 + 3*w - 2. Let m(q) be the first derivative of o(q). Factor m(y).
-2*(y - 1)*(y + 1)*(5*y - 2)
Let j(n) be the second derivative of -n**7/840 + n**4/6 - 6*n. Let c(w) be the third derivative of j(w). Suppose c(o) = 0. What is o?
0
Let m(o) be the third derivative of -o**6/24 + o**5/20 + o**4/12 + 26*o**2. Suppose m(b) = 0. What is b?
-2/5, 0, 1
Suppose 19 = -i + 20, -4*w - i + 1 = 0. Let 6/7*h**2 + w*h + 3/7*h**3 + 0 = 0. Calculate h.
-2, 0
Let z(g) be the first derivative of -g**6/80 + 3*g**4/32 - g**3/8 + 7*g - 4. Let b(i) be the first derivative of z(i). Find t such that b(t) = 0.
-2, 0, 1
Factor 1/4*l**2 - 1/4*l**3 + 0 - 1/4*l**4 + 1/4*l.
-l*(l - 1)*(l + 1)**2/4
Let h(q) be the second derivative of -5*q**4/3 - 2*q**3/3 - 2*q. Factor h(r).
-4*r*(5*r + 1)
Let a(h) be the second derivative of -2*h**6/15 - 2*h**5/5 + h**4/3 + 4*h**3/3 + 8*h. Factor a(f).
-4*f*(f - 1)*(f + 1)*(f + 2)
Factor 0*q - 2/3*q**3 + 0 + 0*q**4 - 4/9*q**2 + 2/9*q**5.
2*q**2*(q - 2)*(q + 1)**2/9
Let d(i) be the third derivative of 0 + 0*i - 1/60*i**4 + 1/150*i**5 + 7*i**2 - 2/15*i**3. Solve d(v) = 0 for v.
-1, 2
Suppose 5*x = -z + 11 - 34, -x - 5 = 0. Let j be (3 - z) + 4/(-6). Factor 0 + j*a**5 + a**3 - a**4 - 1/3*a**2 + 0*a.
a**2*(a - 1)**3/3
What is t in -15/7*t**3 - 9/7*t**4 + 0*t - 6/7*t**2 + 0 = 0?
-1, -2/3, 0
Let x(r) be the first derivative of 2*r**5/15 + 7*r**4/18 - 2*r**3/27 - 7*r**2/9 - 4*r/9 - 30. Solve x(i) = 0 for i.
-2, -1, -1/3, 1
Determine k, given that 5*k**2 + 0*k**2 - 11*k**2 + 5*k**2 - 2*k + k**3 = 0.
-1, 0, 2
Let m = 12 - 14. Let l be (-80)/10*1/m. Factor 0*h + 0*h**3 + 0*h**l + 0 + 1/3*h**5 + 0*h**2.
h**5/3
Suppose 4*g = 3*g. Let f(j) = -2*j + 2. Let z be f(g). Determine x so that 0 - 3/4*x**z - 3/4*x**3 - 1/4*x**4 - 1/4*x = 0.
-1, 0
Let i(p) be the first derivative of -p**7/14 + 7*p**6/10 - 27*p**5/10 + 5*p**4 - 4*p**3 - 2*p + 4. Let m(s) be the first derivative of i(s). Factor m(h).
-3*h*(h - 2)**3*(h - 1)
Let p(m) = 4*m - 20. Let q be p(5). Let w(s) be the first derivative of q*s**3 + 3/4*s**4 + 0*s + 2 + 0*s**2 + 3/5*s**5. What is k in w(k) = 0?
-1, 0
Solve -o**3 - 1/2*o**5 + o**2 - 3/2*o**4 + 3/2*o + 1/2 = 0 for o.
-1, 1
Let c = -5 - -7. Find n such that 0*n**c - 2*n**2 - 5*n + 6*n - 4 + 5*n = 0.
1, 2
Let z(g) be the second derivative of -g**6/75 + 3*g**5/25 - 13*g**4/30 + 4*g**3/5 - 4*g**2/5 - 19*g. Factor z(c).
-2*(c - 2)**2*(c - 1)**2/5
Let a be (-7 - -7)/(1 - 3). Suppose -2*h - 13 + 17 = a. Factor 0*s - 1/3*s**h + 0.
-s**2/3
Let r(c) be the second derivative of -c**6/10 - 9*c**5/10 - 3*c**4 - 5*c**3 - 9*c**2/2 - 2*c. Factor r(z).
-3*(z + 1)**3*(z + 3)
Let l(b) = -25*b**2 + 63*b - 39. Let x(p) = 25*p**2 - 64*p + 40. Let d(a) = -4*l(a) - 3*x(a). Factor d(t).
(5*t - 6)**2
Let v(k) be the third derivative of k**7/840 - k**6/120 + k**5/120 + k**4/24 - k**3/8 + 8*k**2. Factor v(t).
