p) be the third derivative of 2*p**7/105 + p**6/15 + p**5/15 + p**2. What is h in c(h) = 0?
-1, 0
Let k(w) be the first derivative of 1/24*w**4 + w - 1 + w**2 - 1/3*w**3. Let a(b) be the first derivative of k(b). Factor a(r).
(r - 2)**2/2
Suppose 0 = -2*w + 5*s - 5, -3 + 0 = -w - 3*s. Factor 4*a**2 + 7*a**2 - 9*a**2 + 2 + w + 4*a.
2*(a + 1)**2
Let d(m) be the second derivative of m**8/672 - m**7/420 - m**6/240 + m**5/120 - m**2/2 - m. Let w(s) be the first derivative of d(s). Factor w(z).
z**2*(z - 1)**2*(z + 1)/2
Factor 0 + 0*j - 1/2*j**2 + 1/2*j**3.
j**2*(j - 1)/2
Factor -3*o**3 - 1 - 5*o + 12*o**2 + 7 - 10*o.
-3*(o - 2)*(o - 1)**2
Let u be (-5)/(-52) - (3 - 3). Let f = u - -193/156. Factor 2/3*g**2 + f*g + 2/3.
2*(g + 1)**2/3
Let x(t) be the first derivative of -t**3/2 + 9*t**2/4 - 3*t - 22. Determine c so that x(c) = 0.
1, 2
Suppose 0 = -0*p - 2*p + 8. Let v be (p/(-24))/(1/(-3)). What is b in v - 3/2*b**3 + 3/2*b - 1/2*b**2 = 0?
-1, -1/3, 1
Let q be (-18)/27 + (-2)/(-3). Let d be (1 - q)*(11 - 11). Factor 4/5*j + d*j**2 + 2/5 - 4/5*j**3 - 2/5*j**4.
-2*(j - 1)*(j + 1)**3/5
Let v be (28/18)/((-14)/(-28)). Find d, given that -4/9*d + v*d**5 - 62/9*d**4 + 0 + 4*d**3 + 2/9*d**2 = 0.
-2/7, 0, 1/2, 1
Suppose 6*b - 5 = 5*b. Let y(o) be the third derivative of -3*o**2 + 1/6*o**3 + 1/210*o**7 + 1/6*o**4 + 0 + 1/10*o**b + 1/30*o**6 + 0*o. Factor y(z).
(z + 1)**4
Let v = 3 - 1. Let h(t) be the second derivative of -1/135*t**6 + 1/27*t**4 + 1/189*t**7 - 1/9*t**v + 0 + 1/27*t**3 - 1/45*t**5 - 2*t. Factor h(x).
2*(x - 1)**3*(x + 1)**2/9
Let d(n) = -3*n - 7. Let a be d(5). Let j = a - -45/2. Let 0*k - j*k**2 + 0 = 0. What is k?
0
Let g(q) be the first derivative of q**6/2 + 9*q**5/5 + 3*q**4/2 - 2*q**3 - 9*q**2/2 - 3*q - 26. Factor g(y).
3*(y - 1)*(y + 1)**4
Factor 0 - 1/4*c**2 + 1/2*c - 1/4*c**3.
-c*(c - 1)*(c + 2)/4
Suppose -z + 3*j - 1 - 9 = 0, -3*j + 20 = 4*z. Let y be z/(-3) + (-33)/(-36). Factor 1/4*a**2 - y*a**4 + 0 + 1/4*a - 1/4*a**3.
-a*(a - 1)*(a + 1)**2/4
Let t = 0 + 7. Suppose -4*q + 5 = -t. Factor -8/5*n + 16/5*n**2 + 0 - 18/5*n**4 + 6/5*n**q.
-2*n*(n + 1)*(3*n - 2)**2/5
Let r(i) = 3*i**2 + 4*i + 5. Let k(z) = 7*z**2 + 11*z + 14. Let t(d) = -3*k(d) + 8*r(d). Solve t(l) = 0 for l.
-2/3, 1
Let a(u) = 0*u + 4*u + u**3 + 1 + 6*u**2 - 3. Let d be a(-5). Suppose -2 + 8*s**2 - 2 + 2*s - 2*s**d - 4*s**3 = 0. What is s?
-2/3, 1
Suppose -13*x - 12*x = -17*x. Factor 3/7*d**2 + 9/7*d**3 + 9/7*d**4 + 3/7*d**5 + 0*d + x.
3*d**2*(d + 1)**3/7
Suppose -6 = 11*z - 14*z. Let a be (-2)/(-4)*1*0. Suppose 0*b**z - 1/2*b**5 + a*b + 0 + 1/2*b**3 + 0*b**4 = 0. What is b?
-1, 0, 1
Let n(u) = 4*u + 34. Let k be n(-8). What is b in 3/5*b - 1/5 - 2/5*b**k = 0?
