erivative of d(x). Find t such that n(t) = 0.
0
Let k(h) be the third derivative of -h**6/660 - h**5/110 - h**4/44 - h**3/33 - 4*h**2. Factor k(o).
-2*(o + 1)**3/11
Let u be -1 - -4 - (-2 + 2). Let b(f) be the second derivative of 1/50*f**5 - 1/15*f**4 - 2*f + 0 + 1/15*f**u + 0*f**2. Factor b(o).
2*o*(o - 1)**2/5
Suppose 0 + 6/11*p**3 - 26/11*p**4 + 32/11*p**2 + 8/11*p**5 - 8/11*p = 0. Calculate p.
-1, 0, 1/4, 2
Factor 27*h**2 + 2*h**3 + 41 - 39 + h**3 + 19 + 45*h.
3*(h + 1)**2*(h + 7)
Let c(z) be the second derivative of -z**5/270 + z**4/54 - 3*z**2/2 - z. Let b(o) be the first derivative of c(o). Factor b(v).
-2*v*(v - 2)/9
Let o(s) be the second derivative of 2*s**7/21 + 8*s**6/15 + s**5 + 2*s**4/3 + 12*s. Find w such that o(w) = 0.
-2, -1, 0
Let y(c) = -c**4 + c**2 - c + 1. Let z(t) = -t**2 + 5*t**2 + 4*t**3 - 15*t**2 + 7*t - 9 + 9*t**4. Let n(k) = -22*y(k) - 2*z(k). Suppose n(o) = 0. What is o?
-1, 1
Let m be 20/6 - ((-10)/15 - -1). Let b(z) be the first derivative of m + 0*z - 1/10*z**2 + 1/15*z**3. Factor b(y).
y*(y - 1)/5
Let m(r) = -r**3 - 6*r**2 - 6*r - 1. Let c be m(-5). Let b = -127 - -129. Let 3/2*v**3 + 0*v - 3/4*v**b + 0 - 3/4*v**c = 0. Calculate v.
0, 1
Let y(v) be the third derivative of 2*v**3 - 5*v**2 + 1/10*v**6 + 0 + 3/2*v**4 - 3/4*v**5 + 0*v. Factor y(u).
3*(u - 2)**2*(4*u + 1)
Let s(c) be the first derivative of -c**3 - 3*c**2 - 15. Factor s(a).
-3*a*(a + 2)
Let k(g) be the second derivative of 3*g - 2*g**2 + 1/10*g**5 + 1/15*g**6 + 0 - 1/2*g**4 - 5/3*g**3. Factor k(s).
2*(s - 2)*(s + 1)**3
Let r(g) be the second derivative of 0 + 7/12*g**4 + 3/2*g**3 + g**2 + g. Determine q so that r(q) = 0.
-1, -2/7
Let s(y) be the second derivative of y**5/40 - y**4/24 + 2*y. Let s(l) = 0. Calculate l.
0, 1
Suppose 2*r**3 - r**4 + 0*r**4 + 5*r**3 - 8*r**3 = 0. Calculate r.
-1, 0
Let c(y) = y + 1. Let x be ((-8)/10)/((-2)/10). Let n be c(x). Factor 25*m**3 - 3*m**3 - 32*m**4 + 0*m**3 + 8*m**n + 6*m**5 - 4*m**2.
2*m**2*(m - 1)**2*(7*m - 2)
Let i = -70 + 70. Find z, given that -3/2*z**3 + i - 3/2*z**4 + 3/2*z + 3/2*z**2 = 0.
-1, 0, 1
Let z(y) be the first derivative of y**9/13608 - y**8/3780 + y**3/3 + 7. Let h(k) be the third derivative of z(k). Solve h(l) = 0 for l.
0, 2
Let w = -3 - -5. Factor 0 + 1/6*s**w - 1/6*s.
s*(s - 1)/6
Let n = -9 + 19. Let y be n/(-85) + (-59)/(-68). Factor 1/4*v**3 - 1/2 + 1/4*v**4 - 5/4*v - y*v**2.
(v - 2)*(v + 1)**3/4
Let f(z) be the first derivative of -2*z**3/9 - z**2/3 + 8. Factor f(d).
-2*d*(d + 1)/3
Let t(q) = q. Let i = -5 - -9. Suppose -r - 3 = -i*r. Let d(k) = -k**2 - 4*k - 1. Let v(z) = r*d(z) + 2*t(z). Determine c so that v(c) = 0.
-1
Suppose -3*k = 3*i - 12, -k + 2*k - 5*i = 10. Factor -1/2*t**k + 1/2*t**2 + 0*t + 0 + 1/2*t**3 - 1/2*t**4.
