. Let m be -1 - (l/(-21) + -1). Suppose -24/7*g + 2/7*g**4 + m*g**2 - 12/7*g**3 + 8/7 = 0. What is g?
1, 2
Let h(a) be the second derivative of a**6/360 + a**5/90 + a**4/72 + 2*a**2 - 2*a. Let f(g) be the first derivative of h(g). Determine v, given that f(v) = 0.
-1, 0
Let z(i) be the second derivative of i**6/10 - 9*i**5/10 + i**4 + 3*i**3 - 15*i**2/2 + 14*i. Factor z(g).
3*(g - 5)*(g - 1)**2*(g + 1)
Let x = 1/2 + -20/3. Let g = x - -20/3. Suppose 9/4*n**3 + 0*n - g*n**2 + 0 = 0. Calculate n.
0, 2/9
Let n(f) be the second derivative of -f**5/5 + 16*f + 2. Factor n(k).
-4*k**3
Factor -1/3*r**3 - 5/3*r**2 - 7/3*r - 1.
-(r + 1)**2*(r + 3)/3
Let i(j) be the second derivative of -j**7/840 + j**6/120 - 5*j**4/12 + 3*j. Let x(o) be the third derivative of i(o). Determine n, given that x(n) = 0.
0, 2
Let c(o) be the third derivative of -o**7/315 + o**6/90 - o**5/90 + 2*o**2. Factor c(z).
-2*z**2*(z - 1)**2/3
Let r(i) be the second derivative of i**7/1260 - i**6/360 - i**4/6 + i. Let m(t) be the third derivative of r(t). Factor m(f).
2*f*(f - 1)
Let f be 105/60 - 1/(-4). Let b(j) be the second derivative of f*j + 0*j**3 + 3/70*j**5 + 0 + 0*j**2 + 1/21*j**4. Factor b(l).
2*l**2*(3*l + 2)/7
Let c be (14/(-42))/((-2)/24). Let f be 11 + -7 + c/(-3). Let 24*n + 54*n**2 + f = 0. What is n?
-2/9
Let f(j) = 2*j**3 + j**2 - 2. Let x be f(2). Let m be (-12)/x*36/(-5). What is b in 0 - m*b**2 + 2*b**3 + 8/5*b = 0?
0, 2/5, 2
Suppose l = -l + 6. What is v in 0*v + 5*v - 4*v - v**l = 0?
-1, 0, 1
Let p be (-8)/(-40)*(-10)/(-12). Let c(f) be the first derivative of -3/8*f**4 + p*f**3 + 2 - 1/10*f**5 + 0*f**2 + 0*f + 1/4*f**6. What is a in c(a) = 0?
-1, 0, 1/3, 1
Factor 2/19*j**2 - 2/19*j**3 + 10/19*j + 6/19.
-2*(j - 3)*(j + 1)**2/19
Suppose -3*m + 10 = 2*m. Factor m*v**2 - 6*v**2 + v**5 + 3*v**4 + 0*v**4 + 0*v**2.
v**2*(v - 1)*(v + 2)**2
Let r = -1543/5 + 309. Let a = 6 - 4. Determine c, given that 0*c + 0 + r*c**a = 0.
0
Let p(h) = -h**4 + 2*h**3 - 3*h. Let b(y) = -2*y**4 + 4*y**3 - 5*y. Let j(n) = -3*b(n) + 5*p(n). Solve j(d) = 0 for d.
0, 2
Suppose -2*w = 5*k - 6, 3*w + 12 = 7*w + 5*k. Factor 0*h**2 - 7*h**2 - 5*h**2 + 9 + w*h.
-3*(h - 1)*(4*h + 3)
Factor -1/2*m**3 + 0 + m**2 + 0*m - 1/2*m**4.
-m**2*(m - 1)*(m + 2)/2
Suppose -21*g - 2 = -22*g. Let o(x) be the first derivative of 7/4*x**4 - 2/3*x**3 - 7/2*x**2 + 2 + g*x. Suppose o(i) = 0. What is i?
-1, 2/7, 1
Let g(t) be the second derivative of -t**5/90 - t**4/36 - t**2/2 - t. Let r(o) be the first derivative of g(o). Determine l, given that r(l) = 0.
-1, 0
Let g(t) be the second derivative of t**4/6 - t**3 + 2*t**2 - 32*t. Factor g(k).
2*(k - 2)*(k - 1)
Let v(r) = 16*r**4 - 16*r**3 - 16*r**2 + 44*r. Let p(o) = 3*o**4 - 3*o**3 - 3*o**2 + 8*o. Let l(n) = 28*p(n) - 5*v(n). Solve l(y) = 0 for y.
