et g(f) be the third derivative of 0*f**3 + 0 - 1/210*f**5 - l*f**4 + 0*f + f**2. Find k such that g(k) = 0.
-1, 0
Suppose 10 = -3*s + 5*s. Factor 1 + f**2 - 16*f + 20*f - f**3 - s.
-(f - 2)*(f - 1)*(f + 2)
Determine a, given that -3/10*a**3 - 2/5*a**4 + 4/5*a + 1/10*a**5 + a**2 + 0 = 0.
-1, 0, 2, 4
Let x be 2*1 + 1/(-1). Let r(l) = 3*l**2 - l. Let h be r(x). Factor -o**4 - o**3 + o**5 - o**2 + 0*o**h + 2*o**2.
o**2*(o - 1)**2*(o + 1)
Let g(x) be the second derivative of 2*x + 1/36*x**4 + 0 + 1/3*x**2 + 1/6*x**3. Factor g(j).
(j + 1)*(j + 2)/3
Let n(f) = -4*f - 7 + 8*f + 3. Let q be n(3). Factor -5*j**4 - 3 + 1 + 3*j**4 - 12*j**2 - q*j - 8*j**3.
-2*(j + 1)**4
Let n = 1057/3 - 351. Suppose 0 + 11/3*j**4 - 1/3*j + n*j**5 + 3*j**3 + 1/3*j**2 = 0. What is j?
-1, 0, 1/4
Let f(l) be the third derivative of -l**5/420 + l**4/168 + l**3/21 - 7*l**2. Solve f(r) = 0.
-1, 2
Let v(r) be the first derivative of 0*r**2 + 0*r - 1 + 2/5*r**5 + 0*r**3 - 1/2*r**4. Suppose v(f) = 0. Calculate f.
0, 1
Let d(b) be the third derivative of -b**5/330 - b**4/44 - 8*b**2. Factor d(n).
-2*n*(n + 3)/11
Let t(n) be the first derivative of -n**6/33 - 2*n**5/55 + 3*n**4/11 + 8*n**3/33 - 8*n**2/11 - 15. Determine m so that t(m) = 0.
-2, 0, 1, 2
Let x(g) be the second derivative of g**8/6720 - g**7/2520 - g**6/360 - g**4/4 - 4*g. Let z(v) be the third derivative of x(v). Factor z(t).
t*(t - 2)*(t + 1)
Let w(h) be the first derivative of -h**4/12 + 2*h**3/9 + 7*h**2/6 + 4*h/3 - 9. Factor w(n).
-(n - 4)*(n + 1)**2/3
Let c be (0/(2/(10/(-5))))/(-2). Let q(m) be the third derivative of 1/6*m**4 + 0 + c*m**3 - 1/30*m**5 + 0*m + 4*m**2. What is s in q(s) = 0?
0, 2
Let n(w) be the second derivative of -w**4/6 - 2*w**3/3 + 8*w**2 + 19*w. Factor n(t).
-2*(t - 2)*(t + 4)
Factor -2*m**5 - 3*m + 2*m**5 + m**5 - 1 - 2*m**2 + 3*m**4 + 2*m**3.
(m - 1)*(m + 1)**4
Let n(u) be the first derivative of u**5/120 + u**4/48 - u**3/6 - u**2 - 3. Let r(q) be the second derivative of n(q). Factor r(d).
(d - 1)*(d + 2)/2
Suppose 5*p - 12 = 2*p. Suppose 5*f + 4*s = 6, 4*s + 2 = 3*f - p*f. Factor -2*w**2 - 3*w**4 + 2*w**5 + 0*w**f + 5*w**4 - 2*w**3.
2*w**2*(w - 1)*(w + 1)**2
Let v(g) = -9*g**2 + 7*g - 6. Let h(o) = o**2. Let d(k) = -3*h(k) - v(k). Let m(q) = 21*q**2 - 24*q + 21. Let r(c) = 18*d(c) - 5*m(c). Let r(b) = 0. What is b?
1
Let l(a) be the third derivative of -a**5/210 + 5*a**4/84 - 2*a**3/7 - 2*a**2. Find o such that l(o) = 0.
2, 3
Let f be ((-5)/(-3) + -1)*2/6. Let q be 16/(-9) + 0 - -2. Factor f*v + q*v**2 + 0.
2*v*(v + 1)/9
Factor -36/5*c**3 - 28/5*c**2 - 8/5*c - 4*c**4 + 0 - 4/5*c**5.
-4*c*(c + 1)**3*(c + 2)/5
Let r(u) be the third derivative of -u**6/60 - u**5/15 + 5*u**4/12 + 2*u**3 + 16*u**2. Factor r(j).