1/2, 1
Let l(c) = 10*c - 3. Let m be l(3). Let p be 74/90 + (-6)/m. Factor 0*f - 9/5*f**3 + 0 + p*f**2.
-3*f**2*(3*f - 1)/5
Let d be (-352)/(-112) - (-6)/(-3). Let -2/7*p**2 - 6/7 + d*p = 0. What is p?
1, 3
Let s(j) be the second derivative of 1/12*j**4 - 1/6*j**3 + 0 + 0*j**2 - 3*j - 1/30*j**6 + 1/20*j**5. Factor s(m).
-m*(m - 1)**2*(m + 1)
Suppose -2*y - 2 = -6. Suppose 0 = -w - 0*w + 4. Determine j so that 0*j**3 + y*j**w - 2*j**2 + 0*j**4 + 0*j**3 = 0.
-1, 0, 1
Let s(r) be the first derivative of -r**8/168 - 2*r**7/105 + r**5/15 + r**4/12 - 3*r**2/2 - 2. Let o(y) be the second derivative of s(y). Solve o(v) = 0 for v.
-1, 0, 1
Let b(d) be the second derivative of -1/5*d**6 + 3/10*d**5 + 0 + 0*d**2 + 3*d + 0*d**3 - 1/6*d**4 + 1/21*d**7. Factor b(r).
2*r**2*(r - 1)**3
Let b(w) = w**3. Let g(i) = 4*i**2 - 11*i**2 + 3*i**2 + 3*i**3 + 4*i + 8*i**2. Suppose 5 = -3*c - 2*c. Let s(h) = c*g(h) + 2*b(h). Let s(o) = 0. Calculate o.
-2, 0
Let v(a) be the first derivative of -2 + 0*a - a**2 + 2/3*a**3. Factor v(c).
2*c*(c - 1)
Let d(t) = -24*t**3 - 6*t**2 + 17*t - 3. Let a(l) = l**3 - l**2 + l + 1. Let v(x) = a(x) - d(x). Determine k so that v(k) = 0.
-1, 2/5
Let f(o) be the first derivative of 0*o + 0*o**2 + 2/3*o**3 - 1. Factor f(b).
2*b**2
Let l be ((-6)/90)/((-2)/5). Let d(a) be the first derivative of -2/9*a**3 + 2/3*a**2 - 3 - l*a**4 + 0*a. Factor d(t).
-2*t*(t - 1)*(t + 2)/3
Let r be -17*3/(-99) + (-10)/55. Let 0 + r*w + 2/3*w**2 + 1/3*w**3 = 0. Calculate w.
-1, 0
Let r(i) be the first derivative of i**8/1680 - i**7/504 - i**6/1080 + i**5/72 - i**4/36 - i**3/3 + 4. Let c(s) be the third derivative of r(s). Factor c(h).
(h - 1)**2*(h + 1)*(3*h - 2)/3
Let r = 43 - 214/5. Let c(q) = -2*q**2 + 36*q + 80. Let p be c(20). Factor -1/5*i**4 + 0*i**3 + p*i + 0 + r*i**2.
-i**2*(i - 1)*(i + 1)/5
Factor 2/23*l**2 - 8/23*l + 6/23.
2*(l - 3)*(l - 1)/23
Suppose 105*a = 111*a. Factor -1/2*t**4 + a*t**2 + 0*t + 1/4*t**5 + 0 + 1/4*t**3.
t**3*(t - 1)**2/4
Let q = 0 - -3. Let v(f) = -3*f + 1. Let u be v(-1). Factor y**5 - 4*y**u - q*y**3 + y**2 + 2*y**3 + 3*y**4.
y**2*(y - 1)**2*(y + 1)
Let u(k) be the first derivative of -1/5*k**5 - 4 - 5/4*k**2 + 5/8*k**4 + 0*k**3 + k. Determine p so that u(p) = 0.
-1, 1/2, 1, 2
Let z be (-8 + -14 + 30)/(1 - -1). Solve 1/2*m**3 - 2*m + 3*m**2 - 1/2*m**4 - z = 0 for m.
-2, -1, 2
Let h be (6/(-21) - (-10)/35)/(-1). Find d, given that 0*d**2 + 1/2*d + h - 1/2*d**3 = 0.
-1, 0, 1
Let z(b) be the first derivative of -b**4 + 4*b**3 - 16*b + 7. Find i such that z(i) = 0.
-1, 2
Let u(a) be the third derivative of -a**6/160 + 3*a**4/32 + a**3/4 + 20*a**2. Factor u(l).
-3*(l - 2)*(l + 1)**2/4
Let v be (-2)/(-3 - (-10)/4). Let p = v - -3. Determine z so that -7*z**3 - p*z - 2*z**4 + 7*z + 2*z**2 + 7*z**5 = 0.
-1, 0, 2/7, 1
Factor -1/7*k**2 + 4/7*k + 5/7.
