*h + 5*f = -8 - 3. What is s in 2/7*s + 0 - 2/7*s**h = 0?
0, 1
Let -16/3 + 8/3*a + 1/3*a**3 + 7/3*a**2 = 0. What is a?
-4, 1
Let y = 18 + -9. Factor 20*b**2 + 8*b**2 + 3 - 7*b**2 - y*b**3 - 15*b.
-3*(b - 1)**2*(3*b - 1)
Let i(j) be the second derivative of -j**6/75 + 2*j**5/75 - j**4/60 - j**2 + 2*j. Let a(v) be the first derivative of i(v). Find u, given that a(u) = 0.
0, 1/2
Let w be 760/(-18) + (-2)/(-9). Let s = -25 - w. Determine p, given that 5*p**2 - 2*p**2 - s*p**3 + 20*p**3 = 0.
-1, 0
Let j(c) be the first derivative of -c**6/240 + c**5/40 - c**4/24 - c**2/2 + 3. Let v(s) be the second derivative of j(s). Let v(g) = 0. What is g?
0, 1, 2
Let a(j) be the third derivative of -j**9/75600 + j**7/12600 - j**4/24 - 3*j**2. Let x(k) be the second derivative of a(k). What is n in x(n) = 0?
-1, 0, 1
Let d(q) be the second derivative of q**5/5 - 4*q**4/3 - 2*q**3/3 + 8*q**2 + 6*q. Factor d(j).
4*(j - 4)*(j - 1)*(j + 1)
What is r in -56/3*r - 196/3 - 4/3*r**2 = 0?
-7
Let w = -22 + 22. Let t be 3*4/3 + w. Find p such that -2/9*p**t + 0 + 0*p**2 + 2/9*p**3 + 0*p = 0.
0, 1
Suppose 4/3*a**3 - 4/3*a - 4/3*a**4 + 4/3*a**2 + 0 = 0. Calculate a.
-1, 0, 1
Let m be (2 + 8/(-6))/((-210)/(-63)). Let s(i) be the first derivative of -2/5*i**2 + 1/25*i**5 + m*i - 1/5*i**4 - 2 + 2/5*i**3. Find p, given that s(p) = 0.
1
Factor -7/8*k + 5/8*k**2 + 1/4.
(k - 1)*(5*k - 2)/8
Factor 2*t**4 - 17*t**4 - 203*t + 188*t + 10*t**2 + 5*t**5 + 5 + 10*t**3.
5*(t - 1)**4*(t + 1)
Let b(a) be the first derivative of -a**7/84 + a**6/60 + a**5/30 - a**3/3 - 1. Let f(h) be the third derivative of b(h). What is x in f(x) = 0?
-2/5, 0, 1
Let h(b) be the first derivative of 1/6*b**3 + 0*b - 1 + 1/2*b**2. Find t such that h(t) = 0.
-2, 0
Let k = 15 + -9. Let y be (-20)/k*(-12)/70. Determine j, given that 2/7*j**2 + y - 6/7*j = 0.
1, 2
Let w(c) be the second derivative of -c**7/2520 + c**5/120 - c**4/36 - c**3/2 + 3*c. Let b(i) be the second derivative of w(i). Factor b(v).
-(v - 1)**2*(v + 2)/3
Let g(d) = 2*d + 18. Let f be g(-9). Let 0 + 0*x**3 + 0*x - 3/4*x**4 + f*x**2 = 0. What is x?
0
Let o = 9 + -5. Let -39*m**2 - 34*m**2 - 84*m**5 - 21*m**5 - 249*m**3 + 84*m + 24 + 348*m**o - 29*m**2 = 0. What is m?
-2/5, -2/7, 1, 2
Let b(n) be the first derivative of -50*n**3/3 - 60*n**2 - 72*n - 27. Factor b(i).
-2*(5*i + 6)**2
Suppose o = -4*d + 2, -4*o + 2*o + 4 = -2*d. Let z = d + 3. Factor 1 + u**2 + z*u - 3*u - 2*u.
(u - 1)**2
Let q(n) be the second derivative of -7*n**6/60 - 19*n**5/40 - 5*n**4/8 - n**3/12 + n**2/2 - 2*n. Factor q(a).
-(a + 1)**3*(7*a - 2)/2
Factor 1/2*j**3 - 1/2*j**5 + 0*j**2 + 0 + 0*j**4 + 0*j.
-j**3*(j - 1)*(j + 1)/2
Let x(g) be the second derivative of g**6/45 - g**5/2 - 8*g**4/9 + 48*g. Factor x(k).
2*k**2*(k - 16)*(k + 1)/3
Let t be (-99)/(-22)*(-4)/(-9). Suppose -2/9*q - 2/9*q**t + 0 = 0. What is q?
