20*w**6 + 1/80*w**5 + 1 + 0*w**3 + 0*w**4 - 2*w. Let c(a) be the first derivative of q(a). Solve c(u) = 0.
-1, 0
Let k be 6 + (-3)/(63/112). Factor 0 + 1/3*a**2 - k*a.
a*(a - 2)/3
Let u(o) be the third derivative of -7*o**5/30 - 5*o**4/12 + 2*o**3/3 - 13*o**2. Solve u(y) = 0.
-1, 2/7
Find f such that 4*f**2 + 126*f + 20*f**2 + 4*f**3 - 90*f = 0.
-3, 0
Let p(k) = k**3 - k**2 - 19*k - 1. Let x be p(5). Determine j, given that 0 + 6*j**x + 9*j**3 + 6*j**2 + 3/2*j + 3/2*j**5 = 0.
-1, 0
Let h be 28*(-1)/3*(-150)/525. Factor -z**3 - 7/3*z - h*z**2 - 2/3.
-(z + 1)**2*(3*z + 2)/3
Solve 1/2*f**4 - 1/2*f**3 + 1/2*f**5 + 0*f - 1/2*f**2 + 0 = 0 for f.
-1, 0, 1
Let v(k) be the third derivative of -1/2*k**4 + 0 + 2/3*k**3 + 3*k**2 + 1/12*k**5 + 0*k. Factor v(w).
(w - 2)*(5*w - 2)
Factor 3/5*c**4 + 0*c + 0 + 3/5*c**5 - 3/5*c**3 - 3/5*c**2.
3*c**2*(c - 1)*(c + 1)**2/5
Let v be (-1)/(-1) + -33 + -4. Let t be v/(-8)*(-2)/(-3). Find p such that -2/3*p**4 + 1/3*p + 0*p**t + 2/3*p**2 + 0 - 1/3*p**5 = 0.
-1, 0, 1
Let a(d) = -d**2 + d - 1. Let p(c) = -3*c**4 - 3*c**3 + c**2 + 5*c - 2. Let r = -7 + 5. Let f(k) = r*a(k) + p(k). Factor f(l).
-3*l*(l - 1)*(l + 1)**2
Let l = 300 + -298. Factor -4/3*k + 4/3 + 1/3*k**l.
(k - 2)**2/3
Let g be 12/9*(-6)/(-4). Suppose -2 = 2*v - 3*v. Let g - 5 + 1 - 2*j**3 - 2 + 4*j**2 + v*j = 0. Calculate j.
-1, 1, 2
Suppose 0*b = -b + 5. Suppose -b*x + z + 1 = -1, -3*z - 6 = -4*x. Factor -1/4*i**4 - 1/4 + x*i**3 + 0*i + 1/2*i**2.
-(i - 1)**2*(i + 1)**2/4
Suppose -2*w + 25 = -25. Let f = w + -173/7. Factor -6/7*h**2 - 6/7*h - f - 2/7*h**3.
-2*(h + 1)**3/7
Let m(c) be the third derivative of -2*c**7/21 - 3*c**6/8 + c**5/6 + 15*c**4/8 + 5*c**3/3 - 8*c**2. Let m(i) = 0. Calculate i.
-2, -1, -1/4, 1
Let p(l) be the first derivative of -l**3/6 + l**2/2 - l/2 + 1. Factor p(g).
-(g - 1)**2/2
Factor -3/2*x**2 - 1/2*x + 5/3*x**3 + 1/3.
(x - 1)*(2*x + 1)*(5*x - 2)/6
Let x(k) be the first derivative of -5*k**4/4 + 5*k**3/3 + 5*k**2 - 18. Solve x(d) = 0 for d.
-1, 0, 2
Let i be 2/(-10)*11/(-55). Let u(h) be the second derivative of 0 + i*h**5 + 0*h**3 + 1/75*h**6 + 0*h**2 + 2*h + 1/30*h**4. Factor u(q).
2*q**2*(q + 1)**2/5
Suppose -8 = 21*g - 23*g. Factor 4/5*m**3 - 4/5*m**g + 14/5*m - 2/5*m**5 + 4/5 + 16/5*m**2.
-2*(m - 2)*(m + 1)**4/5
Factor -185*d**4 - 197*d**5 - 940*d**3 - 642*d**2 + d**5 - 515*d**4 + 62*d**2 - 16 - 160*d.
-4*(d + 1)**3*(7*d + 2)**2
Suppose -4/3*r - 4/9*r**2 - 8/9 = 0. What is r?
-2, -1
Let s(l) be the first derivative of -2*l**5/5 + 5*l**4/2 + 2*l**3/3 - 5*l**2 + 23. Determine a, given that s(a) = 0.
-1, 0, 1, 5
Let m(v) be the third derivative of -v**5/15 - v**2. Factor m(a).