-1, 0, 1
Suppose -15 = -5*p + 10. Let v be 2/4*2/p. Let -v - 2/5*o - 1/5*o**2 = 0. What is o?
-1
Let q(i) be the second derivative of -i**5/30 + i**4/6 - i**3/3 + 3*i**2 + 3*i. Let z(s) be the first derivative of q(s). Suppose z(o) = 0. Calculate o.
1
Let z = 2 - 0. Let n(b) = -b**3 + 3*b**2 - 2*b + 2. Let w be n(z). Let 2*t - 3*t + t**w + 0*t = 0. What is t?
0, 1
Let n(u) be the third derivative of u**8/504 - u**6/45 - u**5/45 + u**4/12 + 2*u**3/9 + 8*u**2. Factor n(s).
2*(s - 2)*(s - 1)*(s + 1)**3/3
Let i(t) be the first derivative of 1/40*t**5 + 0*t - 1/360*t**6 - 2 + 0*t**2 - t**3 - 1/12*t**4. Let y(s) be the third derivative of i(s). Factor y(p).
-(p - 2)*(p - 1)
Let a(j) be the third derivative of -15*j**8/224 + 53*j**7/140 - 31*j**6/48 + 5*j**5/24 + 5*j**4/12 - j**3/3 + j**2. Suppose a(d) = 0. Calculate d.
-1/3, 1/5, 2/3, 1, 2
Let l(x) = -x - 6. Suppose -3*r + 6*r + 24 = 0. Let y be l(r). Factor -11*t**3 + 9*t**3 - t**4 + y*t**3.
-t**4
Suppose -2 - 15*k**3 - 1 + 12*k**3 + 3*k + 3*k**2 = 0. What is k?
-1, 1
Let t be (1 - (2 - 1))/((-3)/(-3)). Factor 0*f - 6/5*f**4 + t*f**2 + 0 - 3/5*f**5 - 3/5*f**3.
-3*f**3*(f + 1)**2/5
Let x be (-108)/189 + (-114)/(-28). Solve 3/2*i**3 + 5/2*i - 1/2 - x*i**2 = 0 for i.
1/3, 1
Let h(a) be the second derivative of 1/8*a**6 + 5/8*a**4 - 5/8*a**3 + 0 + a - 1/56*a**7 + 3/8*a**2 - 3/8*a**5. Factor h(b).
-3*(b - 1)**5/4
Factor 3 - 21*i**3 + 19*i**3 - 3 - 2*i**2.
-2*i**2*(i + 1)
Let n(x) be the second derivative of x**5/60 + x**4/12 - 2*x**2/3 - 6*x. Factor n(v).
(v - 1)*(v + 2)**2/3
Factor 2*j**2 + 0 + 2/3*j**4 + 2/3*j + 2*j**3.
2*j*(j + 1)**3/3
Factor o**3 - 3*o**3 - 2*o**4 - 2*o**4 - 3*o**4.
-o**3*(7*o + 2)
Let s(l) be the second derivative of -5/12*l**5 - 2*l**2 + 0 - 32/9*l**3 + l - 95/36*l**4. Solve s(z) = 0 for z.
-3, -2/5
Suppose k + a - 3 = 1, -3*k + 5*a - 20 = 0. Determine w so that 2*w**3 + w + k*w + 4*w**2 + w = 0.
-1, 0
Let a(z) be the first derivative of -z**5/20 + z**3/4 + z**2/4 + 23. Suppose a(o) = 0. What is o?
-1, 0, 2
Let z(u) = 5*u**4 - u**3 - 17*u - 5. Let m(n) be the third derivative of n**7/210 - n**4/6 - n**3/6 - 3*n**2. Let d(j) = 18*m(j) - 4*z(j). Factor d(h).
-2*(h - 1)**3*(h + 1)
Let m(n) be the first derivative of 4/11*n**2 + 13/22*n**4 + 0*n + 1/33*n**6 - 8/11*n**3 - 12/55*n**5 - 5. Suppose m(y) = 0. Calculate y.
0, 1, 2
Suppose -8/5*q**2 - 4/5*q + 4/5*q**3 + 6/5 + 2/5*q**4 = 0. What is q?
-3, -1, 1
Let q(k) be the first derivative of -1/3*k**3 - 3 + 1/420*k**5 + 0*k + 0*k**2 - 1/1260*k**6 + 0*k**4. Let x(o) be the third derivative of q(o). Factor x(d).
-2*d*(d - 1)/7
Let h(v) be the first derivative of -v**6/9 - 8*v**5/15 - v**4 - 8*v**3/9 - v**2/3 + 7. Suppose h(k) = 0. What is k?
