3 - 12*y**2 = 0.
-2, -2/5, 0
Let m(u) be the first derivative of -7*u**3 - 18*u**2 + 12*u - 2. What is a in m(a) = 0?
-2, 2/7
Let o = -1037/5360 + 2/335. Let s = 17/80 - o. Find y, given that -s + 2/5*y**3 + 2/5*y**2 - 2/5*y = 0.
-1, 1
Let l(k) be the first derivative of 3/5*k**5 + 0*k**4 + 0*k**2 - 1/6*k**6 + 0*k + 6 - 4/3*k**3. What is q in l(q) = 0?
-1, 0, 2
Let t = 1 + 1. Let h(i) = 3*i**5 - 4*i**4 + i**3 - 2*i**2 + 2. Let y(s) = 4*s**5 - 5*s**4 + s**3 - 3*s**2 + 3. Let j(r) = t*y(r) - 3*h(r). Factor j(p).
-p**3*(p - 1)**2
Let r(f) be the first derivative of -2*f**5/95 + f**4/38 - 49. Factor r(k).
-2*k**3*(k - 1)/19
Let v = -6/11 - -45/22. Let z = v + -1. Factor -z*l**3 + 2 - 3/2*l**2 + 0*l.
-(l - 1)*(l + 2)**2/2
Let n(l) be the first derivative of -1/3*l - 1/24*l**4 + 0*l**3 - 6 + 1/4*l**2. Find r such that n(r) = 0.
-2, 1
Let s(d) be the third derivative of -7/20*d**6 + 0 - 4/5*d**5 - 3/35*d**7 - 9/8*d**4 - 1/112*d**8 - 5*d**2 - d**3 + 0*d. Let s(i) = 0. What is i?
-2, -1
Suppose -5*c + 10 = -5*b, c - 3*b + b = 0. Factor -a + c*a - 3*a - a**5 + 2*a**4.
-a**4*(a - 2)
Let b(p) = p**2 + p. Let l be b(1). Factor -3 + 4*t + 2*t**l + 1 + 6*t**3 - 10*t.
2*(t - 1)*(t + 1)*(3*t + 1)
Let p(f) be the first derivative of -35/18*f**4 - 8/27*f**3 + 0*f + 3 + 4/9*f**2. Factor p(m).
-2*m*(5*m + 2)*(7*m - 2)/9
Let k(r) be the first derivative of 0*r + 0*r**3 + 1/2*r**4 - 4 - r**2. Factor k(m).
2*m*(m - 1)*(m + 1)
Let p(n) = -n**3 + 3*n**2 + n - 1. Let d be p(3). Suppose d*k - 10 = -h, 11 = k + h + h. Solve b + 2/3 + 0*b**2 - 1/3*b**k = 0.
-1, 2
Let a be (-5)/((-30)/(-16))*(-18)/8. What is w in -a*w + 6*w**3 - 6 + 3/2*w**4 + 9/2*w**2 = 0?
-2, -1, 1
Let m(r) be the second derivative of -2*r**7/105 - 3*r**6/50 - 3*r**5/50 - r**4/60 - 20*r. Find j, given that m(j) = 0.
-1, -1/4, 0
Let b be 30/(-4)*(-2)/3. Suppose -3*w = -2*w. Suppose -2*s**5 + s**3 + s**3 + w*s**b = 0. Calculate s.
-1, 0, 1
Let r(p) be the first derivative of -1/60*p**5 + p**2 - 3 + 1/12*p**3 + 1/48*p**4 + 0*p. Let d(s) be the second derivative of r(s). Factor d(b).
-(b - 1)*(2*b + 1)/2
Suppose -25*y - 12 = -28*y. Let 2/7*x**5 - 4/7*x**3 + 2/7*x + 2/7 + 2/7*x**y - 4/7*x**2 = 0. Calculate x.
-1, 1
Let p(i) be the second derivative of -1/14*i**7 - 1/4*i**4 + 0*i**2 + 0*i**3 + 2*i - 9/20*i**5 - 3/10*i**6 + 0. Factor p(x).
-3*x**2*(x + 1)**3
Let t(q) = q**2 + 11*q + 5. Suppose 0 = -3*n - 2*c - 11, 0*c + 5*c - 5 = -n. Let h(u) = 2*u**2 + 16*u + 7. Let i(j) = n*h(j) + 7*t(j). Factor i(f).
-3*f*(f + 1)
Let y(x) be the first derivative of -x**6/36 - 4*x**5/15 - 25*x**4/24 - 19*x**3/9 - 7*x**2/3 - 4*x/3 - 4. Factor y(o).
-(o + 1)**2*(o + 2)**3/6
Let g(z) be the third derivative of z**5/12 - 5*z**4/2 + 30*z**3 + 8*z**2. Let g(s) = 0. Calculate s.