-2*(j - 2)*(j + 1)*(j + 3)
Let k = -5 + 6. Let o(s) be the third derivative of -s**4/24 + s**3/6 + s**2. Let h(a) = a**2 + 5*a - 6. Let g(i) = k*h(i) + 5*o(i). Factor g(c).
(c - 1)*(c + 1)
Let g(p) be the first derivative of -p**4/6 - 4*p**3/9 + p**2/3 + 4*p/3 + 10. Factor g(u).
-2*(u - 1)*(u + 1)*(u + 2)/3
Let q be ((-350)/(-6))/1 - -3. Let d = q - 60. Factor -27*w**2 - d - 12*w.
-(9*w + 2)**2/3
Suppose 4*m + 6 = -5*z - 19, -3*m - 4*z = 20. Let c(f) = -f + 3. Let k be c(m). Suppose 8/9*p**k - 2/9*p + 0 + 2/3*p**2 = 0. What is p?
-1, 0, 1/4
Let x(j) = j - 3. Let b be x(8). Factor 2/11 + 20/11*u**2 + 10/11*u + 10/11*u**4 + 2/11*u**b + 20/11*u**3.
2*(u + 1)**5/11
Suppose -z + 7 = 2. Let u(o) = 0 - 12*o - 10*o**2 - z + 0. Let x(a) = a**2 + a + 1. Let y(c) = u(c) + 3*x(c). Factor y(v).
-(v + 1)*(7*v + 2)
Let o(y) = -2*y**3 + y**2 + 5*y - 1. Let c(w) = 5*w**3 - w**2 - 10*w + 3. Let u(j) = -3*c(j) - 7*o(j). Factor u(s).
-(s + 1)**2*(s + 2)
Let j(v) be the first derivative of v**5/50 + v**4/30 - v**3/15 - v**2/5 + 5*v - 4. Let y(d) be the first derivative of j(d). Determine h so that y(h) = 0.
-1, 1
Let o(j) be the third derivative of j**8/504 - 2*j**7/315 - j**6/60 + 2*j**5/45 + j**4/9 + 2*j**2 - 1. Factor o(n).
2*n*(n - 2)**2*(n + 1)**2/3
Let k(d) be the third derivative of 1/10*d**6 + 0*d**3 + 5*d**2 + 0*d + 0 + 1/8*d**4 - 1/4*d**5. Suppose k(n) = 0. What is n?
0, 1/4, 1
Suppose 0 = 2*x + 2*x - 8. Let v(g) be the first derivative of -1/14*g**4 + 0*g - 2/35*g**5 + 1 + 2/21*g**3 + 0*g**x + 1/21*g**6. Let v(b) = 0. Calculate b.
-1, 0, 1
Suppose 2*c + 19 = 23. Solve -2/3*y + 0*y**3 + 0 - y**c + 1/3*y**4 = 0 for y.
-1, 0, 2
Suppose -1 - 3 = -2*h. Let t(w) be the second derivative of 2/3*w**2 - h*w - 2/9*w**3 + 1/36*w**4 + 0. What is p in t(p) = 0?
2
Let t(k) = 3*k**3 - 6*k**2 + 9*k - 9. Let d(y) = -y**3 + 3*y**2 - 4*y + 4. Let u(g) = 9*d(g) + 4*t(g). Factor u(l).
3*l**2*(l + 1)
Let k(c) = -c**3 - 7*c**2 - 6*c + 4. Let a be k(-6). Factor 5*h - 2*h**2 - a*h + h**3 + 0*h.
h*(h - 1)**2
Suppose 0 = 4*h + 1 - 13. Suppose -6 = h*m - 3*l, -2*m - 2*l = 2*l - 26. Suppose 0*j**m + 3/2*j**2 + j + 0 - 1/2*j**4 = 0. What is j?
-1, 0, 2
Let t be (-2)/8 - (-102)/24. Let z(s) be the second derivative of 1/20*s**5 - 1/2*s**2 + 0 + 1/12*s**t + 3*s - 1/6*s**3. Factor z(u).
(u - 1)*(u + 1)**2
Let a(j) = -j**4 - j**2 - 1. Let u(f) = 7*f**5 - 20*f**4 - 17*f**3 + 58*f**2 - 44*f + 4. Let c(x) = 4*a(x) - u(x). Determine g, given that c(g) = 0.
-2, 2/7, 1, 2
Let t = 17/35 - 3/35. Let g(n) be the second derivative of 0 + 2*n + t*n**2 - 1/3*n**3 - 7/30*n**4. Factor g(o).
-2*(o + 1)*(7*o - 2)/5
Let c(b) be the third derivative of 0*b**3 + 3/160*b**6 + 1/280*b**7 + 1/32*b**4 + 0 + 0*b + 9*b**2 + 3/80*b**5. What is w in c(w) = 0?
-1, 0
Let w(p) be the first derivative of 0*p**2 + 0*p - 2 - 1/9*p**3. Let w(c) = 0. Calculate c.