-1, 0
Suppose 4 + 1 = 3*p + j, 1 = -j. Solve -8*r**2 - 3*r**2 - 4*r + 7*r**p = 0 for r.
-1, 0
Let a(p) be the first derivative of 4*p**5/15 - 4*p**3/3 - 4*p**2/3 + 1. Factor a(b).
4*b*(b - 2)*(b + 1)**2/3
Suppose -1 - 4/5*y + 1/5*y**2 = 0. What is y?
-1, 5
Suppose 0 = 6*n - 5*n - 5. Let i(c) be the first derivative of 2/5*c**n + 1 + 9/8*c**4 + 1/4*c**2 + c**3 + 0*c. Factor i(s).
s*(s + 1)**2*(4*s + 1)/2
Let v(u) be the second derivative of -4*u**7/147 - u**6/15 + 3*u**5/35 + u**4/6 - 2*u**3/21 - 13*u. Find y such that v(y) = 0.
-2, -1, 0, 1/4, 1
Suppose 4*x - 2*r - 21 = r, -2*r = 2*x. Let t(a) be the second derivative of -1/42*a**4 + a + 0*a**x - 2/105*a**6 + 3/70*a**5 + 0 + 0*a**2. Factor t(g).
-2*g**2*(g - 1)*(2*g - 1)/7
Solve 8/7*d**2 + 0 - 4/7*d**3 + 0*d = 0.
0, 2
Let d(g) be the third derivative of 0*g - 2/5*g**5 + 1/4*g**4 + 0 - g**2 + 4/15*g**6 - 1/12*g**3. Factor d(u).
(4*u - 1)**3/2
Let m(n) = -n**2 + 7*n + 8. Let s be m(8). Suppose -6*x + 4*x + 8 = s. Suppose -4 + h + 6*h**2 - 4*h**2 + x + h**3 = 0. What is h?
-1, 0
Let p(f) be the second derivative of -f**5/35 + f**4/3 - 22*f**3/21 + 10*f**2/7 + 11*f. Determine w so that p(w) = 0.
1, 5
Let x(z) be the second derivative of -z**6/60 - z**5/40 + 5*z**4/24 - z**3/4 + 12*z. Solve x(v) = 0 for v.
-3, 0, 1
Let o(j) be the second derivative of -j**7/420 - j**6/180 + j**5/60 + j**4/12 + j**3/3 + 4*j. Let r(b) be the second derivative of o(b). Factor r(k).
-2*(k - 1)*(k + 1)**2
Let k be (2/6)/((-10)/150). Let q be ((-3)/9)/(k/30). Let 6/5*r**3 - 3*r**q - 3/5 + 12/5*r = 0. Calculate r.
1/2, 1
Let t(o) = o**4 + o**3 + o + 1. Let x(w) = 2*w**4 - 3*w**2 + 2*w + 3. Let u(c) = -6*t(c) + 2*x(c). Factor u(p).
-2*p*(p + 1)**3
Let l(g) be the second derivative of g**7/483 + 2*g**6/345 + g**5/230 + 22*g. Suppose l(w) = 0. What is w?
-1, 0
Let s(w) be the third derivative of w**10/302400 - w**9/60480 + w**7/5040 - w**6/1440 - w**5/60 - 4*w**2. Let m(r) be the third derivative of s(r). Factor m(t).
(t - 1)**3*(t + 1)/2
Let i = -115 - -117. Factor 0*z + 0 + 2/7*z**i.
2*z**2/7
Let j(y) be the first derivative of -2*y**6/21 + 12*y**5/35 - 2*y**4/7 - 8*y**3/21 + 6*y**2/7 - 4*y/7 - 7. Factor j(z).
-4*(z - 1)**4*(z + 1)/7
Let x be (-51)/68*(-8)/3. Factor 2/13 + 2/13*q - 2/13*q**x - 2/13*q**3.
-2*(q - 1)*(q + 1)**2/13
Let c = -6 - -4. Let l be (c - -3) + 9/(-12). Factor 1/4*m + 1/2 - l*m**2.
-(m - 2)*(m + 1)/4
Let f = 1/641 - -12175/2564. Determine b, given that -7/4*b**5 + 1/2*b + 1/4*b**2 + f*b**4 + 0 - 15/4*b**3 = 0.
-2/7, 0, 1
Factor -7*z - 3*z**3 + 10*z - 2*z**4 + 0*z + 3*z**2 - z**4.
-3*z*(z - 1)*(z + 1)**2
Let p(y) = 2*y + 31. Let g be p(-13). Let b(c) be the first derivative of 2 - 1/5*c**g + 1/9*c**3 + 0*c + 0*c**2 - 1/6*c**4. Factor b(o