- 5*z**2.
(z - 1)*(z + 1)*(3*z - 1)
Let x(k) be the third derivative of k**6/120 - k**4/8 - k**3/3 - 2*k**2 + 26*k. Factor x(f).
(f - 2)*(f + 1)**2
Let n(h) be the first derivative of 20*h**5 + 95*h**4 + 152*h**3 + 104*h**2 + 32*h - 37. Suppose n(d) = 0. Calculate d.
-2, -1, -2/5
Let k(s) = s**3 - 15*s**2 + s - 15. Let t be k(15). Let i(r) be the second derivative of 1/9*r**3 + 1/18*r**4 + t*r**2 - r + 0. Factor i(x).
2*x*(x + 1)/3
Let r(s) be the third derivative of -s**7/105 + s**6/60 + 7*s**2. Solve r(i) = 0.
0, 1
Let l = 28 + 133. Let b = l - 479/3. Determine y so that -8/3*y + b - 1/3*y**3 + 5/3*y**2 = 0.
1, 2
Let v(q) be the second derivative of q**6/40 - 3*q**5/40 + q**4/16 - 3*q**2/2 + 4*q. Let t(k) be the first derivative of v(k). Find f, given that t(f) = 0.
0, 1/2, 1
Let c(a) be the third derivative of a**6/480 + a**5/240 - a**4/96 - a**3/24 + 5*a**2. Suppose c(f) = 0. Calculate f.
-1, 1
Let j(u) be the second derivative of 3*u**5/40 + u**4/2 - u**3/4 - 3*u**2 + 4*u. What is y in j(y) = 0?
-4, -1, 1
Let n(t) be the second derivative of t**7/70 + 3*t**6/25 + 9*t**5/25 + 2*t**4/5 - 28*t. Determine l so that n(l) = 0.
-2, 0
Suppose -28*p - 10 = -30*p. Let d = -722/153 + 84/17. Factor -2/9*f**4 + 2/9*f**p + 0*f - 2/9*f**3 + 0 + d*f**2.
2*f**2*(f - 1)**2*(f + 1)/9
Factor 0 - 8/5*x + 28*x**4 - 10*x**5 + 56/5*x**2 - 138/5*x**3.
-2*x*(x - 1)**2*(5*x - 2)**2/5
Let a = 20/3 - 6. Let -2/3*p**2 + a + 0*p = 0. Calculate p.
-1, 1
Find t such that 1/4*t**2 - 1/8*t + 0*t**3 + 1/8*t**5 - 1/4*t**4 + 0 = 0.
-1, 0, 1
Let x(f) be the second derivative of 11/40*f**6 + 0 + 0*f**2 + 9/16*f**4 + 1/4*f**3 + 9/16*f**5 + 4*f + 3/56*f**7. Solve x(r) = 0.
-1, -2/3, 0
Let o = -697/28 - -7169/288. Let u = o - -120971/22176. What is v in 8/11 - 24/11*v - 2*v**2 + u*v**3 + 50/11*v**4 = 0?
-1, 2/5
Let c(i) = -8*i**4 - 10*i**3 - i**2 - 8*i. Let n(o) = -o**4 - o**3 - o. Let h(r) = 4*c(r) - 36*n(r). Factor h(t).
4*t*(t - 1)**2*(t + 1)
Let j be 6 + (1 - 5) + (-1 - -1). Find g such that 8/3*g - 8/3 - 2/3*g**j = 0.
2
Let w(i) = -i**3 - 5*i**2 - 2*i - 6. Let s be w(-5). Let d(c) = 18*c - 2. Let t be d(s). Let -56*j - 103*j**2 - 49*j**2 + 34*j**2 - 8 - t*j**3 = 0. Calculate j.
-1, -2/5, -2/7
Let j(u) be the first derivative of -u**4/4 - u**3/3 - u - 1. Let v(p) = -6*p**3 - 5*p**2 + p - 5. Let z(c) = -5*j(c) + v(c). Factor z(t).
-t*(t - 1)*(t + 1)
Let d(b) be the third derivative of b**7/560 + b**6/120 - 7*b**3/6 + 8*b**2. Let w(x) be the first derivative of d(x). Suppose w(h) = 0. What is h?
-2, 0
Let v(b) be the first derivative of -b**5/3 - 8*b**4/9 - 2*b**3/9 + 4*b**2/3 - 3*b - 4. Let x(z) be the first derivative of v(z). Solve x(p) = 0 for p.
-1, 2/5
Let d(q) = -q**4 + q**2 - 1. Let k(s) = -425*s**4 + 1800*s**3 - 2340*s**2 + 800*s - 100. Let b(p) = 20*d(p) - k(p). Factor b(n).
