4 - 0/1. Solve 2*w**3 + b - 20 = 0 for w.
0
Let h(s) be the second derivative of s**7/350 - s**6/200 + 3*s**2/2 + 2*s. Let c(a) be the first derivative of h(a). Factor c(q).
3*q**3*(q - 1)/5
Let p(w) = w**2 - 2*w - 1. Let h(o) = -o**2 + o + 1. Let r(u) = 10*h(u) + 5*p(u). Factor r(i).
-5*(i - 1)*(i + 1)
Let s(j) be the third derivative of j**8/336 - j**7/70 + j**6/120 + j**5/20 - j**4/12 - 6*j**2. Factor s(a).
a*(a - 2)*(a - 1)**2*(a + 1)
Let a(m) = -m**2 + m + 1. Let h(s) = 21*s**2 - 21*s - 18. Let j(z) = -18*a(z) - h(z). Factor j(g).
-3*g*(g - 1)
Solve -9*w**4 + 2*w**3 + 48*w - 4*w**5 + 0*w**3 + 80*w**2 + w**4 + 26*w**3 = 0 for w.
-2, -1, 0, 3
Factor -2*y**3 - 57*y**2 + 2*y**5 - y**4 - 61*y**2 - y**4 + 120*y**2.
2*y**2*(y - 1)**2*(y + 1)
Solve -4*j**2 - 3*j**4 + 2*j + 0*j**2 + 7*j**4 - 2*j**5 = 0 for j.
-1, 0, 1
Let q(y) = -19*y**4 - 30*y**3 + 18*y**2 + 25*y + 6. Let j(l) = 9*l**4 + 15*l**3 - 9*l**2 - 12*l - 3. Let a(n) = -5*j(n) - 3*q(n). What is x in a(x) = 0?
-1, -1/4, 1
Factor -33*n**2 - 2*n + 2*n**4 + 62*n**2 + 4 - 35*n**2 + 2*n**3.
2*(n - 1)**2*(n + 1)*(n + 2)
Let o(c) = 8*c + 1. Let d be o(1). Factor d + w**5 + 2*w**5 - 9.
3*w**5
Let y = 0 + 17. Suppose m + 2*m - 2*x = 2, 2*m + y = 5*x. Solve -2*r**5 + r**5 + 3*r + 2*r**3 - m*r = 0 for r.
-1, 0, 1
Let v(k) be the first derivative of -1/30*k**6 + 0*k**2 - 3*k + 2 + 2/3*k**3 - 2/3*k**4 + 1/4*k**5. Let g(b) be the first derivative of v(b). Factor g(h).
-h*(h - 2)**2*(h - 1)
Let t = 0 + 3. Let f(l) be the first derivative of -2/15*l**5 + 0*l + 0*l**2 - 1 + 0*l**t - 1/6*l**4. Factor f(w).
-2*w**3*(w + 1)/3
Let z = 110 - 110. Factor 0*r + 0*r**3 - 1/3*r**2 + z + 1/3*r**4.
r**2*(r - 1)*(r + 1)/3
Let s(d) be the third derivative of -1/240*d**6 - 1/60*d**5 + 0*d**3 + 0*d**4 + 10*d**2 + 0*d + 0. Factor s(t).
-t**2*(t + 2)/2
Let c(x) be the third derivative of -x**6/1140 + x**5/570 + x**4/114 + 12*x**2. Factor c(m).
-2*m*(m - 2)*(m + 1)/19
Let t be (-38 - -14) + (-2)/(-1). Let f(a) = a**2 + 23*a + 22. Let h be f(t). Factor 2/3*y - 1/3*y**2 + h.
-y*(y - 2)/3
Let d(z) be the second derivative of -3*z**7/14 - 13*z**6/10 - 33*z**5/10 - 9*z**4/2 - 7*z**3/2 - 3*z**2/2 + 36*z. Factor d(p).
-3*(p + 1)**4*(3*p + 1)
Let k(z) = -z - z + 4*z + 9 - z. Let h be k(-7). Let 2/7*x**h - 2/7 + 0*x = 0. What is x?
-1, 1
Let b = 1/38 - -28/19. Let 3/2*u**4 - 3/2*u**2 + 0 + 0*u - b*u**5 + 3/2*u**3 = 0. What is u?
-1, 0, 1
Factor 0 - 50/9*a**4 - 4/9*a - 40/3*a**3 - 14/3*a**2.
-2*a*(a + 2)*(5*a + 1)**2/9
Let v(w) be the third derivative of 0*w - 6*w**2 + 1/30*w**5 + 1/40*w**6 + 0*w**3 + 1/210*w**7 + 0*w**4 + 0. Factor v(l).
l**2*(l + 1)*(l + 2)
Let t(l) = 4 - 1 - 3*l - 3*l**2 + 0 + l**3. Let q(x) = -4*x**3 + 11*x**2 + 11*x - 11. Let a(i) = 6*q(i) + 22*t(i). Factor a(h).