(t - 3)*(t - 1)**2*(t + 1)/4
Let z(b) be the first derivative of -b**6/21 - 8*b**5/35 + 3*b**4/7 + 8*b**3/21 - 5*b**2/7 + 16. Find c, given that z(c) = 0.
-5, -1, 0, 1
Suppose -2*n = 5*z + 20, -5*n + 16 = -6*n - 4*z. Let j(b) be the third derivative of n + 1/240*b**5 + 0*b + b**2 - 1/32*b**4 + 1/12*b**3. Factor j(v).
(v - 2)*(v - 1)/4
Let q(d) be the second derivative of -d - 1/42*d**4 - 2/21*d**3 + 0*d**2 + 0. Determine a so that q(a) = 0.
-2, 0
Suppose 0 = -t - 0 + 2. Factor -8/5*c**t - 4/5 + 2/5*c**3 + 2*c.
2*(c - 2)*(c - 1)**2/5
Let l be 8/(-2) + 0/(-11). Let h be (l/5)/((-4)/20). Factor -2/3*x**2 + 4/9 - 2/9*x**3 + 2/9*x + 2/9*x**h.
2*(x - 2)*(x - 1)*(x + 1)**2/9
Let y(b) = 36*b**2 + 67*b - 16. Let w(z) = -252*z**2 - 468*z + 112. Let d(x) = 3*w(x) + 20*y(x). Factor d(p).
-4*(p + 2)*(9*p - 2)
Factor 4/15*w**3 - 2/3*w**2 + 4/15*w + 0.
2*w*(w - 2)*(2*w - 1)/15
Let q be (-72)/(-40) - (-2)/10. Suppose -c - q = -2*c. Factor -2/7 + 0*f + 2/7*f**c.
2*(f - 1)*(f + 1)/7
Let p be 21/9 - (-2)/(-6). Let t(m) be the first derivative of 2 - 2*m + 10*m**3 - 7*m**3 - 2*m + 3*m**p + 5*m. Factor t(r).
(3*r + 1)**2
Factor b**2 - 29*b**2 + 4*b**4 - 12 + 32*b + 4*b**2.
4*(b - 1)**3*(b + 3)
Solve -11*o - 5*o**3 - 5*o**2 + 10*o + 5*o**4 + 5*o + o = 0 for o.
-1, 0, 1
Let c be (-120)/(-10)*(24/(-9) + 3). Factor c*q + 7/2*q**3 + 19/2*q**2 - 2.
(q + 1)*(q + 2)*(7*q - 2)/2
Let j = 4 - 10. Let n be (-20)/j - 3/9. Solve -n*v**2 + 4*v**2 - 4*v + 2 + v**2 = 0.
1
Factor -2/7 - 6/7*o + 2/7*o**2 + 6/7*o**3.
2*(o - 1)*(o + 1)*(3*o + 1)/7
Let z(g) be the first derivative of -2*g**5/5 + g**4/2 + 2*g**3 - g**2 - 4*g + 14. Suppose z(s) = 0. Calculate s.
-1, 1, 2
Let n(g) be the first derivative of -g**6/6 - g**5/3 + g**4/12 + 5*g**3/9 + g**2/3 + 3. Let n(y) = 0. Calculate y.
-1, -2/3, 0, 1
Let r = -2 + 5. Let z(s) be the second derivative of 1/5*s**6 + 1/30*s**7 + 1/5*s**2 + 0 + 1/2*s**5 + 2/3*s**4 + 1/2*s**r - 2*s. Find g, given that z(g) = 0.
-1, -2/7
Let o(t) = -5*t**5 - 14*t**4 + 4*t**3 + 12*t**2 + t. Let j(u) = -u**5 + u**4 + u**2 + u - 1. Let m(k) = 2*j(k) + o(k). Factor m(a).
-(a - 1)*(a + 1)**3*(7*a - 2)
Let r = -8 + 26/3. Factor 0 - r*k**2 - 2/3*k**3 + 0*k.
-2*k**2*(k + 1)/3
Determine w, given that 33*w**3 + 189/2*w + 81/2 + 81*w**2 + 13/2*w**4 + 1/2*w**5 = 0.
-3, -1
Let q(a) be the third derivative of a**5/30 - a**4/12 - 2*a**3/3 + 26*a**2. Factor q(r).
2*(r - 2)*(r + 1)
Let y(s) = -s**3 - 26*s**2 - s. Let v(a) = -18*a**2 - 9*a. Let d(r) = 9*r**2 + 4*r. Let u(f) = 9*d(f) + 4*v(f). Let k(i) = 8*u(i) + 3*y(i). Factor k(c).
-3*c*(c + 1)**2
Let b be (-7)/2*(-2)/83. Let c = b - -712/415. Factor -9/5*a + 3/5 + c*a**2 - 3/5*a**3.
