r x(t).
2*t*(t - 2)*(t - 1)*(t + 1)/11
Let l(r) be the third derivative of 0 + 7*r**2 + 0*r + 1/60*r**5 - 1/12*r**4 + 1/6*r**3. Suppose l(f) = 0. Calculate f.
1
Let 4*p - 27*p**3 - 11*p**2 + 26*p**3 + 25*p**3 - 16*p**4 + 4*p**5 - 5*p**2 = 0. What is p?
0, 1
Let g(p) = 250*p**5 - 390*p**4 - 335*p**3 + 265*p**2 - 45*p. Let t(v) = v**5 - v**4 - v**3 + v**2 - v. Let a(f) = -g(f) + 5*t(f). Determine c so that a(c) = 0.
-1, 0, 2/7, 2
Factor 1/2*p**2 - 1/2*p**3 + 0 + 0*p.
-p**2*(p - 1)/2
Let o(t) be the third derivative of t**7/42 + t**6/12 - t**5/12 - 5*t**4/12 - t**2 - 16*t. Factor o(g).
5*g*(g - 1)*(g + 1)*(g + 2)
Let 6 + 12*p - 20*p - 2*p**2 - 14 = 0. Calculate p.
-2
Suppose i = -3*i + 4. Let r be 6*2/(-4) + 5. Factor -i + 5 - 2*x - 4*x + r*x**3.
2*(x - 1)**2*(x + 2)
Let i(w) be the third derivative of -5*w**8/336 - w**7/21 + w**6/24 + w**5/6 - 9*w**2. What is h in i(h) = 0?
-2, -1, 0, 1
Let r(h) = 3*h + 7. Let q be r(-7). Let n = q + 14. Determine a so that -4/11*a**2 + n + 2/11*a**3 + 2/11*a = 0.
0, 1
Let z(k) = -9*k**2 - 10*k - 8. Let f(h) = 6*h**2 + 7*h + 5. Let s(r) = 8*f(r) + 5*z(r). Factor s(o).
3*o*(o + 2)
Suppose 0 = -4*a - 5*s + 21, 4*a - 6 = -3*s + 13. Let 3*f**a + f**3 - f**2 - 6*f**5 + 5*f**5 - 2*f**4 = 0. Calculate f.
-1, 0, 1
Suppose 0 = w - 7 + 3. Factor 0*i**5 - 2*i**5 - w*i**4 + 0*i**4 - 2*i**3.
-2*i**3*(i + 1)**2
Suppose 8*x = 3*x - 4*t + 19, -2*x + 10 = 4*t. Factor -18*k - 28*k**2 - 4 + 8*k**2 - 8*k**x + 2*k**3.
-2*(k + 1)*(k + 2)*(3*k + 1)
Let z(t) be the third derivative of -t**6/40 + t**5/10 + 3*t**4/8 - 49*t**2. Factor z(d).
-3*d*(d - 3)*(d + 1)
Let w = -86 + 86. Determine b so that -4/7*b**5 + 0 + w*b + 4/7*b**3 + 4/7*b**4 - 4/7*b**2 = 0.
-1, 0, 1
Let n(w) be the second derivative of -w**7/126 - w**6/18 - w**5/6 - 5*w**4/18 - 5*w**3/18 - w**2/6 - 48*w. Find r such that n(r) = 0.
-1
Factor 0*i + 3/7*i**4 - 24/7*i**2 + 48/7 + 0*i**3.
3*(i - 2)**2*(i + 2)**2/7
Let d be 1*3 - 65/25. Let 0 - 2/5*z**2 - 2/5*z**3 + d*z**5 + 2/5*z**4 + 0*z = 0. What is z?
-1, 0, 1
Let h(w) be the third derivative of 1/96*w**4 - 5*w**2 + 0*w - 1/24*w**3 - 1/240*w**6 + 1/120*w**5 + 0 - 1/840*w**7 + 1/1344*w**8. Factor h(x).
(x - 1)**3*(x + 1)**2/4
Let r = -1/119005 - -16541807/13328560. Let s = r + 3/16. Factor s*w + 4/7 - 2*w**2.
-2*(w - 1)*(7*w + 2)/7
Let f(w) be the third derivative of -w**6/1020 + w**5/255 + 7*w**4/204 + 4*w**3/51 - 14*w**2. Determine h, given that f(h) = 0.
-1, 4
Let n(u) = -u. Let j be n(-3). Let b(v) = -2*v - 10. Let g be b(-6). Determine q so that -8*q - 4*q**3 + 12*q**j + q**2 - 3*q**g + 2 = 0.
-1, 1/4, 1
Let -3*d**5 + 9 + 15*d**4 - 128*d - 119*d**3 + 23 + 17*d**4 + 186*d**2 = 0. What is d?
