m. Determine g, given that 3*g**4 - p*g**5 + g**4 + 6*g**2 - 15*g**3 + 8*g**4 = 0.
0, 1, 2
Let c = 12 - 8. Factor -4*w**3 + 2*w**3 - c*w + 6*w**2 + 0*w**3.
-2*w*(w - 2)*(w - 1)
Let s = 30 - 30. Let x(u) be the third derivative of 0*u**5 + 0*u**4 + 1/420*u**7 + s*u + 0 - u**2 + 1/240*u**6 + 0*u**3. Factor x(g).
g**3*(g + 1)/2
Let x(i) be the first derivative of -i**6/6 + i**5/5 + i**4/4 - i**3/3 - 2. Determine g, given that x(g) = 0.
-1, 0, 1
Let r(f) be the third derivative of 0 - 4/105*f**7 + 0*f**3 + 3*f**2 + 1/168*f**8 - 2/15*f**5 + 1/12*f**4 + 0*f + 1/10*f**6. Factor r(y).
2*y*(y - 1)**4
Let g(w) = w**4 - w**3 - w**2 + w - 1. Let s(r) = 2*r**4 - r**3 - 10*r**2 - 5*r + 6. Let j(x) = -4*g(x) - s(x). Let j(q) = 0. What is q?
-1, -1/2, 1/3, 2
Let p(f) be the first derivative of f**5/270 - f**4/36 + 2*f**3/27 + 3*f**2/2 - 1. Let c(b) be the second derivative of p(b). Factor c(w).
2*(w - 2)*(w - 1)/9
Let z(r) be the second derivative of r**7/560 - r**6/720 - r**4/4 + 2*r. Let q(d) be the third derivative of z(d). Solve q(w) = 0.
0, 2/9
Suppose 0*q - 5*q + 15 = 0. Let s = 2 + 0. Factor -f - 2*f**q - f**3 + s - 4*f**2 + 2*f.
-(f + 1)**2*(3*f - 2)
Let h be (-2)/(-7) - 4*(-2)/(-28). Let g(j) be the third derivative of -2*j**2 + 0*j + 1/30*j**5 + h*j**3 + 1/6*j**4 + 0. Factor g(o).
2*o*(o + 2)
Let h(x) be the first derivative of -x**6/24 - 7*x**5/20 - 9*x**4/8 - 11*x**3/6 - 13*x**2/8 - 3*x/4 + 2. Factor h(t).
-(t + 1)**4*(t + 3)/4
Let p(x) be the second derivative of -3*x + 0 + x**3 + 9/2*x**2 + 1/12*x**4. Determine r so that p(r) = 0.
-3
Let q(u) be the third derivative of -u**9/45360 - u**8/20160 + u**7/7560 + u**6/2160 + 5*u**4/24 + u**2. Let x(w) be the second derivative of q(w). Factor x(p).
-p*(p - 1)*(p + 1)**2/3
Suppose -3*j - 120 = 2*f, 0 = 2*f - 0*f + 2*j + 122. Let k be 2/7 + 18/f. Factor -2*h**2 + 0 - 2*h**3 + k.
-2*h**2*(h + 1)
Let r be (-18)/(-3 - -1) - 0. Let q be -1*1*(-11 + r). Suppose m**3 - m - 1/3*m**q - 1/3 + 2/3*m**4 = 0. What is m?
-1, -1/2, 1
Let i(d) be the second derivative of -1/48*d**4 + 0 + 1/12*d**3 - 1/8*d**2 - 3*d. Find w such that i(w) = 0.
1
Let x(d) be the third derivative of d**7/1155 + d**6/660 - d**5/110 - d**4/132 + 2*d**3/33 + 21*d**2. Find i, given that x(i) = 0.
-2, -1, 1
Let f = 122 - 118. Factor 2*n - 6*n**2 + 0 + 13/2*n**3 - 3*n**f + 1/2*n**5.
n*(n - 2)**2*(n - 1)**2/2
Let c(f) = f**5 + f**3 + f + 1. Let h(i) = 8*i**5 + 2*i**4 + 4*i**3 - 8*i**2 + 3*i + 7. Let p(g) = -14*c(g) + 2*h(g). Factor p(b).
2*b*(b - 2)*(b + 1)**2*(b + 2)
Let i(r) be the third derivative of -r**6/30 - r**5/15 + r**4/6 + 2*r**3/3 + 8*r**2. Factor i(x).
-4*(x - 1)*(x + 1)**2
Let m(g) be the first derivative of 4 + 0*g**2 - 2/9*g**3 + 1/12*g**4 + 0*g. Find k, given that m(k) = 0.
0, 2
Let w(x) be the first derivative of -2/33*x**3 - 1/66*x**4 + 3 - x + 0*x**2. Let q(a) be the first derivative of w(a). Determine j so that q(j) = 0.
-2, 0
Let j(w) = 2*w**2 - 3*w + 1. Let d be j(2). Suppose -6 = x - d*x. Factor 8*c**x - 8*c**3 - 2*c**4 + 2*c**2.
