 -l**i - 6*l**4 + 4*l**4 = 0. Calculate l.
0
Let h be ((-5)/20)/((-7)/4). Let t(d) be the second derivative of -2*d + 1/42*d**4 + 0 + 0*d**3 - h*d**2. Let t(g) = 0. What is g?
-1, 1
Factor 0*m + 1/7*m**3 - 1/7*m**2 + 0.
m**2*(m - 1)/7
Let d(k) be the first derivative of -4/5*k + 2 - 9/5*k**2 - 14/15*k**3. Find p such that d(p) = 0.
-1, -2/7
Let u(c) = -3*c - 12. Let q be u(-5). Suppose -v - q*k = 3, 3 - 4 = -3*v + k. Factor -4/7*l**4 + v + 0*l - 6/7*l**3 - 2/7*l**2.
-2*l**2*(l + 1)*(2*l + 1)/7
Let l(w) be the second derivative of 5*w**4/48 + w**3/3 + 3*w**2/8 - 9*w. Find h such that l(h) = 0.
-1, -3/5
Suppose 3*n - 18 = -0*n. Let h(i) be the first derivative of -1/4*i**4 + 1/6*i**n + 1/5*i**5 - 1 + 0*i**2 + 0*i - 1/3*i**3. Let h(c) = 0. What is c?
-1, 0, 1
Let i = -253/35 - -59/7. Factor -3/5*w**2 - 3/5*w + i.
-3*(w - 1)*(w + 2)/5
Find p, given that 3/7*p**4 - 9/7*p**2 - 6/7 + 15/7*p - 3/7*p**3 = 0.
-2, 1
Let m(o) = 4*o**4 + 6*o**3 - 4*o - 3. Let v(c) = 5*c**4 + 7*c**3 - 4*c - 4. Let i(h) = 4*m(h) - 3*v(h). Factor i(j).
j*(j - 1)*(j + 2)**2
Suppose -6*a + 4/3 + 8/3*a**2 = 0. Calculate a.
1/4, 2
Let l(h) be the second derivative of -5*h**7/84 - h**6/30 + h**5/4 + h**4/6 - 5*h**3/12 - h**2/2 + 7*h. What is y in l(y) = 0?
-1, -2/5, 1
Suppose 2*u - 7 = -3. Suppose -z = -0*z - u. Factor 0 + 4/5*v + 6/5*v**z + 2/5*v**3.
2*v*(v + 1)*(v + 2)/5
Let z(q) = 2*q**3. Let c(a) = 4*a**3 - a**2. Let f = -4 - -2. Let i(p) = f*c(p) + 5*z(p). Let i(j) = 0. What is j?
-1, 0
Let n(k) be the third derivative of k**6/1440 - k**5/240 - k**3/6 + 2*k**2. Let m(t) be the first derivative of n(t). What is v in m(v) = 0?
0, 2
Let c(n) be the second derivative of n**4/66 + n**3/11 - 7*n. Suppose c(h) = 0. What is h?
-3, 0
Determine d so that 0 + 3/4*d**5 - 3/4*d + 3/2*d**2 - 3/2*d**4 + 0*d**3 = 0.
-1, 0, 1
Let f(b) = -6*b**3 + 7*b**2 - 7*b. Let y(z) = -z**3 + z**2 - z. Let r(o) = 4*f(o) - 28*y(o). Let r(w) = 0. Calculate w.
0
Let l(o) be the second derivative of o**7/315 + o**6/75 + o**5/75 - o**4/45 - o**3/15 - o**2/15 - 3*o. Determine c so that l(c) = 0.
-1, 1
Suppose 4*g - 5*o = 36, -o + 21 = 3*g - 6. Factor 9 - s**3 - g.
-s**3
Let q(y) be the second derivative of 0*y**3 + 0*y**4 - 1/120*y**6 + 0*y**5 - 1/2*y**2 + 0 + y. Let b(c) be the first derivative of q(c). Solve b(l) = 0.
0
Let y be (-8)/(-12) + 620/6. Let g be y/84 - 2/3. Determine j, given that -2/7*j + g - 2/7*j**2 = 0.
-2, 1
Suppose -20*n**2 - 9/2*n - 1/3 - 175/6*n**3 = 0. What is n?
-2/7, -1/5
Suppose 2*l - 6*g = -5*g + 4, 4*l - 4*g = 8. Factor -2/5 + 6/5*f - 4/5*f**l.
-2*(f - 1)*(2*f - 1)/5
Let u(v) = 3*v**2 - 2. Let x be u(-2). Suppose 5 = b + p, 0*b = -2*b + 2*p - x. Factor -1/3*f**2 + 0*f - 1/3*f**3 + b.
-f**2*(f + 1)/3
Factor 4/7*g**3 - 4/7*g + 0 - 2/7*g**2 + 2/7*g**4.