2/3, 1, 4
Factor 4*d**2 + 6*d + 2/3*d**3 + 0.
2*d*(d + 3)**2/3
Let n(t) be the second derivative of -t**4/48 + t**3/24 + t**2/4 - 6*t + 4. Let n(r) = 0. What is r?
-1, 2
Suppose 0 + 3/7*y**4 - 9/7*y**3 + 0*y + 6/7*y**2 = 0. Calculate y.
0, 1, 2
Let g be 6/18 - 8/(-3). Let q(n) be the third derivative of 0 + n**2 + 0*n**4 + 0*n**g + 1/120*n**6 + 0*n + 0*n**5. Let q(v) = 0. Calculate v.
0
Let m(n) = n**2 - n - 2. Suppose 13 - 1 = 3*b, -12 = -2*i - 2*b. Let g be m(i). Factor 0 + g*d**3 + 0*d - 1/3*d**2 + 1/3*d**4.
d**2*(d - 1)*(d + 1)/3
Let v(c) be the third derivative of -1/240*c**5 + 1/24*c**3 - 4*c**2 + 1/96*c**4 + 0 + 0*c - 1/480*c**6. Factor v(y).
-(y - 1)*(y + 1)**2/4
Suppose 7*h = 11*h - 36. What is c in 3*c**3 + h*c**2 + 5 - 7*c**2 - 5 - c = 0?
-1, 0, 1/3
Let h be 143/26 + (-3)/(-2). Let k(n) be the second derivative of -1/42*n**h + 0*n**2 + 1/6*n**3 + 1/6*n**4 - 1/15*n**6 + 0*n**5 + n + 0. Factor k(b).
-b*(b - 1)*(b + 1)**3
Suppose -o + 9 = 3*n - 0*o, 2*n + 2*o - 2 = 0. Suppose 3*g**3 - 6*g**4 - 2*g**2 + 5*g**2 - 3*g + 3*g**n = 0. What is g?
-1, 0, 1
Let b(j) = -j**2 - 4*j. Let i be b(-3). Factor -1 - 8*x**2 + 11/2*x + 7/2*x**i.
(x - 1)**2*(7*x - 2)/2
Let p(t) be the first derivative of 2*t**5/65 + t**4/26 - 2*t**3/39 - t**2/13 + 3. Determine m, given that p(m) = 0.
-1, 0, 1
Let h(k) be the first derivative of k**6/1620 + k**5/135 + k**4/36 - k**3 - 1. Let p(x) be the third derivative of h(x). Let p(i) = 0. What is i?
-3, -1
Let u(h) be the first derivative of -h**7/735 + h**6/210 - h**5/210 + 2*h**2 + 2. Let f(n) be the second derivative of u(n). Suppose f(r) = 0. Calculate r.
0, 1
Let u(i) be the third derivative of -i**5/60 + i**4/24 + i**3 - 22*i**2. Let u(g) = 0. What is g?
-2, 3
Let x(v) = -3*v**2 - 2*v + 5. Let r(j) = j**2 + j - 1. Let h(q) = -q - 1. Suppose -5*s + 12 = -s. Let k be h(s). Let m(n) = k*r(n) - x(n). Factor m(b).
-(b + 1)**2
Factor -o**3 + 5/4*o**2 + 0 + 1/4*o**4 - 1/2*o.
o*(o - 2)*(o - 1)**2/4
Let k(w) be the second derivative of -1/30*w**4 + 0 + 2*w + 1/5*w**2 - 1/50*w**5 + 1/15*w**3. Determine z, given that k(z) = 0.
-1, 1
Let c(y) = y**3 + 13*y**2 + 12*y - 10. Let o be c(-12). Let h be (-1)/3 - o/3. Let v**4 - 1/2*v + 0 + 0*v**h + 1/2*v**5 - v**2 = 0. What is v?
-1, 0, 1
Let l be (-2)/(-8)*(-32)/(-42). Let z(u) be the first derivative of -l*u**3 - 1/14*u**4 + 0*u**2 - 1 + 0*u. Let z(m) = 0. Calculate m.
-2, 0
Let d(w) be the first derivative of w**6 + 2*w**5/5 - w**4 + 7. Factor d(g).
2*g**3*(g + 1)*(3*g - 2)
Let p(k) = -k**4 - k**3 - k**2 - k. Let m(j) = -4*j**4 - 4*j. Suppose -w - 3 = 5*n, -5*w + 7 + 8 = -5*n. Let g(x) = n*m(x) + 2*p(x). Factor g(r).
2*r*(r - 1)**2*(r + 1)
Let t(q) be the first derivative of 3*q**4/4 - q**3 - 6*q**2 + 12*q + 1. Suppose t(p) = 0. What is p?