-2*c**2*(c - 1)*(c + 1)
Let y(w) be the third derivative of -w**5/210 + 5*w**4/42 - 25*w**3/21 - 16*w**2. Factor y(b).
-2*(b - 5)**2/7
Let 2*k + 0*k**3 - k**2 - 5*k**2 - k**3 + 5*k**2 = 0. Calculate k.
-2, 0, 1
Let o(i) = -14*i**2 + 30*i + 56. Let a(v) = v**2 - v. Let x(c) = -10*a(c) - o(c). Factor x(y).
4*(y - 7)*(y + 2)
Find a such that 2/9*a**5 + 4/9*a**4 - 4/9*a**2 - 2/9*a + 0*a**3 + 0 = 0.
-1, 0, 1
Let x(m) = 9*m**4 - 12*m**3 - m**2 - 4*m + 4. Let r(w) = -36*w**4 + 48*w**3 + 3*w**2 + 15*w - 15. Let f(p) = 4*r(p) + 15*x(p). Factor f(t).
-3*t**2*(t - 1)*(3*t - 1)
Let w(o) be the first derivative of -o**4/5 + 44*o**3/15 + 10*o**2 + 52*o/5 + 55. Factor w(f).
-4*(f - 13)*(f + 1)**2/5
Let k(j) = -6*j**3 - 2*j**2 + 2*j + 2. Let u(f) = -f**3 + f**2 - 1. Let v(c) = k(c) - 4*u(c). Suppose v(w) = 0. Calculate w.
-3, -1, 1
Suppose -d + 4 = -0*d. Let b be d/(-4*1/(-2)). Suppose -b*a**2 + 8*a**3 - 3*a + 4*a**4 - a + 0*a + 2*a**4 = 0. What is a?
-1, 0, 2/3
Let w(n) = -n**2 - 5*n + 6. Let z be w(-6). Factor 0*t**3 + 0 + z*t + 1/4*t**4 + 0*t**2.
t**4/4
Let l(t) = 3*t - 9. Let i be l(4). Let o(u) be the first derivative of 0*u**2 + 1/5*u**5 + 1/3*u**i - 1 + 0*u - 1/2*u**4. Let o(r) = 0. What is r?
0, 1
Let g = -1/352 + 707/1056. Let 5/6*h**4 + 1/6*h**2 + g*h**3 + 1/3*h**5 + 0 + 0*h = 0. Calculate h.
-1, -1/2, 0
Let q = 39 - 37. Let n(d) be the first derivative of d + q + 1/3*d**3 - d**2. What is v in n(v) = 0?
1
Let a(g) be the third derivative of -g**6/120 - g**5/60 - g**3/2 + 2*g**2. Let v(z) = 3*z**3 + 3*z**2 + 7. Let l(c) = 7*a(c) + 3*v(c). Let l(m) = 0. What is m?
-1, 0
Let p(b) be the third derivative of b**8/1176 + b**7/735 - b**6/420 - b**5/210 - 10*b**2. Factor p(y).
2*y**2*(y - 1)*(y + 1)**2/7
Let t(v) be the first derivative of v**3 - 9*v**2 - 21*v + 15. Determine l so that t(l) = 0.
-1, 7
Let y(w) be the second derivative of 0 + 1/20*w**4 - w + 2/5*w**3 + 9/10*w**2. Factor y(a).
3*(a + 1)*(a + 3)/5
Determine r so that -2/9*r**2 + 28/9*r - 98/9 = 0.
7
Suppose k - 8 = -k. Suppose 5*h + 2*m + 6 = -2*m, -5*h = -2*m - 18. Solve 2*p**3 - h*p**3 - 6*p**4 + 7*p**k = 0 for p.
0
Factor -3*v**4 - 4*v**2 + 9*v**2 + 3*v - 2*v**2 + 0*v - 3*v**3.
-3*v*(v - 1)*(v + 1)**2
Let i = -293/5 + 59. Solve 0*t**4 + 0 + 3/5*t**3 - 1/5*t**5 - i*t**2 + 0*t = 0.
-2, 0, 1
Let p(w) = w**2 - w + 1. Let n be p(3). Determine v, given that 0 + n - 2*v**2 - v**3 - v - 7 = 0.
-1, 0
Let f(p) = p**3 - 14*p**2 + 13*p - 4. Let h(m) = m**3 - 29*m**2 + 25*m - 7. Let g(a) = 5*f(a) - 2*h(a). What is y in g(y) = 0?
1, 2
Let q(g) = 2*g**2 - 3*g - 1. Let h be q(-2). Factor 24*j**2 + 8*j**4 - 2*j**3 - 5*j**4 - 12*j - h*j**3.
3*j*(j - 2)**2*(j - 1)
Let b(j) be the first derivative of -j**6/27 - 4*j**5/45 - j**4/18 + 23. Factor b(g).
-2*g**3*(g + 1)**2/9
Let n = 940/7 + -134. Suppose 0*d + 4/7*d**2 + n*d**4 + 0 + 6/7*d**3 = 0. What is d?
-2, -1, 0
Let z(t) be the third derivative of