-3*(a - 1)**3/5
Let k(m) be the second derivative of -m**7/168 - m**6/24 - m**5/10 - m**4/12 + 17*m. Determine u, given that k(u) = 0.
-2, -1, 0
Let r(z) = -z**3 + 19*z**2 - 50*z + 34. Let o be r(16). Factor -2/3 + 2*p - 2/3*p**5 - 4/3*p**3 - 4/3*p**2 + o*p**4.
-2*(p - 1)**4*(p + 1)/3
Factor 2/15*b + 0*b**2 + 0 - 4/15*b**3 + 2/15*b**5 + 0*b**4.
2*b*(b - 1)**2*(b + 1)**2/15
Let m(s) = -s**3 - 4*s**2 + 6*s + 10. Let d(p) = -p**3 - 5*p**2 + 7*p + 11. Let z be ((-8)/(-6))/((-30)/45). Let k(l) = z*d(l) + 3*m(l). Solve k(i) = 0 for i.
-2, 2
Let y = 26/9 + -14/9. Let i(b) be the second derivative of -1/30*b**5 + 1/6*b**4 + 0*b**3 + 0 + b - y*b**2. Factor i(m).
-2*(m - 2)**2*(m + 1)/3
Let t = 6 + -8. Let m be 5*2/(-10)*t. Factor w**2 + w**3 + 0*w + 2*w - 4*w**m.
w*(w - 2)*(w - 1)
Let b(v) be the first derivative of v**6 - 22*v**5/5 + 6*v**4 - 8*v**3/3 + 29. Solve b(p) = 0 for p.
0, 2/3, 1, 2
Let c = 128/45 - 12/5. Find u, given that 0 + 14/3*u**4 + c*u**2 - 26/9*u**3 + 0*u = 0.
0, 2/7, 1/3
Let i(u) = u - 3. Let a be i(6). Suppose -2 = -0*x + a*x - 4*l, 2 = -2*x + 3*l. Let s**2 + x*s**2 - 2*s**2 = 0. What is s?
0
Let v(g) be the third derivative of 2*g**7/35 - 7*g**6/30 + g**5/3 - g**4/6 + 3*g**2. Factor v(t).
4*t*(t - 1)**2*(3*t - 1)
Let t(m) be the third derivative of m**6/780 - m**5/65 + m**4/13 - 8*m**3/39 - 7*m**2. Factor t(a).
2*(a - 2)**3/13
Factor 3 - 3/2*a + 3/2*a**3 - 3*a**2.
3*(a - 2)*(a - 1)*(a + 1)/2
Let o be -8 - 3/(-1) - (-210)/21. Factor 1/3*u**o + 0*u + 2/3*u**4 + 1/3*u**3 + 0*u**2 + 0.
u**3*(u + 1)**2/3
Let k(c) be the first derivative of c**5/330 + c**4/66 + 3*c**2/2 + 6. Let p(t) be the second derivative of k(t). Factor p(b).
2*b*(b + 2)/11
Let s be (-5 + 2)/(-1) + 0. Suppose s*t + 2*t = 0. Find b such that 0*b**2 + 2/5*b**3 - 2/5*b + t = 0.
-1, 0, 1
Let r(s) = 4 - s + s**3 - 5*s**4 + s**2 + 0 - 3 + 4*s**4. Let g(m) = -5*m**4 + 2*m**3 + 5*m**2 - 2*m + 1. Let t(w) = g(w) - r(w). Factor t(b).
-b*(b - 1)*(b + 1)*(4*b - 1)
Let m be 4 + (8880/(-25))/(-6). Let v = 322/5 - m. Factor 3*b**2 - 3/5*b**4 + v*b + 0 - 3/5*b**5 + 9/5*b**3.
-3*b*(b - 2)*(b + 1)**3/5
Let l be 10/4 + (-8)/16. Suppose 4*i + 21 + 19 = 4*y, 2*y = -2*i. Factor l*s**4 - 2*s**2 + 2*s**3 - 2*s**y + 0 + 0.
-2*s**2*(s - 1)**2*(s + 1)
Suppose 0*r + 2*r = -8. Let u = r - -6. Factor -1/5*i + 1/5*i**u + 0.
i*(i - 1)/5
Let a(g) be the third derivative of -g**7/350 + g**6/50 - g**5/25 + 13*g**2. Factor a(m).
-3*m**2*(m - 2)**2/5
Factor 3/4*c**3 - 3/4*c**2 + 3/4 - 3/4*c.
3*(c - 1)**2*(c + 1)/4
Let c(y) be the third derivative of 5*y**8/336 + 5*y**7/14 + 25*y**6/12 + 35*y**5/6 + 75*y**4/8 + 55*y**3/6 - 20*y**2 - 2. Determine p, given that c(p) = 0.
-11, -1
Let a(f) be the second derivative of -4*f + 0*f**3 + 