-4*a**2
Let a(f) be the third derivative of -f**7/42 - f**6/6 - f**5/3 + 2*f**2. Factor a(b).
-5*b**2*(b + 2)**2
Let a(y) be the third derivative of y**7/210 - y**6/40 + y**5/20 - y**4/24 - 21*y**2. Factor a(t).
t*(t - 1)**3
Let a(i) be the first derivative of 5*i**3/3 - 25*i**2/2 - 38. Factor a(v).
5*v*(v - 5)
Let f(l) = -6*l - 14. Let k(q) = -3*q - 7. Let p(m) = -3*f(m) + 7*k(m). Let g be p(-3). Suppose -1/2*o**3 + 1/2 - 1/2*o**g + 1/2*o = 0. What is o?
-1, 1
Determine x so that 6*x - x - 9*x - 4*x**2 = 0.
-1, 0
Let k be (-28)/12*(-66)/308. Let 0*b**2 + k*b**3 - 1/4*b + 0 + 0*b**4 - 1/4*b**5 = 0. What is b?
-1, 0, 1
Let m(l) be the first derivative of 2*l**5/5 + l**4 - 2*l**2 - 2*l - 4. Suppose m(x) = 0. What is x?
-1, 1
Let n(r) be the first derivative of -r**6/6 - r**5/5 + r**4 + 4*r**3/3 - 17. Solve n(p) = 0.
-2, -1, 0, 2
Let u(i) = 17*i**3 - 10*i**2 - 27*i + 7. Let l(h) = 9*h**3 - 5*h**2 - 14*h + 4. Let c(v) = 7*l(v) - 4*u(v). Factor c(w).
-5*w*(w - 2)*(w + 1)
Let y = 75 - 223/3. Let v = -8 - -12. Determine o, given that -2/3*o**5 - y*o**2 + 0*o + 2/3*o**3 + 2/3*o**v + 0 = 0.
-1, 0, 1
Let p = 4 + -13. Let t = -6 - p. Find c such that -c + c + 2*c**t + 0*c - 2*c = 0.
-1, 0, 1
Let v = 4 + -4. Suppose 0 = -v*n - 2*n + 6. What is c in -n*c**2 - 3*c**2 + 12*c**4 - 7*c**5 + 4*c**2 - 3*c**3 = 0?
-2/7, 0, 1
Let d(f) be the second derivative of -1/3*f**3 + 0*f**2 + 3*f - 1/15*f**6 + 0 + 1/10*f**5 + 1/6*f**4. Suppose d(t) = 0. Calculate t.
-1, 0, 1
Factor 0*o**2 + 0 + 1/4*o**4 + o - 3/4*o**3.
o*(o - 2)**2*(o + 1)/4
Let w(l) be the first derivative of 4 + 0*l**5 + 0*l**3 + 0*l - 2/3*l**6 + 2*l**4 - 2*l**2. Determine j so that w(j) = 0.
-1, 0, 1
Let g(h) be the third derivative of h**5/210 + h**4/84 - 4*h**2 + 3. Suppose g(j) = 0. What is j?
-1, 0
Let d(h) be the second derivative of -h**7/252 + h**6/45 + h**5/15 + h**4/4 + 2*h. Let g(i) be the third derivative of d(i). What is l in g(l) = 0?
-2/5, 2
Suppose -d + 12 = -5*i - 0*i, 0 = 5*d + 3*i - 4. Factor 0 + 0*n - 1/6*n**d.
-n**2/6
Let u(x) be the second derivative of 5*x + 0*x**3 + 0*x**2 - 1/60*x**4 - 1/75*x**6 + 0 - 3/100*x**5. Factor u(n).
-n**2*(n + 1)*(2*n + 1)/5
Let i = 1 - -3. Suppose -2 - 35*r**2 + 38*r**2 - 3*r**i + 2 = 0. Calculate r.
-1, 0, 1
Let l(y) = 13*y**2 + 4*y. Let z(g) = 37*g**2 + 11*g. Let a(q) = 11*l(q) - 4*z(q). Determine t so that a(t) = 0.
0
Let c be 15/(-6) + 1 + 124/80. Let n(y) be the second derivative of -1/6*y**3 - 1/4*y**2 + 0 + 0*y**4 - 3*y + c*y**5 + 1/60*y**6. Solve n(p) = 0.
-1, 1
Let z = 3581/12 + -298. Let u(l) be the second derivative of z*l**4 - 2*l**2 + 4/3*l**3 + 2*l + 0. Find f, given that u(f) = 0.
-2, 2/5
Let v(r) be the third derivative of r**7/280 + r**6/120 + 2*r**3/3 - r**2. Let n(d) be the first derivative of v(d). Factor n(i).
