.
5*c*(c - 2)
Let z(c) be the first derivative of 145/6*c**3 + 6 + 49/12*c**6 + 2*c + 10*c**2 + 235/8*c**4 + 35/2*c**5. Factor z(j).
(j + 1)**3*(7*j + 2)**2/2
Let o be ((-18)/8 - -3)/(3/12). Solve 27/2*s**3 - 18*s**2 + 6*s - o*s**4 + 0 = 0 for s.
0, 1/2, 2
Let d(f) = 2*f**2 + 2*f + 3. Let y(h) = 2*h**2 - 3*h**2 - 2 - 3 + h + 4. Let w(r) = -d(r) - 5*y(r). Factor w(q).
(q - 2)*(3*q - 1)
What is y in 1/6*y**3 - 1/2*y**2 + 0 + 1/3*y = 0?
0, 1, 2
Let v be (2/(-4))/((-1)/(-6)). Let p be (v - -2)*(0 + -4). What is i in i**5 - i**p - i**4 + i**3 + 0*i**3 = 0?
0, 1
Let f(h) be the third derivative of -h**8/1344 - h**7/560 + h**6/120 - h**5/60 - h**2. Let r(t) be the third derivative of f(t). Find u such that r(u) = 0.
-1, 2/5
Suppose 0 = 3*w + 5*u - 140, -7*u = -4*w - 3*u + 144. Let o be w/(-30)*6/(-2). Find t such that 27/2*t**2 - 3/2*t + 6*t**o - 33/2*t**3 - 3/2 = 0.
-1/4, 1
Let n be -3 + -1 + (-307)/(-55). Let u = 24/11 - n. Let u*x**5 - 9/5*x**4 + 6/5*x**3 + 6/5*x**2 + 3/5 - 9/5*x = 0. Calculate x.
-1, 1
Let k(n) be the second derivative of -n**8/4200 + n**6/450 - n**4/60 + n**3/2 - n. Let y(w) be the second derivative of k(w). Suppose y(b) = 0. Calculate b.
-1, 1
Let f(s) = s**3 - 5*s**2 + 4. Let b be f(5). Suppose 0*x - 4*x = -5*m + 4, -x - 12 = -b*m. Factor -u**2 - u - u**2 + m*u**2 - u**3.
-u*(u - 1)**2
Suppose 7*a = t + 4*a - 14, -2*a - 4 = 2*t. Solve -4*w**2 - t*w**5 + 0*w**5 + 4*w**4 + 0*w + 2*w = 0.
-1, 0, 1
Let c = 52 - 46. Let r(n) be the third derivative of 1/735*n**7 + 0*n**3 + 0*n - 1/210*n**c + 0*n**4 + 0 + 1/210*n**5 + 3*n**2. Determine a so that r(a) = 0.
0, 1
Let r(v) = -8*v**3 - 8. Suppose 4*f - f - 4*q = 12, 0 = 2*f - 5*q - 8. Let w = -2 - f. Let k(z) = -z**3 + z**2 + z - 1. Let c(p) = w*k(p) + r(p). Factor c(j).
-2*(j + 1)**3
Let s(j) be the third derivative of -j**6/420 + j**5/210 + 2*j**4/21 - 4*j**3/7 - 5*j**2. Factor s(w).
-2*(w - 2)**2*(w + 3)/7
Let g(j) = -3*j**5 - 15*j**4 - 30*j**3 - 21*j**2 - 3*j - 3. Let x(y) = -y**3 + y - 1. Let a(m) = -g(m) + 3*x(m). Factor a(q).
3*q*(q + 1)**3*(q + 2)
Let j(r) = -r**2 - r + 1. Let f(l) be the second derivative of l**6/30 - 3*l**5/20 + l**4/2 + l**3/3 - 3*l**2/2 + 3*l. Let i(v) = -f(v) - 3*j(v). Factor i(q).
-q*(q - 1)**3
Let p(m) be the third derivative of -m**7/840 - m**6/120 - m**5/60 - 3*m**3/2 - 4*m**2. Let j(h) be the first derivative of p(h). Factor j(l).
-l*(l + 1)*(l + 2)
Suppose -5 = -2*f - 5*p + 9, -2*f = -3*p - 14. Suppose -s**3 + 3*s**5 - f*s**3 + 3*s + 2*s**3 = 0. What is s?
-1, 0, 1
Let w be 8/(-12) - (-52)/60. Factor 2/5 + w*t**2 - 3/5*t.
(t - 2)*(t - 1)/5
Solve 4 + 16*o**4 + 7*o - 8*o**2 - 4*o**5 - 12 - 8*o + 21*o - 16*o**3 = 0 for o.
-1, 1, 2
What is h in 4/9*h - 2/9*h**2 + 0 = 0?