-1, 0
Let j(r) be the second derivative of r**4/3 - 68*r**3/3 + 578*r**2 + 24*r - 2. Let j(l) = 0. Calculate l.
17
Let z(p) be the second derivative of -2*p**5/35 + 5*p**4/21 + 2*p**3/7 + 9*p. Determine b, given that z(b) = 0.
-1/2, 0, 3
Let v(k) be the second derivative of k**5/110 + 2*k**4/33 + 5*k**3/33 + 2*k**2/11 + 11*k. Find q, given that v(q) = 0.
-2, -1
Factor 91*o**2 - 186*o**2 + 94*o**2.
-o**2
Let i(b) be the third derivative of b**7/6 - 5*b**6/4 + 43*b**5/12 - 5*b**4 + 10*b**3/3 - b**2. Factor i(z).
5*(z - 2)*(z - 1)**2*(7*z - 2)
Suppose 0 = -43*k - 18 + 104. Let w = 47 + -187/4. Factor 0 - 1/4*r**k - w*r.
-r*(r + 1)/4
Let r(l) = l**2 - 4*l. Let q be r(5). Let n = q - 5. Factor -3 + 3*i**3 + 3*i**2 - i - 2*i + n*i**2.
3*(i - 1)*(i + 1)**2
Let i(r) be the second derivative of -1/60*r**6 + 0*r**3 + 1/24*r**4 + 0*r**2 - 1/84*r**7 + 0 + 1/40*r**5 - 3*r. Find q, given that i(q) = 0.
-1, 0, 1
Find d, given that 21/2*d + 2*d**3 + 12*d**2 - 49/2 = 0.
-7/2, 1
Suppose -3*r - 5*i - 13 = -3, 2*r = -2*i. Let 0*l**4 - 12/5*l**3 - 6/5 + 3/5*l**r + 9/5*l + 6/5*l**2 = 0. Calculate l.
-2, -1, 1
Let a be (12/(-10))/((-6)/(-40)). Let z = 8 + a. Factor 2/3*p - 1/3*p**2 - p**3 + z.
-p*(p + 1)*(3*p - 2)/3
Let o(p) be the first derivative of -p**3 + 9*p**2/2 - 6*p + 7. Factor o(h).
-3*(h - 2)*(h - 1)
Let n(s) be the second derivative of s**6/105 - s**5/35 - s**4/14 + 35*s. Let n(m) = 0. Calculate m.
-1, 0, 3
Suppose 12 = 5*r + 3*z, -3*z + 17 - 5 = 0. Find t, given that r*t + 0 + 1/3*t**2 - 1/3*t**4 + 0*t**3 = 0.
-1, 0, 1
Let k(a) be the third derivative of a**8/20160 + a**7/5040 - a**6/360 + a**5/12 - 5*a**2. Let c(i) be the third derivative of k(i). Find d such that c(d) = 0.
-2, 1
Let m(x) be the second derivative of -x**4/4 + x**3/2 - x. Suppose m(c) = 0. Calculate c.
0, 1
Let o(h) = -h**2 - 4*h + 35. Let x be o(-8). Suppose -2/3*y**2 + 0 + 2/3*y**x - 4/3*y = 0. What is y?
-1, 0, 2
Let m = 149/34 - -2/17. Factor -3/2*b**4 - m*b**3 + 0*b - 3*b**2 + 0.
-3*b**2*(b + 1)*(b + 2)/2
Let u(d) be the first derivative of -d**6/18 + 7*d**5/30 - d**4/3 - 5*d**3/3 + 8. Let g(x) be the third derivative of u(x). Determine p, given that g(p) = 0.
2/5, 1
Let r(d) = -d + 4*d**3 - 3*d + 5 + 0*d**3 + 4*d**2 - 4. Let h(b) = -3*b**3 - 3*b**2 + 3*b - 1. Let x = -5 + 10. Let v(f) = x*h(f) + 4*r(f). Factor v(l).
(l - 1)*(l + 1)**2
Suppose -6 = -13*m + 11*m. Determine q, given that -3/4*q**2 + 0*q - 1/4*q**m + 1 = 0.
-2, 1
Let m be 14/(-21)*3*6/(-3). Suppose -5*b + h + 6 = 0, 3*b - 10 = 8*b - 5*h. Find u, given that -2/7*u**m + 0 + 2/7*u**3 - 2/7*u**5 + 2/7*u**b + 0*u = 0.
-1, 0, 1
Find r such that 24/7*r + 4/7*r**2 + 20/7 = 0.
-5, -1
Let b(s) be the second derivative of -s**6/720 + s**5/180 + s**4/144 - s**3/18 - 2*s**2 - s. Let f(d) be the first derivative of b(d). Factor f(t).