2*g*(g - 1)*(g + 1)*(g + 2)/7
Suppose 0 = 4*c - 5*c. Let t(s) be the first derivative of -2/5*s**5 + 0*s**2 + c*s**4 + 0*s**3 + 0*s - 2. What is p in t(p) = 0?
0
Let t(f) be the third derivative of -f**6/360 - f**5/36 - f**4/9 - 2*f**3/9 - 15*f**2. Solve t(d) = 0 for d.
-2, -1
Let j(w) = -w**3 + 8*w**2 - 8*w + 10. Let b be j(7). Solve 8*a**2 - 3*a**3 + 4*a - a**3 + 6*a**b + a**3 = 0.
-2, -2/3, 0
Factor 6*i**4 - 26 + 12 - 6*i**2 + 3*i**5 - 3*i + 14.
3*i*(i - 1)*(i + 1)**3
Let y(w) = 8*w**4 - w**3 - 18*w**2 - w - 14. Let m(t) = -3*t**4 + 6*t**2 + 5. Let b(u) = -11*m(u) - 4*y(u). Factor b(h).
(h + 1)**4
Find g such that 0 - 3 - 22*g**2 - 30*g - 2 - 23*g**2 = 0.
-1/3
Factor 0 + 0*j - 1/5*j**3 - 1/5*j**2.
-j**2*(j + 1)/5
Suppose 0 + 4/5*d**2 - 8/5*d = 0. Calculate d.
0, 2
Let r(l) be the first derivative of -2 + 1/60*l**5 + 2/3*l**3 + 0*l**2 - 1/24*l**4 - 1/480*l**6 + 0*l. Let y(b) be the third derivative of r(b). Factor y(q).
-(q - 2)*(3*q - 2)/4
Let i(a) be the second derivative of 1/60*a**6 + 0*a**2 + 1/6*a**3 - a - 1/8*a**4 + 0*a**5 + 0. Factor i(w).
w*(w - 1)**2*(w + 2)/2
Let d be 2*15/6*1. Suppose -16 = -d*w - 6. Solve 0 + 1/3*i**3 + 0*i - 1/3*i**w = 0 for i.
0, 1
Let f(r) = 9*r**3 + 8*r**2 - 9*r - 3. Let q = 3 + -1. Let h(c) = 4*c**3 + 4*c**2 - 4*c - 2. Let k(m) = q*f(m) - 5*h(m). Solve k(u) = 0.
-2, -1, 1
Let l(b) be the second derivative of -b**7/56 + b**6/40 + 9*b**5/80 - b**4/16 - b**3/4 + b. Solve l(y) = 0 for y.
-1, 0, 1, 2
Let l(o) be the second derivative of -o**7/42 + o**6/10 - 3*o**5/20 + o**4/12 - o. Factor l(t).
-t**2*(t - 1)**3
Factor 5*p**4 - 4*p**3 - 8*p**3 + 10*p - 5*p**2 + 2*p**3.
5*p*(p - 2)*(p - 1)*(p + 1)
Let k(a) be the third derivative of -a**7/35 - 17*a**6/60 - a**5 - a**4 + 8*a**3/3 - 15*a**2. Suppose k(r) = 0. What is r?
-2, 1/3
Factor 2/5*x - 1/5*x**2 + 3/5.
-(x - 3)*(x + 1)/5
Let i(w) be the first derivative of 3*w**4/16 + 5*w**3/4 + 21*w**2/8 + 9*w/4 - 5. Factor i(r).
3*(r + 1)**2*(r + 3)/4
Let w be 2/(-1)*(-1)/2. Let h be w - (-2 - 0 - -1). Factor 0 - 7/2*l**3 - l**2 - h*l**4 + 1/2*l.
-l*(l + 1)**2*(4*l - 1)/2
Let g(h) = -4*h**3 - 11*h**2 - 7*h. Let o(d) be the second derivative of -d**5/10 - d**4/2 - 2*d**3/3 + 4*d. Let v(f) = -6*g(f) + 11*o(f). Factor v(y).
2*y*(y - 1)*(y + 1)
Let t(s) = 3*s - 37. Let m be t(13). Determine o, given that 2/5 + m*o - 18/5*o**3 + 6/5*o**2 = 0.
-1/3, 1
Let x(f) be the first derivative of -5*f**3/6 + 10*f - 6. Factor x(p).
-5*(p - 2)*(p + 2)/2
Let g(y) be the first derivative of 3*y**5/5 - 9*y**4/4 - y**3 + 9*y**2/2 - 6. Factor g(u).
3*u*(u - 3)*(u - 1)*(u + 1)
Factor -30 - 55*h - 4 + 3*h**2 - 13*h**2 + 9.
-5*(h + 5)*(2*h + 1)
Let f(l) be the first derivative of 1/720*l**6 + 2 + 0*l + 1/12*l**4 - 4/3*l**3 - 1/60*l**5 + 0*l**2. Let k(w) be the third derivative of f(w). Factor k(a).