-2, 1, 2
Solve -1/3*f**4 + 0 + 0*f - 16/3*f**2 - 8/3*f**3 = 0.
-4, 0
Let m(r) = -15*r**2 + 45*r - 20. Let g(n) = -n**2 + n + 1. Let f(h) = -10*g(h) + m(h). Determine k so that f(k) = 0.
1, 6
Let m = -11 + 11. Let s(i) = -i**2 - 9*i. Let t be s(-9). Find n, given that m*n**3 - 1/2*n**2 + t + 1/2*n**4 + 0*n = 0.
-1, 0, 1
Let g(y) be the third derivative of y**7/1365 + y**6/390 - y**4/78 - y**3/39 - 11*y**2. Factor g(w).
2*(w - 1)*(w + 1)**3/13
Let s = -4/169 + 1541/845. Find l such that -6/5 - 3/5*l**2 + s*l = 0.
1, 2
Let k(b) be the second derivative of -b**7/210 - b**6/80 - b**5/120 - 3*b**2/2 + 3*b. Let v(q) be the first derivative of k(q). Factor v(t).
-t**2*(t + 1)*(2*t + 1)/2
Let z(j) be the third derivative of j**5/240 + 5*j**4/96 + j**3/6 + 10*j**2. Factor z(x).
(x + 1)*(x + 4)/4
Let v(n) be the first derivative of 7*n**5/55 + n**4 + 32*n**3/11 + 40*n**2/11 + 16*n/11 + 26. Factor v(i).
(i + 2)**3*(7*i + 2)/11
Let v be (-12)/(-4)*(-2)/(-1503). Let d = 1994/2505 + v. Solve d + 14/5*p**3 - 14/5*p - 4/5*p**2 = 0 for p.
-1, 2/7, 1
Let r(f) = -36*f + 5. Let l be r(4). Let o = -693/5 - l. Factor o*g**3 + 2/5*g**2 - 2/5*g - 2/5.
2*(g - 1)*(g + 1)**2/5
Let n(l) be the second derivative of 0*l**2 + 0 + 0*l**3 + 1/48*l**4 - 2*l. Factor n(h).
h**2/4
Let u be (-5 - -2 - -3 - -2)/16. Let c(a) be the third derivative of 0 - 1/40*a**6 + 1/105*a**7 - 1/60*a**5 - 1/6*a**3 + 0*a + u*a**4 - 4*a**2. Factor c(l).
(l - 1)**2*(l + 1)*(2*l - 1)
Let q be (-9)/12*-16*2/18. Let i(b) be the second derivative of -1/30*b**5 - 8/9*b**3 + b + q*b**2 + 5/18*b**4 + 0. Find p such that i(p) = 0.
1, 2
Suppose -5*w = 4*r - 28, 12 = 4*r + 4. Factor -w*q**4 + 6*q**4 + 7*q**4 + 7*q**4 + 8*q**2 - 36*q**3.
4*q**2*(q - 2)*(4*q - 1)
Let d(l) be the second derivative of -l**5/4 - 35*l**4/12 - 55*l**3/6 - 25*l**2/2 - 5*l - 2. Solve d(r) = 0 for r.
-5, -1
Factor 0 - 2*f**3 + 2*f + 1/2*f**2 - 1/2*f**4.
-f*(f - 1)*(f + 1)*(f + 4)/2
Let w(g) be the third derivative of -g**8/1680 + g**7/350 + g**6/120 - g**5/100 - g**4/30 + 25*g**2. Suppose w(t) = 0. Calculate t.
-1, 0, 1, 4
Let u(l) be the second derivative of -l**4/3 + 8*l. Find v, given that u(v) = 0.
0
Let t(a) be the third derivative of 0*a**6 + 0*a**3 + 0*a + 1/24*a**4 + 1/30*a**5 + 0 - a**2 - 1/336*a**8 - 1/105*a**7. Factor t(m).
-m*(m - 1)*(m + 1)**3
Let w = 9 + -6. Let j be (-9)/(-3) + (1 - -1). What is a in -1 + 14*a**3 + 3*a + w*a - 24*a**2 + j = 0?
-2/7, 1
Let z be 2 - (-1 - -7)/(-3). Let j(n) = -2*n**3 + 6*n**2 + 6*n - 6. Let y(r) = 4*r**3 - 13*r**2 - 13*r + 13. Let x(m) = z*y(m) + 9*j(m). Factor x(g).
-2*(g - 1)**2*(g + 1)
Let z(x) be the third derivative of 1/10*x**5 - 4*x**2 + 1/2*x**3 + 0 + 0*x + 3/8*x**4. Factor z(c).
3*(c + 1)*(2*c + 1)
Let s(u) be the first derivative of -7*u**4/20 - 3*u**3/5 - u**2/5 - 8.