6
Let m(z) = z**3 + 10*z**2 - z - 7. Let l be m(-10). Factor -12*r + 4*r**3 - 9 - 18*r**2 + 1 + 5 - 16*r**3 - l*r**4.
-3*(r + 1)**4
Let i be ((-90)/24)/((-27)/24). Factor i*h**2 + 2*h - 4/3.
2*(h + 1)*(5*h - 2)/3
Let y(u) = -u - 17. Let c be y(-20). Suppose 0*n - c*n**3 + 0 - 1/4*n**5 + 2*n**2 + 3/2*n**4 = 0. What is n?
0, 2
Let d(b) = -b**3 + 8*b**2 + 10*b + 6. Let h be d(9). Determine r, given that 9*r - 4*r**2 + 10*r - h*r = 0.
0, 1
Let b(i) = -i**2 - 10*i - 18. Let y be b(-7). Let f be (9/15 + -1)/(-1). Factor -8/5*h - f*h**y - 8/5*h**2 + 0.
-2*h*(h + 2)**2/5
Let n(s) = 17*s**3 - s**2 + 25*s + 4. Let h(r) = -4*r**3 - 6*r - 1. Suppose 0 = -m - 11 - 15. Let g(v) = m*h(v) - 6*n(v). Determine i so that g(i) = 0.
-1
Let z(w) = 3*w - 15. Let d be z(11). Let j be 0 + 1 - 14/d. What is t in 0 - j*t - 2/9*t**2 = 0?
-1, 0
Let c(q) = 5*q**2 + 2*q - 6. Let m(i) = -6*i**2 - i + 7. Let j(u) = -5*c(u) - 4*m(u). Let l be j(-6). Factor 17*n**3 + n**2 - n + l*n - 18*n**3 - n**4.
-n*(n - 1)*(n + 1)**2
Let d(b) = 5*b**3 + 13*b**2 + 26*b + 6. Let p(f) = -2*f**2 + f + 1. Let i(k) = d(k) - 6*p(k). Factor i(y).
5*y*(y + 1)*(y + 4)
Suppose v - 1/5*v**2 - 3/5 - 1/5*v**3 = 0. Calculate v.
-3, 1
Suppose -t - 12 = -7*t. Suppose 2/9*m**t - 2/3*m + 4/9 = 0. Calculate m.
1, 2
Let j(s) be the first derivative of -s**4/14 - 16*s**3/21 - s**2 - 36. Suppose j(h) = 0. Calculate h.
-7, -1, 0
Let l(m) be the second derivative of -m**4/6 - m**3/3 + 2*m**2 + 2*m. Find z, given that l(z) = 0.
-2, 1
Let o(p) be the first derivative of 7*p**6/900 - p**5/25 - p**4/15 - 2*p**3 + 5. Let f(i) be the third derivative of o(i). Find k, given that f(k) = 0.
-2/7, 2
Let o(b) be the third derivative of -b**7/1575 + b**6/900 + b**5/450 - b**4/180 + 7*b**2. Factor o(m).
-2*m*(m - 1)**2*(m + 1)/15
Let h(c) be the first derivative of 3/5*c**2 + 0*c + 1/5*c**3 - 7. Factor h(a).
3*a*(a + 2)/5
Let j(q) = -3*q**3 + 17*q**2 + 3*q - 6. Let s(y) = y**3 - 6*y**2 - y + 2. Let i(g) = -4*j(g) - 11*s(g). Factor i(u).
(u - 2)*(u - 1)*(u + 1)
Solve -5*n**2 - 588*n - 13 + 613*n - 7 = 0 for n.
1, 4
Let b = 2 - 2. Determine m, given that b*m**3 - 5*m - 3*m**2 + 4*m - m**3 - m = 0.
-2, -1, 0
Let m be (6/(-8))/(2/(-8)). Let a be (-4)/m*(-9)/6. Factor a*i**3 - 3*i**2 + i**4 + 4*i**2 + 0*i**3.
i**2*(i + 1)**2
Let n = -7 + 13. Let l be 3/n*0 + 2. Factor 6*b + 5*b**2 - 4*b**2 - 3 - 4*b**l.
-3*(b - 1)**2
Suppose -6*z = -3*z + 5*c - 25, 0 = -2*z + 2*c - 10. Solve -10/3*f**3 + 4/3*f**2 + 0*f + z + 8/3*f**4 - 2/3*f**5 = 0.
0, 1, 2
Let w(z) be the second derivative of 0 - 1/45*z**6 + 0*z**3 - 5*z + 1/30*z**5 + 0*z**4 + 0*z**2. Suppose w(a) = 0. Calculate a.
0, 1
Let w be 1*(-6)/(-4)*2. Suppose -w*y - 3*l = -21, 5*y = 5*l - 8 - 7. Determine o, given that -2/5*o + 0 - 2/5*o**y = 0.