-t**2*(t - 1)*(t + 1)**2/2
Let z be (-34)/(-12) - (-94)/188. Factor -6*p**3 - 14/3*p**2 - 2/3*p**5 - z*p**4 - 4/3*p + 0.
-2*p*(p + 1)**3*(p + 2)/3
Let o(f) = f - 3. Let v be o(6). Let x be (-1)/v + (-111)/(-9). Let 0*m**2 - 2*m**3 - x*m + m**3 + 6*m**2 + 8 = 0. What is m?
2
What is k in 1681*k**2 - 74*k**3 - 140*k**4 - 245*k**5 - 1541*k**2 + 135*k**3 + 164*k**3 + 20*k = 0?
-1, -2/7, 0, 1
Suppose x = 2*n - 4*n + 7, -3*x - 9 = n. Let z(v) be the first derivative of -v**3 + 3 - 3/2*v**2 + n*v. Suppose z(h) = 0. What is h?
-2, 1
Suppose h + 0*h = -1. Let c be (6/h)/3*-2. Factor r**2 - 2*r**2 - 2*r**2 + r**2 - c*r.
-2*r*(r + 2)
Let z(d) be the first derivative of -2 + 0*d + 1/6*d**2 - 1/9*d**3 + 1/15*d**5 - 1/12*d**4. Factor z(r).
r*(r - 1)**2*(r + 1)/3
Let n(x) be the first derivative of -5*x**6/4 + x**5 + 25*x**4/4 - 35*x**2/4 - 5*x + 5. Find v, given that n(v) = 0.
-1, -1/3, 1, 2
Let v(q) be the first derivative of 1/4*q**3 + 1/2*q - 1/16*q**4 + 5/8*q**2 + 3 - 1/20*q**5. Factor v(c).
-(c - 2)*(c + 1)**3/4
Let t(l) be the second derivative of l**3/3 - 2*l. Let x be t(1). Suppose -1/3 + 2/3*j - 1/3*j**x = 0. Calculate j.
1
Let k = 404 + -2012/5. Factor k*f - 2/5*f**2 - 6/5.
-2*(f - 3)*(f - 1)/5
Let v(r) = 4*r**2 - 4*r - 30. Let n(z) be the first derivative of z**3/3 - z**2/2 - 6*z + 1. Let u = -53 - -42. Let o(l) = u*n(l) + 2*v(l). Factor o(x).
-3*(x - 2)*(x + 1)
Suppose -p = -m + 2*m - 11, -4*p + 3*m + 23 = 0. Suppose 0*x - 2*h = 2*x - p, 5*x = h + 20. Find d, given that -4*d + 4*d**2 + 14*d**2 - x*d**2 = 0.
0, 2/7
Factor -7/4*u**3 + u**4 + 1/4*u + 1/2*u**2 + 0.
u*(u - 1)**2*(4*u + 1)/4
Let v = 8 - 8. Suppose l + 0*l = v. Factor 2/7*x**2 + 2/7*x**4 + 0 + 4/7*x**3 + l*x.
2*x**2*(x + 1)**2/7
Let 6*l**2 + 15/2*l + 3 + 3/2*l**3 = 0. What is l?
-2, -1
Let v(p) be the third derivative of -p**8/336 - p**7/210 - 20*p**2. Factor v(f).
-f**4*(f + 1)
Find a such that 2/13*a**3 + 40/13 + 2/13*a**2 - 32/13*a = 0.
-5, 2
Determine q so that 4/3*q - 2/9*q**2 - 2 = 0.
3
Let s be ((-4)/(-16))/((-18)/(-48)). Factor 2/3*v - 2/3*v**3 + s*v**2 - 2/3.
-2*(v - 1)**2*(v + 1)/3
Let u(x) be the first derivative of -x**5/15 + x**4/3 - 5*x**3/9 + x**2/3 + 7. Factor u(f).
-f*(f - 2)*(f - 1)**2/3
Suppose -3*a + 0*a = -6. Find w such that 8*w**4 + 6*w**3 - 12*w**2 + 2*w**2 - 2*w - 4*w + a + 0*w = 0.
-1, 1/4, 1
Let d(h) be the third derivative of 0*h + 0 - 1/504*h**8 - 1/36*h**4 + h**2 + 0*h**5 + 0*h**7 + 1/90*h**6 + 0*h**3. Factor d(w).
-2*w*(w - 1)**2*(w + 1)**2/3
Let c be (5 - 36/6)/(5/(-2)). Let -4/5*f - 2/5*f**2 - c = 0. Calculate f.
-1
Let b(q) = -5*q**2 - 6*q - 4. Let v(h) = 26*h**2 + 30*h + 20. Let g = -4 + 1. Let j(u) = g*v(u) - 16*b(u). Let j(c) = 0. Calculate c.