0, 2
Let p(w) be the third derivative of -w**8/10080 - w**7/5040 + w**6/2160 + w**5/720 + w**3/3 - 5*w**2. Let s(c) be the first derivative of p(c). Factor s(j).
-j*(j - 1)*(j + 1)**2/6
Let p(b) be the first derivative of 4*b**3/3 - 10*b**2 + 16*b + 24. Factor p(d).
4*(d - 4)*(d - 1)
Let n(k) be the second derivative of k**3/6 - 3*k. Let m be n(4). Let -4*b**4 + m*b**2 + 6*b**5 + 2*b - 8*b**3 - 3*b + 3*b = 0. Calculate b.
-1, -1/3, 0, 1
Factor -24/13 - 2/13*o**2 - 14/13*o.
-2*(o + 3)*(o + 4)/13
Let v be 3*1/3*5/15. Find g, given that -1/3*g**2 - 2/3*g - v = 0.
-1
Let m(p) be the second derivative of -p**8/30240 + p**4/4 - 3*p. Let u(a) be the third derivative of m(a). Factor u(x).
-2*x**3/9
Let x(d) = -d**2 - 4*d - 3. Let n be x(-2). Let i be n/3 - (-5)/(-105). Factor -i*q**4 + 0 + 0*q**2 + 0*q - 2/7*q**3.
-2*q**3*(q + 1)/7
Find u, given that -2*u**4 + 1/2*u**3 - 1/2*u + 0 + 2*u**2 = 0.
-1, 0, 1/4, 1
Let v be -2 + (32/(-3))/(-4). Let i be (((-28)/18)/2 + 1)*3. Factor -i*c + 0 + v*c**3 - 2/3*c**4 + 2/3*c**2.
-2*c*(c - 1)**2*(c + 1)/3
Let r(j) be the second derivative of -3/100*j**5 + 0*j**3 + 0 + 0*j**2 - 1/60*j**4 + j. Find c, given that r(c) = 0.
-1/3, 0
Let f(z) be the third derivative of z**6/40 - z**5/10 - z**4/8 + z**3 + z**2. Factor f(g).
3*(g - 2)*(g - 1)*(g + 1)
Let d(g) be the first derivative of -7/3*g**3 + 2*g**2 + 2 - 1/3*g**4 - 2*g + 7/10*g**5. Let s(m) be the first derivative of d(m). Factor s(l).
2*(l - 1)*(l + 1)*(7*l - 2)
Suppose -7 = -3*g + 2. Suppose -2*w**3 + 0*w**2 + 2*w**2 - 4*w**4 + 3*w**4 - g*w**2 = 0. What is w?
-1, 0
Let h(f) be the first derivative of -f**6/12 + f**4/8 + 9. Factor h(a).
-a**3*(a - 1)*(a + 1)/2
Let k(v) = -2 - 3*v + 5 + 13*v + 2 - v**2. Let q be k(10). Factor -5*h**2 + 1 + 3*h + q + 2*h**2.
-3*(h - 2)*(h + 1)
Factor 8/9 + 2/9*x**2 - 10/9*x**3 - 2/9*x**4 + 2/9*x**5 + 16/9*x.
2*(x - 2)**2*(x + 1)**3/9
Let m(q) be the third derivative of 0*q + 0*q**3 - 2*q**2 + 0*q**6 + 0*q**4 - 1/120*q**5 + 0 + 1/420*q**7. Factor m(k).
k**2*(k - 1)*(k + 1)/2
Let h(x) = x + 5*x + 11*x**2 - 3*x - x - 4. Let o(a) = 5*a**2 + a - 2. Let u(n) = -4*h(n) + 9*o(n). Suppose u(y) = 0. What is y?
-2, 1
Let d(j) = j**3 + 6*j**2 - j - 6. Let z be d(-6). Factor 4*m**2 + z*m + 5*m**3 + m + 4*m**4 - 3*m**5 + m**3 + 4*m**5.
m*(m + 1)**4
Let h(z) be the third derivative of -z**6/120 + z**5/36 - z**4/72 - z**3/18 - 26*z**2. Solve h(p) = 0 for p.
-1/3, 1
Factor -8/3*j + 0 - 2/3*j**4 - 16/3*j**2 - 10/3*j**3.
-2*j*(j + 1)*(j + 2)**2/3
Let x(c) = 10*c**4 - 15*c**3 - 13*c**2 + 15*c + 3. Let l(r) = 20*r**4 - 30*r**3 - 25*r**2 + 30*r + 5. Let s(w) = -3*l(w) + 5*x(w). Find d such that s(d) = 0.
-1, 0, 1, 3/2
Let h(k) be the third derivative of -k**6/24 - 5*k**5/12 + 5*k**4/24 + 25*k**3/6 + 43*k**2. Solve h(q) = 0.