-(t - 2)*(t - 1)*(t + 1)/6
Suppose -10*u = -6*u - 8. Suppose 4*c = -u + 14. Factor y - y - y**c + 9*y**5.
y**3*(3*y - 1)*(3*y + 1)
Let h = 216 + -1942/9. Factor -h*t**2 + 0*t + 2/9*t**3 + 0.
2*t**2*(t - 1)/9
Let d(n) = 9*n**3 - 4*n**2 + 5*n - 26. Let z(h) = h**3 - h**2 + h - 1. Let b(p) = 3*d(p) - 24*z(p). Factor b(y).
3*(y - 2)*(y + 3)**2
Let r(y) be the first derivative of y**8/224 + y**7/70 - y**6/80 - y**5/20 + 3*y**2/2 - 7. Let l(v) be the second derivative of r(v). Let l(f) = 0. What is f?
-2, -1, 0, 1
Let w = -6 + 6. What is a in a**2 + 3*a + 4*a + w*a**2 - 5*a = 0?
-2, 0
Let d = 89/80 + -17/15. Let l = 5/16 - d. Let l*n + 5/3*n**2 + n**3 - 1/3 = 0. What is n?
-1, 1/3
Let y(s) = -s**2 + s - 1. Let x(q) = -3 - 3 + 3 + 4. Let u(b) = -2*x(b) - 2*y(b). Suppose u(j) = 0. What is j?
0, 1
Let u = -21 - -31. Solve 0*b**3 - 6 + u - 7*b**2 + b**5 - b**3 + 3*b**4 = 0.
-2, -1, 1
Let s(j) be the third derivative of 0*j**3 - 3*j**2 + 0 + 0*j - 1/210*j**7 + 0*j**4 - 1/30*j**5 + 1/40*j**6. Factor s(w).
-w**2*(w - 2)*(w - 1)
Let w be 12/(-50)*(-30)/9. Let f be (-6)/(-9)*1*3. Solve -8/5*j**f + 2/5*j**3 - w + 2*j = 0 for j.
1, 2
Factor 4/9*n**2 + 2/9*n**5 + 0*n**3 - 2/9*n - 4/9*n**4 + 0.
2*n*(n - 1)**3*(n + 1)/9
Find d such that d**2 - 1/2*d**3 + 1/4 + d - 5/4*d**4 - 1/2*d**5 = 0.
-1, -1/2, 1
Factor 0*b**2 + 12/7*b - 8/7 - 4/7*b**3.
-4*(b - 1)**2*(b + 2)/7
Let w(n) be the second derivative of -n**4/6 + 6*n**3 - 81*n**2 - 8*n. Let w(c) = 0. What is c?
9
Factor i + 1/2*i**2 - 1/2*i**3 + 0.
-i*(i - 2)*(i + 1)/2
Let h(r) = -7 - 2*r**3 - 6*r**2 + 11 + r**3. Let i be h(-6). Factor 2*l**4 - 4*l**4 + 2 + i*l**3 + 0*l - 4*l.
-2*(l - 1)**3*(l + 1)
Let p be (-1)/(-14) - 3/63*-3. Let s(q) be the first derivative of p*q**4 - 2/21*q**3 + 0*q**2 + 0*q + 1/21*q**6 - 6/35*q**5 + 1. Factor s(k).
2*k**2*(k - 1)**3/7
Let u be (4 - (-18)/(-5))/(0 + 1). Let p(g) be the second derivative of 0 + 1/50*g**5 - 1/5*g**3 + 0*g**4 + g - u*g**2. Let p(y) = 0. Calculate y.
-1, 2
Let v(o) = 8*o**2 - 4*o + 9. Let b(c) = -4*c**2 + 2*c - 4. Let p(t) = -13*b(t) - 6*v(t). Let p(w) = 0. Calculate w.
-1/2, 1
Let u(z) be the third derivative of 1/840*z**6 + 0 + 1/1470*z**7 + 0*z**4 - 4*z**2 + 0*z + 0*z**3 - 1/210*z**5. Factor u(d).
d**2*(d - 1)*(d + 2)/7
Suppose -7 = 6*i - 31. Factor -2/13*r - 2/13*r**i + 2/13*r**3 + 0 + 2/13*r**2.
-2*r*(r - 1)**2*(r + 1)/13
Let o be (-12)/2 - (-1150)/161. Determine v, given that 10/7*v**2 + 16/7*v + o + 2/7*v**3 = 0.
-2, -1
Factor 4*f**5 - 5 - 2 + 8 - 8*f**2 + 1 + 6*f**4 - 4*f**3.
2*(f - 1)*(f + 1)**3*(2*f - 1)
Suppose 2*s = a + 7, 0*s + 5*a 