-2, -1
Let g(i) be the third derivative of -i**8/112 - i**7/35 + i**6/5 - i**5/10 - 7*i**4/8 + 2*i**3 + 4*i**2. Find h such that g(h) = 0.
-4, -1, 1
Suppose 14*g - 7*g = 49. Let r = -4 + 9. Factor 2*p**r - 4*p**4 + 0*p**5 + g*p**3 - 5*p**3.
2*p**3*(p - 1)**2
Let z(b) be the first derivative of -3*b**4/4 + 3*b**3 - 3*b**2 - 2. Factor z(n).
-3*n*(n - 2)*(n - 1)
Let j(l) be the third derivative of -l**6/180 + l**5/90 + l**4/18 - 7*l**2. Factor j(a).
-2*a*(a - 2)*(a + 1)/3
Suppose 0 = -4*a + 2*v + 80, -84 = -4*a - 4*v + 8. Let p = a + -13. Factor -6*f - 5*f**4 + p*f**3 + 3*f**4 + 2*f + 2*f**2 - 4*f**3.
-2*f*(f - 2)*(f - 1)*(f + 1)
Let p(k) be the first derivative of k**3/8 - 9*k**2/8 + 15*k/8 + 5. Find h such that p(h) = 0.
1, 5
Let l(v) be the third derivative of 0 + 1/120*v**5 - 1/240*v**6 - 4*v**2 + 0*v + 0*v**3 + 0*v**4. Factor l(o).
-o**2*(o - 1)/2
Let z(a) be the third derivative of -a**6/280 - a**5/35 - a**4/14 - 6*a**2. Factor z(y).
-3*y*(y + 2)**2/7
Factor x**4 - 3/2*x + 0 - 9/2*x**3 + 5*x**2.
x*(x - 3)*(x - 1)*(2*x - 1)/2
Let d(l) be the third derivative of -l**8/784 - l**7/98 - l**6/28 - l**5/14 - 5*l**4/56 - l**3/14 + 4*l**2. Factor d(u).
-3*(u + 1)**5/7
Let y(q) be the third derivative of -1/270*q**5 + 0*q**3 + 1/945*q**7 + 0*q - 1/54*q**4 + 1/270*q**6 + 0 + 2*q**2. Solve y(j) = 0 for j.
-2, -1, 0, 1
Suppose -4*m + 6 + 2 = 0. Let 0*z**2 + 2*z**2 - z**2 - m*z**2 = 0. What is z?
0
Let p(c) be the second derivative of c**8/280 + 17*c**7/1260 + c**6/120 - c**5/30 - c**4/6 + 4*c. Let m(y) be the third derivative of p(y). Factor m(u).
2*(u + 1)*(3*u + 2)*(4*u - 1)
Suppose -103*f - 158 = -467. What is d in -2/3 - 8/3*d**2 - 4/3*d**f - 20/9*d - 2/9*d**4 = 0?
-3, -1
Let z(t) be the second derivative of t**10/30240 + t**9/6048 + t**8/3360 + t**7/5040 - t**4/6 - t. Let s(r) be the third derivative of z(r). Solve s(y) = 0.
-1, -1/2, 0
Find a, given that 4*a + 183 + 30*a**2 + 23*a**3 - 93 - 98 + 5*a**4 = 0.
-2, -1, 2/5
Let g(u) = 3*u**3 - u**2 + 2*u - 2. Let a be g(1). Factor n**3 + 2*n**a + 2*n**4 + n**3 + 2*n**3.
2*n**2*(n + 1)**2
Suppose -3 = o, -k = 2*k - 4*o. Let i be 1 + 0 - k/(-12). Determine f, given that 1/3 - 1/3*f**4 - 2/3*f + 0*f**2 + i*f**3 = 0.
-1, 1
Let r(m) be the third derivative of -m**6/1620 - m**5/270 + m**3/6 - 2*m**2. Let y(o) be the first derivative of r(o). Factor y(b).
-2*b*(b + 2)/9
Determine j, given that 0 + 4/5*j**4 + 4/5*j**2 + 0*j - 8/5*j**3 = 0.
0, 1
Let p be ((-12)/40)/3 - (-4)/40. Determine s so that 3/2*s**3 + p + 3/2*s**2 + 0*s - 3/2*s**4 - 3/2*s**5 = 0.
-1, 0, 1
Let u be -4 - 22*10/(-45). Solve -2/9 + 4/9*h**2 - 4/9*h + u*h**3 - 4/9*h**5 - 2/9*h**4 = 0.
-1, -1/2, 1
Let q = 6 + -3. Suppose q*s - 3 = 2*s. Suppose i**3 + 5*i + 0*i**2 - 2 - s*i**2 - i**2 = 0. Calculate i.
1, 2
Let g(r) be the se