-5, -1, 1
Let h(r) be the third derivative of r**8/56 + 4*r**7/105 - r**6/30 - 2*r**5/15 - r**4/12 + 5*r**2. Suppose h(t) = 0. What is t?
-1, -1/3, 0, 1
Let j be ((-4)/(-12))/((-22)/(-33)). Suppose f**4 + 0*f + 0*f**2 + 0 + j*f**3 = 0. Calculate f.
-1/2, 0
Let k(r) be the first derivative of 0*r**2 - 2/35*r**5 + 3/14*r**4 + 0*r - 4/21*r**3 - 5. Solve k(t) = 0 for t.
0, 1, 2
Let u(s) = -s**2 - 1. Let o = 32 + -23. Let z(m) = -18*m**2 - 21*m + 15. Let l(f) = o*u(f) + z(f). Factor l(j).
-3*(j + 1)*(9*j - 2)
Let j(p) be the second derivative of -2*p**7/21 + 3*p**5/5 - 2*p**4/3 - 8*p. Factor j(g).
-4*g**2*(g - 1)**2*(g + 2)
Let c(n) = -6*n**3 - 6*n**2 + 37*n - 11. Let t(m) = 3*m**3 + 3*m**2 - 18*m + 6. Let h(a) = -3*c(a) - 7*t(a). Factor h(j).
-3*(j - 1)**2*(j + 3)
Suppose 3*d = 5*i - 16 - 13, 9 = -3*d. Factor -2*n - 1/2 - 2*n**3 - 1/2*n**i - 3*n**2.
-(n + 1)**4/2
Let -2*c - 8*c**3 + 2*c**4 + 12*c**2 - c + 2*c - 7*c + 2 = 0. Calculate c.
1
Let v(t) = 2*t + 1. Let h(p) be the third derivative of -p**5/60 + p**2. Let z(s) = 2*h(s) - 2*v(s). Factor z(j).
-2*(j + 1)**2
Let i(j) = 33*j - 9. Let o be i(6). Let c be o/35 - (-2)/(-5). Factor -1/5 - 2*g**3 - g**4 - 1/5*g**c - 2*g**2 - g.
-(g + 1)**5/5
Let m(n) be the first derivative of -n**9/6048 + n**7/1680 + 2*n**3/3 - 8. Let l(f) be the third derivative of m(f). Let l(i) = 0. What is i?
-1, 0, 1
Suppose 8 = 5*b - 7. Let s(t) be the first derivative of 2 + 7/6*t**3 + b*t**2 - 2*t. Factor s(u).
(u + 2)*(7*u - 2)/2
Let t be ((65/(-70))/(-13))/((-2)/(-8)). Determine z, given that 2/7*z**2 - 2/7*z**3 + 2/7*z + 0 - t*z**4 = 0.
-1, 0, 1
Let g(c) be the third derivative of -c**5/80 + c**4/8 + 3*c**3/2 - 9*c**2. Factor g(a).
-3*(a - 6)*(a + 2)/4
Determine x so that 2 - 3*x**2 - x**3 + 35*x**4 + x - 18*x**4 - 16*x**4 = 0.
-1, 1, 2
Let y = 52/87 - -2/29. Let q(d) be the first derivative of -1 - y*d**3 + 2*d - d**2 + 1/2*d**4. Factor q(o).
2*(o - 1)**2*(o + 1)
Let a(u) = 8 + 2*u**3 - 9 - u**2 - 3*u**3. Let x(d) = -4*d**3 - 8*d**2 + 2*d - 5. Let r(m) = -15*a(m) + 3*x(m). Determine b, given that r(b) = 0.
0, 1, 2
Factor -399*i**3 - 36*i**2 + 108*i + i**4 + 371*i**3 + 216 - 5*i**4.
-4*(i - 2)*(i + 3)**3
Let n = 124 + -122. Factor 6*b**3 - 2*b**n + 18*b**4 + 0 - 2/3*b.
2*b*(3*b - 1)*(3*b + 1)**2/3
Let z be (-136)/(-24) + (-2)/(-6). Let n(j) be the first derivative of 8/15*j**z + 1/5*j**2 + 9/5*j**4 - 8/5*j**5 - 14/15*j**3 + 3 + 0*j. Factor n(x).
2*x*(x - 1)*(2*x - 1)**3/5
Let 10/3*h**3 - 2/3*h**5 + 0*h**4 - 8/3*h + 0*h**2 + 0 = 0. What is h?
-2, -1, 0, 1, 2
Let i(b) = 2*b**3 + 10*b**2 + 3*b + 18. Let o be i(-5). Factor 1/2*t**5 + 1/2*t**4 - 1/2*t**o - 1/2*t**2 + 0 + 0*t.
t**2*(t - 1)*(t + 1)**2/2
Let j(h) be the first derivative of -2*h**3/15 - 2*h**2/5 -