-(k - 5)*(k + 1)/7
Suppose -8*r + 20 = -3*r. Let s(t) be the second derivative of -1/3*t**2 + 0 - 1/3*t**r + 2/15*t**5 + 2*t + 4/9*t**3 - 1/45*t**6. Factor s(f).
-2*(f - 1)**4/3
Let h be (-62)/93*3/(-8). Solve 1/2*n + 3/4 - h*n**2 = 0.
-1, 3
Let g(j) be the first derivative of -j**5/25 + 2*j**3/15 - j/5 - 4. Factor g(s).
-(s - 1)**2*(s + 1)**2/5
Let x(h) be the second derivative of -2*h**2 - 1/2*h**4 - h - 5/3*h**3 + 0. What is d in x(d) = 0?
-1, -2/3
Let t(q) be the second derivative of -625*q**4/8 - 25*q**3 - 3*q**2 - 46*q. Suppose t(f) = 0. What is f?
-2/25
Suppose 2*q + 3 = -4*b + 15, 0 = 3*q + 3*b - 15. Solve 4/3*k**q + 0 - 7/3*k**3 + 1/3*k + 2/3*k**2 = 0 for k.
-1/4, 0, 1
Suppose -9*h**3 - 2*h**4 - h**4 + 2*h**4 + 4*h**4 = 0. Calculate h.
0, 3
Determine g so that -42*g**3 - 3 + 3 + 2*g**4 + 40*g**3 + 2*g - 2*g**2 = 0.
-1, 0, 1
Let l(q) be the third derivative of -1/18*q**4 - 1/30*q**5 + 2*q**2 + 0 + 0*q + 1/9*q**3. Factor l(d).
-2*(d + 1)*(3*d - 1)/3
Suppose 5*z - 17 - 3 = 0. Let a be (-32)/72*(-3)/z. Factor -1/3*w**3 + 1/3 + a*w - 1/3*w**2.
-(w - 1)*(w + 1)**2/3
Let n(b) = 7*b**3 - 10*b**2 + 11*b - 13. Let h(m) = m**3 - m - 1. Let p(u) = 10*h(u) - 2*n(u). Suppose p(q) = 0. Calculate q.
1, 2
Let v(t) be the second derivative of -t**5/20 - 7*t**4/36 + 2*t**2/3 - 5*t. What is k in v(k) = 0?
-2, -1, 2/3
Let x(q) = q**3 + q**2 + q. Let k(a) = -a**3 - 13*a**2 + 11*a - 6. Let j(y) = 2*k(y) + 6*x(y). Factor j(t).
4*(t - 3)*(t - 1)**2
Let y be (2 - 1)/((-100)/(-40)). Suppose -3*u + 4 = -2. Let 4/5*k - 2/5 - y*k**u = 0. Calculate k.
1
Let q be -2 - (2 + -2 - -1). Let c(v) = v**3 + 3*v**2 - v - 1. Let u be c(q). Solve -1 - 4*y**u + 3*y + 2*y + 0*y = 0 for y.
1/4, 1
Suppose 0 - 7/3*b**3 - 1/3*b - b**4 - 5/3*b**2 = 0. Calculate b.
-1, -1/3, 0
Determine r, given that -3*r**5 - 3*r + 2*r + 6*r**3 - 2*r = 0.
-1, 0, 1
Let w(q) be the second derivative of -q**4 + 0*q**2 + 0 + 2*q**3 + 3/20*q**5 + 2*q. Suppose w(h) = 0. What is h?
0, 2
Factor 30 + 4*k + 350*k**3 - 355*k**3 + 40*k**2 - 69*k.
-5*(k - 6)*(k - 1)**2
Let h(r) be the second derivative of 2*r**3 - 7/20*r**5 + 3/4*r**4 + 0 - 5*r - 2*r**2. Solve h(f) = 0 for f.
-1, 2/7, 2
Let o(c) be the first derivative of c**4/38 + 4*c**3/57 - c**2/19 - 4*c/19 + 45. Factor o(k).
2*(k - 1)*(k + 1)*(k + 2)/19
Determine y so that -5*y**4 - y + 2*y**3 - y**2 - y**3 + 6*y**4 = 0.
-1, 0, 1
Let q(t) be the first derivative of -2*t + 9*t**2 + 7/2*t**4 - 16/3*t**6 - 7 + 48/5*t**5 - 46/3*t**3. Find j, given that q(j) = 0.
-1, 1/4, 1
Suppose -4/9 - 2*t**2 + 10/9*t**3 + 14/9*t - 2/9*t**4 = 0. What is t?
1, 2
Let a be 0 + 1 + -5 - (-455)/105. Solve 1/3*u**2 + 2/3*u + a = 0.
-1
Let o(z) be the first derivative of 2*z**3/15 - z**2/5 - 1. Le