5*(n - 2)**2*(9*n - 2)**2
Let y(t) be the second derivative of -t**9/1680 + t**8/560 - t**7/840 - 5*t**4/12 - 5*t. Let h(b) be the third derivative of y(b). Factor h(d).
-3*d**2*(d - 1)*(3*d - 1)
Let j(v) be the second derivative of v**6/135 + v**5/90 - v**4/54 - v**3/27 - 14*v. Factor j(t).
2*t*(t - 1)*(t + 1)**2/9
Let l(m) = -2*m**3 - m**2 + m + 1. Let z = 3 - 5. Let b(h) = h**3. Let w(a) = z*b(a) - 2*l(a). Factor w(r).
2*(r - 1)*(r + 1)**2
Let k(c) be the third derivative of c**5/60 + c**4/3 + 8*c**3/3 + 2*c**2. Factor k(o).
(o + 4)**2
Let r = -48 + 54. Let w(p) = p**3 + 4*p**2 + 3*p + 1. Let k be w(-2). Factor -r*q**2 - 14/9*q**4 - 4/9 - 26/9*q - 46/9*q**k.
-2*(q + 1)**3*(7*q + 2)/9
Let w(o) be the first derivative of o**5/70 + o**4/42 - 2*o**3/21 - 5*o + 5. Let d(y) be the first derivative of w(y). Factor d(q).
2*q*(q - 1)*(q + 2)/7
Let l(v) be the second derivative of -35*v**4/12 + 15*v**3/2 - 5*v**2 + 3*v. Factor l(b).
-5*(b - 1)*(7*b - 2)
Let y(u) be the first derivative of u**3/9 + u**2/3 + 1. Factor y(z).
z*(z + 2)/3
Suppose 4*z - 28 = -0*z + 3*v, 0 = 3*z - v - 16. Suppose 4*j - 8 = z*b, 0*j = 3*j + 2*b - 6. Solve j*c**2 - c**3 - 3/2*c**4 - 1/2 + c = 0 for c.
-1, 1/3, 1
Let w(q) be the second derivative of q - 1/84*q**7 + 0*q**4 + 0 + 1/180*q**6 + 0*q**2 + 1/60*q**5 + 0*q**3. Factor w(d).
-d**3*(d - 1)*(3*d + 2)/6
Determine q, given that 9/2*q**3 - q + 0 + 7/2*q**2 = 0.
-1, 0, 2/9
Let t(o) be the first derivative of -2*o**5/15 - o**4/6 + 4*o**3/9 + 5. Factor t(j).
-2*j**2*(j - 1)*(j + 2)/3
Suppose 16 = 6*j - 2*j, 5*j = 5*a + 10. Find z such that 1/2 + 0*z + 1/2*z**4 - z**a + 0*z**3 = 0.
-1, 1
Factor 28/5*x**2 + 36/5 + 12*x + 4/5*x**3.
4*(x + 1)*(x + 3)**2/5
Let x(o) be the second derivative of o**4/12 - 2*o**3 + 18*o**2 + o. Factor x(w).
(w - 6)**2
Let h(j) be the second derivative of j**6/270 - j**4/36 + j**3/27 + 8*j. Factor h(g).
g*(g - 1)**2*(g + 2)/9
Let i(c) be the third derivative of -c**7/105 - 7*c**6/60 - 13*c**5/30 + c**4/4 + 6*c**3 + 4*c**2. Factor i(x).
-2*(x - 1)*(x + 2)*(x + 3)**2
Let f be (-13)/(-52)*0/1. Let a(n) be the second derivative of 0*n**2 + 3*n + 1/21*n**7 + 1/6*n**4 + 0 + f*n**3 - 1/10*n**5 - 1/15*n**6. Factor a(d).
2*d**2*(d - 1)**2*(d + 1)
Let i(f) = -43*f**5 - 64*f**4 + 9*f**3 + 20*f**2 + 2*f + 6. Let s(c) = c**5 + c**4 + c**3 + c + 1. Let m(x) = -i(x) + 6*s(x). Suppose m(b) = 0. Calculate b.
-1, 0, 2/7
Let h = -6 - -12. Let b(j) be the first derivative of 0*j**3 + 0*j**4 + 3 - 1/20*j**5 + 0*j - 1/12*j**h + 0*j**2. Let b(p) = 0. What is p?
-1/2, 0
Let q(v) = -9*v**5 + 9*v**4 + 12*v**3 - 20*v**2 + 13*v. Let r(j) = -8*j**5 + 8*j**4 + 12*j**3 - 20*j**2 + 12*j. Let u(i) = 4*q(i) - 5*r(i). Solve u(x) = 0.