-1, 0
Let c(y) be the second derivative of 0*y**2 - 1/3*y**3 - 2*y + 5/12*y**4 + 0. Factor c(f).
f*(5*f - 2)
Let c(p) be the third derivative of -p**6/96 - p**5/24 - 5*p**2 + 2. Suppose c(b) = 0. What is b?
-2, 0
Let q(m) = -7*m**2 - 9*m - 10. Let t(u) = 15*u**2 + 18*u + 21. Let o(l) = -9*q(l) - 4*t(l). Solve o(g) = 0 for g.
-2, -1
Let c(i) = i**3 - 3*i**2 + 3*i - 4. Let b be c(3). Let t(y) be the first derivative of -2/25*y**b + 1 - 2/5*y**3 + 3/10*y**4 + 0*y + 1/5*y**2. Factor t(s).
-2*s*(s - 1)**3/5
Let l(n) be the third derivative of -3*n**6/10 - 5*n**5 + 53*n**4/6 - 6*n**3 + n**2 + 43*n. Factor l(v).
-4*(v + 9)*(3*v - 1)**2
Let w = 25 + -18. Find h, given that -1 + 3*h + 2*h**2 - w*h + 3 = 0.
1
Let x = -41548/405 + 513/5. Let a = x + 53/81. Solve -2/3*h + 4/3*h**2 - a = 0 for h.
-1/2, 1
Suppose -60*p = -58*p, -2*d - 5*p = -8. Let -2/5*m + 8/5*m**d + 0 - 8/5*m**2 + 2/5*m**3 = 0. Calculate m.
-1, -1/4, 0, 1
Let i(w) = 9*w**3 - 22*w**2 + 11*w - 4. Let f(c) be the first derivative of -c**3/3 + c**2/2 - c - 6. Let s(n) = 6*f(n) - i(n). Factor s(y).
-(y - 1)**2*(9*y + 2)
Let z(v) be the first derivative of 0*v + 4/21*v**3 - 2 - 1/7*v**2 - 1/14*v**4. Let z(l) = 0. What is l?
0, 1
Factor 18*c - 6*c**2 + 6*c**3 + 0*c**3 - 3*c**3 - 5*c**3 - 10.
-2*(c - 1)**2*(c + 5)
Let o(j) be the second derivative of -243/5*j**5 - 16*j**2 + 8*j + 486/5*j**6 + 0 - 126*j**4 - 200/3*j**3. Factor o(s).
4*(s - 1)*(9*s + 2)**3
Factor 0 - 5/3*s**3 + 5/3*s**2 + 10/3*s.
-5*s*(s - 2)*(s + 1)/3
Suppose 3*d + 38 = 5*d + 4*p, 3*d + p - 32 = 0. Suppose d = 4*i - 3*y, 4*i = i - 3*y + 12. Suppose -1 + 4*a**2 - 2*a**2 + i + 4*a + 0*a = 0. Calculate a.
-1
Let z(o) be the first derivative of o**7/21 - o**6/30 - 3*o**5/20 + o**4/12 + o**3/6 + 4*o + 3. Let h(l) be the first derivative of z(l). Factor h(b).
b*(b - 1)**2*(b + 1)*(2*b + 1)
Let y(u) = u**4 - u**2 - u + 1. Let l(c) = 8*c**4 - 2*c**3 - 4*c**2 - 8*c + 6. Let i(m) = 2*l(m) - 20*y(m). Let i(d) = 0. Calculate d.
-2, -1, 1
Let f(l) be the second derivative of l**8/6720 - l**7/1680 + l**6/1440 + l**3/2 + l. Let q(w) be the second derivative of f(w). Factor q(z).
z**2*(z - 1)**2/4
Let m = 799/76 - 1/76. Let q = m - 9. Suppose n**2 - 1 - q*n = 0. What is n?
-1/2, 2
Let v(a) be the first derivative of 3 + 1 + 3*a**2 + 3*a**3 + 0*a**3 + 0*a**2. Suppose v(d) = 0. Calculate d.
-2/3, 0
Factor 4*y - y**2 - 5/7*y**3 + 12/7.
-(y - 2)*(y + 3)*(5*y + 2)/7
Let s be (-2)/4*-4 + -2. Let h(r) = r**2 + 2*r + 2. Let l be h(0). Solve -1/3*d + 1/3*d**4 - 1/3*d**l + 1/3*d**3 + s = 0.
-1, 0, 1
Let k = -78/11 + 590/77. Factor 0 + k*g - 2/7*g**3 + 2/7*g**2.
-2*g*(g - 2)*(g + 1)/7
Let f(h) be the first derivative of h**5/20 - 5*h**4/12 + 7*h**3/6 - 3*h**2/2 - 5*h - 1. 