0
Let r(c) = 41*c**4 - 26*c**3 + 8*c**2 - 5. Let n(l) = 42*l**4 - 27*l**3 + 9*l**2 - 6. Let h(y) = -5*n(y) + 6*r(y). Solve h(k) = 0.
0, 1/4, 1/3
Let b(z) be the second derivative of -z**7/525 + z**6/150 + z**5/50 - z**4/15 - 4*z**3/15 - 2*z**2 - 5*z. Let r(l) be the first derivative of b(l). Factor r(x).
-2*(x - 2)**2*(x + 1)**2/5
Let y(g) be the first derivative of g**6/21 - 4*g**5/5 + 73*g**4/14 - 344*g**3/21 + 176*g**2/7 - 128*g/7 - 32. Factor y(a).
2*(a - 4)**3*(a - 1)**2/7
Let k(a) be the second derivative of 0 + 0*a**2 + 0*a**3 + 1/195*a**6 + 1/78*a**4 - 1/65*a**5 + 3*a. Let k(g) = 0. What is g?
0, 1
Suppose -j - 6 = -3*j. Factor -2*g**4 - 3*g**5 + g**5 + g**5 + j*g**5.
2*g**4*(g - 1)
Let t(o) = o**2 - 3*o + 4. Let b be t(3). Let 0*y**2 - 1/3*y**5 - 1/3*y**3 + 0*y + 2/3*y**b + 0 = 0. What is y?
0, 1
Factor 0 + 2/9*q**2 - 4/9*q.
2*q*(q - 2)/9
Let f be (22/77)/((12/(-7))/(-2)). Suppose 2*c**4 + f*c**5 + 4*c**2 + 4/3*c + 0 + 13/3*c**3 = 0. What is c?
-2, -1, 0
Let p(b) = -31*b**5 + 155*b**4 - 91*b**3 - 148*b**2 + 104*b - 16. Let n(t) = t**5 + t**4 - t**3. Let k(w) = 18*n(w) - 2*p(w). What is f in k(f) = 0?
-1, 1/4, 2/5, 2
Let a = 48673/240 + -1014/5. Let i(w) be the third derivative of 0*w**3 + w**2 + 1/96*w**4 + 0 + 0*w - a*w**5. Find t such that i(t) = 0.
0, 1
Let r be (-1)/(-3) + (-10)/(-15). Let i be 3 - (-3 - -3)/r. Factor 10/7*x + 2/7*x**i + 8/7*x**2 + 4/7.
2*(x + 1)**2*(x + 2)/7
Let h = 5 + -2. Let k = 7 - h. Suppose 2/5*m**k + 0 + 2/5*m - 2/5*m**2 - 2/5*m**3 = 0. What is m?
-1, 0, 1
Let c be ((-24)/(-32))/((-3)/(-34)). Let d = c - 8. Factor -1/2*a + d*a**3 + 0*a**2 + 0.
a*(a - 1)*(a + 1)/2
Suppose 2 + 3 = h. Suppose -5*c - 35 = -h*y, -y - 3*c - 5 = -20. Factor 0*w**4 + 2*w - w**4 - 8*w**2 + y*w**2 - 2*w**3.
-w*(w - 1)*(w + 1)*(w + 2)
Let z(x) be the third derivative of -5*x**8/4704 - x**7/1764 + 2*x**6/315 - x**5/105 + x**4/24 - x**2. Let d(n) be the second derivative of z(n). Factor d(g).
-2*(g + 1)*(5*g - 2)**2/7
Let s = 7 + 7. Let r be (4/s)/(3/21). Factor 0*j**2 - 2*j**r + 1 + 3 + 2*j.
-2*(j - 2)*(j + 1)
Let l(y) be the third derivative of 1/28*y**4 + 0 - 9*y**2 + 0*y - 1/140*y**5 + 1/490*y**7 - 3/280*y**6 + 0*y**3 + 1/784*y**8. Suppose l(k) = 0. What is k?
-2, -1, 0, 1
Let s(u) = 26*u**2 + 37*u - 63. Let r(x) = 9*x**2 + 12*x - 21. Let a(v) = -17*r(v) + 6*s(v). Find l, given that a(l) = 0.
-7, 1
Let m(d) = -d**4 - d**3 + d**2 + 1. Let w = -3 - -4. Let x = 29 + -23. Let p(l) = 5*l**4 + 5*l**3 - 4*l**2 - 6. Let t(z) = w*p(z) + x*m(z). Factor t(j).
-j**2*(j - 1)*(j + 2)
Let j(s) be the first derivative of s**6/2 + 9*s**5/5 + 9*s**4/4 + s**3 - 11. What is v in j(v) = 0?
-1, 0
Let h(w) be t