-2, 0, 1
Let m(g) be the third derivative of 1/3*g**3 + 0 + 0*g - 3/40*g**6 - g**2 - 1/30*g**7 + 1/12*g**5 + 3/8*g**4. Let m(p) = 0. Calculate p.
-1, -2/7, 1
Let j(x) be the third derivative of x**8/100800 - x**7/6300 + x**6/900 + x**5/30 + 4*x**2. Let k(g) be the third derivative of j(g). Factor k(v).
(v - 2)**2/5
Let s(w) = -w**3 + 5*w**2 + 8*w - 1. Let a be s(6). Suppose 3*l - a = 1. Factor -1/3 + 0*z**2 + 2/3*z**3 + 1/3*z**l - 2/3*z.
(z - 1)*(z + 1)**3/3
Let q(w) be the third derivative of -w**5/90 - 5*w**4/18 - 25*w**3/9 + 4*w**2. Let q(l) = 0. What is l?
-5
Let d(h) = h**2 - 16*h + 33. Let m be d(14). Suppose 0*t = m*t - 15. Find g, given that 5/3*g - 2/3 + 11/3*g**2 + 4/3*g**t = 0.
-2, -1, 1/4
Let l(i) = -i**3 + 8*i**2 + 2*i - 5. Let j be l(8). Find m such that 34*m**2 - j*m**2 + m**2 + 18*m + 10*m**3 + 4 = 0.
-1, -2/5
Factor 6/19*r**3 + 0*r + 4/19*r**2 + 0 + 2/19*r**4.
2*r**2*(r + 1)*(r + 2)/19
Let o be (-6)/20*(-8)/6. Let n(x) = -3*x + 2. Let h be n(0). Let 8/5*u - 8/5 - o*u**h = 0. Calculate u.
2
Let g be 6*(-3)/(-108)*3*1. Let z(k) be the first derivative of -2 - 8*k - 8*k**2 - 10/3*k**3 - g*k**4. Factor z(i).
-2*(i + 1)*(i + 2)**2
Let n(p) = p**4 + 12*p**3 - 6*p**2 - 7*p + 7. Let u(o) = -o**4 - 6*o**3 + 3*o**2 + 4*o - 4. Let a(d) = -4*n(d) - 7*u(d). Factor a(k).
3*k**2*(k - 1)**2
Let f(z) be the second derivative of 1/6*z**4 + 0 + z + 3/10*z**5 + 1/5*z**6 + 0*z**3 + 1/21*z**7 + 0*z**2. Suppose f(j) = 0. What is j?
-1, 0
Let f(y) = y**4 + 2*y**3 + 3*y**2 + 2*y - 1. Let w(h) = -h**3 + h - 1. Let m(c) = f(c) - w(c). Determine s so that m(s) = 0.
-1, 0
Let g be 44/10 - 8/20. Let m(p) be the first derivative of -1/12*p**g + 5/9*p**3 + 4/3*p - 1 - 4/3*p**2. Solve m(l) = 0 for l.
1, 2
Let l(p) = -p**2 + 10*p - 8. Let r be l(10). Let j be (-26)/(-10) - r/20. Determine w so that 5*w**4 + 8*w**3 - 4*w**j + 2*w**2 - 3*w**4 = 0.
-1, 0
Let v(f) = -f**2 - f - 1. Let r(z) = -5*z**2 + 8*z - 21. Let s(i) = r(i) - 6*v(i). Let j be s(-15). Factor -2/7*u - 2/7*u**3 + j - 4/7*u**2.
-2*u*(u + 1)**2/7
Let h(l) = 7*l**2 - l - 10. Let c(z) = z**2 - z - 1. Let i(t) = -4*c(t) + h(t). Factor i(g).
3*(g - 1)*(g + 2)
Let j(a) be the second derivative of a**7/12600 + a**6/900 + a**5/150 - a**4/12 - 8*a. Let b(n) be the third derivative of j(n). Determine o so that b(o) = 0.
-2
Suppose 2 = -g - 3*y - 10, 5*y + 40 = 5*g. Suppose 23*c**2 + 1 + 2*c - 19*c**2 + g*c = 0. What is c?
-1, -1/4
Let f(w) be the third derivative of -1/54*w**4 - 1/270*w**5 + 0 - 1/27*w**3 + 0*w + 2*w**2. Factor f(k).
-2*(k + 1)**2/9
Let j(u) be the first derivative of -4*u**3/3 - 4*u**2 + 12*u - 8. Factor j(l).
-4*(l - 1)*(l + 3)
Let v(c) be the second derivative of -c**7/42 - c**6/15 - c**5/20 - 10*c. Fact