-2*h**3
Suppose 0*h = -h. Let d = 7 + -5. Solve h + r**d + 1/3*r**3 + 2/3*r = 0 for r.
-2, -1, 0
Factor 4/7 - 2/7*r**3 + 8/7*r**2 - 10/7*r.
-2*(r - 2)*(r - 1)**2/7
Let f(j) be the first derivative of 0*j**4 + 4/55*j**5 + 0*j + 2 - 1/33*j**6 - 4/33*j**3 + 1/11*j**2. Factor f(n).
-2*n*(n - 1)**3*(n + 1)/11
Let i = -3 - -7. Suppose 12 = -f + i*f. Find q such that -2/7*q**f + 0 - 2/7*q**3 + 2/7*q**2 + 2/7*q = 0.
-1, 0, 1
Suppose -4*w + 2*u + 18 = 0, 2 = 2*w - 3*u - 5. Let l(i) = i**2 - 5*i + 5. Let z be l(5). Solve -w + z - 9*y**3 + 8*y**3 - y**4 = 0.
-1, 0
Let d be (-2)/4 - (0 - 1). Let z(w) be the first derivative of -5/4*w**4 - 1/12*w**6 + d*w**5 - 5/4*w**2 + 1/2*w - 2 + 5/3*w**3. Factor z(o).
-(o - 1)**5/2
Let h be 0*(-2 + (-3)/(-1)). Let o(g) be the second derivative of -1/90*g**5 + 0*g**2 - 3*g - 1/27*g**3 - 1/27*g**4 + h. Suppose o(k) = 0. Calculate k.
-1, 0
Factor 0*u**3 - 2*u**2 - 2*u**3 + 6*u**5 - 4*u**5 + 2*u**4.
2*u**2*(u - 1)*(u + 1)**2
Let v(j) be the second derivative of -2*j**7/273 - 3*j**6/65 - 8*j**5/65 - 7*j**4/39 - 2*j**3/13 - j**2/13 + j. Factor v(o).
-2*(o + 1)**4*(2*o + 1)/13
Let m(c) be the first derivative of c**5/30 - c**4/6 + c**3/3 - 9*c**2/2 - 3. Let o(q) be the second derivative of m(q). Factor o(g).
2*(g - 1)**2
Let n(r) = -3*r**2 - 1. Let c(b) = -6*b**2 + 18*b + 24. Let t(z) = c(z) - 3*n(z). Let t(k) = 0. Calculate k.
-3
Let w(c) be the third derivative of 1/6*c**4 - c**2 - 1/2*c**3 + 1/30*c**5 + 1/360*c**6 + 0 + 0*c. Let y(h) be the first derivative of w(h). Factor y(g).
(g + 2)**2
Suppose o - 3*o = 4, -2*g + o = -38. Suppose 3*m - g*m**2 + 4 - m + 4*m + 8*m = 0. Calculate m.
-2/9, 1
Let r(v) be the second derivative of -v**6/180 + 2*v**5/45 - v**4/12 + 4*v**2 + 9*v. Let g(q) be the first derivative of r(q). Find y such that g(y) = 0.
0, 1, 3
Suppose 3*n - 10 = 5. Let c = -5 + n. Factor c*m**3 + 0 + 2/3*m**4 + 0*m - 2/3*m**2.
2*m**2*(m - 1)*(m + 1)/3
Find g, given that 15 + 279*g**2 + 5 + 306*g**2 + 200*g + 237*g**3 + 168*g**3 = 0.
-1, -2/9
Let m be 2/8 - (-5)/12. Let p be -3 + (-17)/(85/(-30)). Solve m*s**p + 2/3*s**2 - 1/3*s - 1/3 - 1/3*s**5 - 1/3*s**4 = 0.
-1, 1
Factor 0*m**2 - 1 + 1/2*m**3 - 3/2*m.
(m - 2)*(m + 1)**2/2
Let b = 5 - 3. Factor -5*g**2 - g + 4*g**3 + 6*g**b - 4*g**2.
g*(g - 1)*(4*g + 1)
What is r in 1/6 + 1/6*r**3 - 1/6*r**2 - 1/6*r = 0?
-1, 1
Let p = -223/30 - -38/5. Let t(y) be the second derivative of 0 + 1/3*y**3 - y**2 + 2*y - 1/10*y**5 + p*y**4. Factor t(w).
-2*(w - 1)**2*(w + 1)
Let t(y) be the second derivative of y**9/2520 + y**8/3360 - y**7/630 + y**4/3 - y. Let g(j) be the third derivative of t(j). Factor g(u).