(a - 2)**2/2
Suppose 2/9*u**5 - 4/9*u**4 - 4/9 - 4/9*u**3 + 2/9*u + 8/9*u**2 = 0. What is u?
-1, 1, 2
Let p(s) be the second derivative of s**2 + 1/2*s**4 + 0 + s**3 + 3*s + 1/10*s**5. Factor p(f).
2*(f + 1)**3
Let t = -345/2 - -174. Let o = -1/2 + 2. Solve 1/2*i**2 + 0*i - 1/2*i**5 - t*i**3 + 0 + o*i**4 = 0.
0, 1
Suppose -4*n - 30 = 2*l - 3*n, 4*l + 60 = 5*n. Let h be 3*(-1)/l*2. Let 2/5*o**3 + 0 + 0*o**2 - h*o = 0. What is o?
-1, 0, 1
Suppose 20*y - 3*y**3 + 44*y**2 + 31*y**3 + 11*y**4 - 7*y**4 = 0. What is y?
-5, -1, 0
Let f = 457 - 453. Factor -5/4*l**3 + 2 + 33/8*l**2 + 1/8*l**f - 5*l.
(l - 4)**2*(l - 1)**2/8
Factor 4*w**5 + 8*w**4 - 34*w**3 - 29*w**3 - 8*w**2 + 59*w**3.
4*w**2*(w - 1)*(w + 1)*(w + 2)
Suppose 5*u - f + 2*f + 8 = 0, 3*f + 6 = 3*u. Let t = 1 - u. Factor 2*i**3 + 0*i**3 - 3*i**4 + 2*i**2 + 2*i**t + i**4.
-2*i**2*(i - 2)*(i + 1)
Factor 2/15*k**2 - 2/15*k + 0.
2*k*(k - 1)/15
Let j = 159 - 787/5. Factor -22/5*i + 4/5 - j*i**3 + 26/5*i**2.
-2*(i - 2)*(i - 1)*(4*i - 1)/5
Let w(l) be the third derivative of 0 + 0*l**3 + 0*l - l**2 - 1/120*l**6 - 1/210*l**7 + 1/60*l**5 + 1/24*l**4. Factor w(q).
-q*(q - 1)*(q + 1)**2
Let t(i) be the first derivative of 10/21*i**3 + 0*i - 3 + 1/7*i**2 + 2/7*i**4. Factor t(y).
2*y*(y + 1)*(4*y + 1)/7
Let k(g) be the third derivative of 1/40*g**6 - 1/6*g**3 + 0*g - 1/8*g**4 + 0 - 2/105*g**7 + 1/12*g**5 + g**2. Factor k(s).
-(s - 1)**2*(s + 1)*(4*s + 1)
Let p(o) be the first derivative of 0*o - 5 + 1/3*o**2 - 1/8*o**4 + 0*o**3 - 1/30*o**5. Determine m, given that p(m) = 0.
-2, 0, 1
Factor -117*u + 53*u + 59*u + 5*u**2.
5*u*(u - 1)
Let m(r) be the third derivative of r**6/200 - 3*r**5/100 + 3*r**4/40 - r**3/10 - 7*r**2. Factor m(c).
3*(c - 1)**3/5
Suppose m - 10 = -m. Let y(d) = -d**2 + 7*d - 6. Let k be y(m). What is b in 0 + 0*b + 1/3*b**3 + 1/3*b**k + 0*b**2 = 0?
-1, 0
Let y(a) be the third derivative of a**2 + 1/945*a**7 + 1/90*a**5 + 0 - 1/180*a**6 - 1/108*a**4 + 0*a**3 + 0*a. Factor y(f).
2*f*(f - 1)**3/9
Find f such that 3 + 8*f**3 - 3 + 6*f**4 - 5*f**5 + 3*f**5 = 0.
-1, 0, 4
Suppose 2*g - 3*a - 22 - 20 = 0, -4*a = -16. Let i = g - 24. Factor 0 + 0*x - 2/9*x**5 + 0*x**4 + 2/9*x**i + 0*x**2.
-2*x**3*(x - 1)*(x + 1)/9
Let f(r) be the first derivative of -r**9/3024 + r**8/560 - r**6/90 + 2*r**3/3 + 3. Let h(l) be the third derivative of f(l). Factor h(t).
-t**2*(t - 2)**2*(t + 1)
Let y(a) be the first derivative of -14*a**5/5 - a**4 + 14*a**3/3 + 2*a**2 - 6. Suppose y(v) = 0. What is v?
-1, -2/7, 0, 1
Let s(n) be the first derivative of 0*n**2 + 1/20*n**4 + 0*n + 0*n**3 + 5. Suppose s(k) = 0. What is k?
0
Find g such that -2/7*g**2 - 2/7*g + 0 = 0.
-1, 0