3*i**2*(i + 1)
Let n be (-60)/9*(-54)/12. Let j be n/(-72) + 2/3. Factor 0*w + 0*w**2 + 1/2*w**4 - 1/4*w**3 + 0 - j*w**5.
-w**3*(w - 1)**2/4
Let f(j) be the third derivative of 0 + 27/20*j**5 + 3*j**2 + 0*j - 3/2*j**4 + 2/3*j**3. Factor f(x).
(9*x - 2)**2
Let o be 1/(-3) - 49/(-21). Suppose -w = -1 - o. Factor 3/2*a + 3/4*a**2 - 3/2*a**w - 3/4*a**4 + 0.
-3*a*(a - 1)*(a + 1)*(a + 2)/4
Let k(r) be the third derivative of r**9/241920 - r**7/20160 - r**5/12 + 5*r**2. Let c(x) be the third derivative of k(x). Factor c(w).
w*(w - 1)*(w + 1)/4
Let s(u) be the second derivative of u**7/1260 + u**6/360 + u**4/4 + 3*u. Let a(y) be the third derivative of s(y). Factor a(t).
2*t*(t + 1)
Suppose 3*k - 4*i - 12 = 0, 4*k = 2*i - 0*i + 16. Solve -5*s**4 + 3*s**2 + 5*s**4 - 2 - 2*s**k + s**2 = 0.
-1, 1
Let a be -3 - -3*(2 + 0). Factor 0*o**3 - o - 2*o**3 + 0*o**a - 4*o**2 - o.
-2*o*(o + 1)**2
Let t(r) be the first derivative of -5*r**4/4 - 25*r**3/3 - 20*r**2 - 20*r + 20. Solve t(v) = 0 for v.
-2, -1
Suppose 0 + 14/5*c**4 + 0*c + 4/5*c**2 + 18/5*c**3 = 0. Calculate c.
-1, -2/7, 0
Let w(v) be the third derivative of -1/9*v**3 + 0*v + 1/45*v**5 + 1/45*v**7 - 1/252*v**8 - 2/45*v**6 + 1/18*v**4 - 8*v**2 + 0. Find k, given that w(k) = 0.
-1/2, 1
Suppose 3*a + 24 = 15*a. Let s(b) = b + 1. Let g be s(-1). Factor 1/4*x + g + 1/2*x**a.
x*(2*x + 1)/4
Factor -2/5 + 2/5*i**2 + 0*i.
2*(i - 1)*(i + 1)/5
Let u(p) = -p - 11. Let d be u(-11). Let y(z) be the second derivative of 0*z**2 + 1/18*z**3 + d - 2*z - 5/36*z**4 + 1/15*z**5. Factor y(w).
w*(w - 1)*(4*w - 1)/3
Let w be ((-1)/3)/(((-49)/6)/7). Let j(a) = a**3 + 3*a**2 - 4*a + 2. Let r be j(-4). Factor 2/7*p**r + 4/7*p + w.
2*(p + 1)**2/7
Find h, given that -1/2*h**2 + 2/3 + 2/3*h = 0.
-2/3, 2
Let l = 112/3 - 37. Let z(c) be the first derivative of 2/3*c**3 + 1/15*c**5 + l*c**4 - 2 + 2/3*c**2 + 1/3*c. Determine v, given that z(v) = 0.
-1
Factor -3/7*b**2 + 8/7*b - 4/7.
-(b - 2)*(3*b - 2)/7
Let s(x) be the third derivative of 0 - 3*x**2 - 2/3*x**3 + 1/30*x**5 - 1/12*x**4 + 0*x. Solve s(d) = 0.
-1, 2
Let z(l) = -2*l**2 - 5*l + 1. Let c be ((-52)/6)/(1/(-3)). Let d(u) = -9*u**2 - 21*u + 4. Let g(x) = c*z(x) - 6*d(x). Factor g(y).
2*(y - 1)**2
Suppose -4*v - 4*d + 10 = -6*d, -2*v + 5*d = 15. Let c(z) be the first derivative of 1/4*z**v - 2 + 1/2*z + 17/16*z**4 + 11/8*z**2 + 7/4*z**3. Factor c(j).
(j + 1)**3*(5*j + 2)/4
Let i be (12/30)/(2/10*1). Factor m**3 + 0 + 0*m**4 - 1/2*m + 0*m**i - 1/2*m**5.
-m*(m - 1)**2*(m + 1)**2/2
Let t be ((-18)/(-9))/(15/((-3)/(-1))). Factor -t*u**2 - 4/5*u**3 + 0*u - 2/5*u**4 + 0.
-2*u**2*(u + 1)**2/5
Let x(m) be the second derivative of m**7/126 - m**5/30 + m**3/18 + 18*m. Let x(p) = 0. What is p?
-1, 0, 1
Let o(n) be the second derivative of n**9/13608 + n**8/3780 - n**7/1260 - n**3/6 - 8