2*u**2*(u + 1)*(3*u - 2)
Let 12/11*z**2 + 2/11*z**3 + 16/11 + 24/11*z = 0. What is z?
-2
Let o(a) be the third derivative of -a**9/12600 + a**8/4200 - a**7/6300 + a**4/8 + 3*a**2. Let n(d) be the second derivative of o(d). Factor n(h).
-2*h**2*(h - 1)*(3*h - 1)/5
Factor 18*m**2 + 18 + 2 - 53*m**2 + 8*m - 25*m**3 + 32*m.
-5*(m - 1)*(m + 2)*(5*m + 2)
Let q(f) be the first derivative of -2*f**5/105 - f**4/7 - 26*f**3/63 - 4*f**2/7 - 8*f/21 + 8. Determine c so that q(c) = 0.
-2, -1
Factor 3/5*f**2 - 2/5 - f.
(f - 2)*(3*f + 1)/5
Let d(g) = -6*g - 5. Let y be d(-1). Let s(t) be the first derivative of 2*t - y + 2/3*t**3 - 2*t**2. Suppose s(v) = 0. Calculate v.
1
Let j be (0/(-10 + 5))/(-4). Factor 1/4*w**3 + j*w + 1/2*w**2 + 0.
w**2*(w + 2)/4
Let j(c) be the first derivative of 0*c**2 + 0*c**5 - 1 + 0*c**3 - 1/2*c**6 + 0*c + 0*c**4. Factor j(i).
-3*i**5
Let y(p) be the second derivative of -p**4/48 - p**3/6 - p**2/2 + 4*p. What is g in y(g) = 0?
-2
Let f(r) = -r**2 + 8*r + 7. Let g be f(8). Factor 0*u**2 + 7*u**2 + g - 4*u - 1 - 9*u**2.
-2*(u - 1)*(u + 3)
Determine b, given that -b + 133 - 2*b - 127 - 3*b**2 = 0.
-2, 1
Let s be 72/90 + (-6)/20. Factor -1/2 + 1/2*b**2 - s*b**3 + 1/2*b.
-(b - 1)**2*(b + 1)/2
Suppose 13 - 4 = 3*s. Let q(h) be the second derivative of 0 + h - 1/120*h**6 + 1/8*h**2 + 0*h**4 - 1/40*h**5 + 1/12*h**s. Let q(d) = 0. Calculate d.
-1, 1
Let f be (-51)/(-595) - (-2)/10. Solve 0 + 2/7*y**3 - f*y + 0*y**2 = 0 for y.
-1, 0, 1
Let d be -17 + 15 + 18/7. Let -2/7*w**5 + 4/7*w**2 - 2/7 - 2/7*w**4 + d*w**3 - 2/7*w = 0. Calculate w.
-1, 1
Let g be (47/(-423))/(10/(-18)). Determine j so that g*j**2 - 1/5*j - 2/5 = 0.
-1, 2
Let r = 4/15 + -1/10. Let p(g) be the third derivative of -r*g**4 + 1/30*g**5 + 0*g**3 + 3*g**2 + 0 + 0*g. Find t, given that p(t) = 0.
0, 2
Let o(k) be the second derivative of -k**4/30 + 4*k**3/15 + k**2 - 18*k. Factor o(x).
-2*(x - 5)*(x + 1)/5
Let c(g) be the first derivative of 2*g**3 + 2 - 6*g + 3*g**2 + g + g - 2*g**2. Factor c(a).
2*(a + 1)*(3*a - 2)
Suppose -57*u**3 + 15*u + 94*u**2 - 84*u + 21*u**4 + 12 + 21*u - 3*u**5 - 19*u**2 = 0. Calculate u.
1, 2
Let h(y) be the first derivative of 3/16*y**2 - 3/8*y**3 - 3 + 0*y. Factor h(r).
-3*r*(3*r - 1)/8
Let s(f) be the second derivative of 4*f**2 + 1/3*f**4 + 2*f**3 + 0 + 4*f. Determine o so that s(o) = 0.
-2, -1
Let m be 1 + 3 + 96/(-28). Factor m + 2*o**2 + 18/7*o.
2*(o + 1)*(7*o + 2)/7
Factor -28/5*q**3 - 4/5 - 2/5*q**5 - 12/5*q**4 - 18/5*q - 32/5*q**2.
-2*(q + 1)**4*(q + 2)/5
Let k(a) be the third derivative of a**8/26880 + a**7/10080 - a**6/2880 - a**5/480 + a**4/12 - 3*a**2. Let j(m) be the second derivative of k(m). Factor j(z).
(z - 1)*(z + 1)**2/4
Let a(p) = -p**3 - 3*p**2 - 2. Let w be a(-3). Let c be ((-24)/(-36))/(w/(-6)). Find j such that 0 + 2/5*j**c + 4/5*j = 0.
-2, 0
Let k(f) be the second d