(d).
-2*d*(d - 1)/5
Let u(x) be the second derivative of -9/14*x**2 - 1/84*x**4 - 1/7*x**3 + 0 + 6*x. Factor u(d).
-(d + 3)**2/7
Let i(c) = -c + 8. Let t(b) = b**3 + 4*b**2 - 2*b - 2. Let a be t(-4). Let n be i(a). Factor 2*w**3 + w + n*w**3 - 5*w**3.
-w*(w - 1)*(w + 1)
Let i(m) be the first derivative of 2*m**3/21 + 5*m**2/7 + 8*m/7 - 4. What is j in i(j) = 0?
-4, -1
Factor 0*z + 1/4*z**5 + 1/4*z**4 + 0*z**3 + 0*z**2 + 0.
z**4*(z + 1)/4
Suppose 7 = -13*t + 14*t. Suppose t*y = y. Factor y - 2/5*x**3 + 8/5*x**2 - 8/5*x.
-2*x*(x - 2)**2/5
Let a(q) = q**5 - q**4 + q**2 - q. Let g(k) = 9*k**5 - 12*k**4 + 12*k**2 - 9*k. Let s(h) = -6*a(h) + g(h). Determine p, given that s(p) = 0.
-1, 0, 1
Suppose -1 = 5*y - 6. Let d be -3 + y - (-170)/1. Factor -8 - d*z**4 - z**5 + 51*z**5 + 64*z - 194*z**2 + 278*z**3 - 22*z**4.
2*(z - 1)**3*(5*z - 2)**2
Let t(q) be the third derivative of q**7/42 + 5*q**6/24 + 3*q**5/4 + 35*q**4/24 + 5*q**3/3 + 5*q**2 + 7. Factor t(j).
5*(j + 1)**3*(j + 2)
Let o(u) be the second derivative of u**6/135 - 2*u**4/27 - 4*u. Solve o(c) = 0 for c.
-2, 0, 2
Let n be ((-1)/(-5))/((-10)/(-100)). Suppose 2/5*k**n - 2/5 + 0*k = 0. Calculate k.
-1, 1
Let w be (4/18)/(125/15 + -8). Determine b so that -2/3 - w*b + 2/3*b**2 + 2/3*b**3 = 0.
-1, 1
Let y(q) be the third derivative of q**5/90 - q**3/9 - 5*q**2. Find m such that y(m) = 0.
-1, 1
Let l = -14/25 - -142/75. Factor -14/3*f**3 + 8/3*f**4 + 0 + 2/3*f + l*f**2.
2*f*(f - 1)**2*(4*f + 1)/3
Let c be 3/6*(-70)/100*-4. Factor -c*s - 2/5 - s**3 - 1/5*s**4 - 9/5*s**2.
-(s + 1)**3*(s + 2)/5
Let h(s) be the second derivative of -s**8/3360 - s**7/560 - s**6/240 - s**5/240 + s**3/2 - 3*s. Let u(f) be the second derivative of h(f). Factor u(r).
-r*(r + 1)**3/2
Let x(a) be the second derivative of a**7/105 + a**6/75 - a**5/50 - a**4/30 - 10*a. Suppose x(t) = 0. Calculate t.
-1, 0, 1
Suppose -3*k + 3 = 0, 0 = 5*s + k - 3*k + 112. Let d = s + 24. Factor 0*n**d + 3*n**4 - 3/2*n**5 - 3/2*n**3 + 0 + 0*n.
-3*n**3*(n - 1)**2/2
Let k(i) = -i + 1. Let c be k(-2). Let g = 0 + c. Factor g*h**3 + 2*h - 5*h**3 + 2*h**2 - 2 + 0*h.
-2*(h - 1)**2*(h + 1)
Suppose t - 5*r + 14 = 0, -4*t + 13 + 31 = 5*r. Suppose 5*y - 20 = -3*p, 0 = p - y + t*y - 20. Factor -3*o**3 - 2/3*o**2 - 5/3*o**5 + p + 0*o - 4*o**4.
-o**2*(o + 1)**2*(5*o + 2)/3
Suppose -3*z + 4*u = -0*u - 20, 2*z - 20 = 4*u. Let p(y) be the second derivative of -2*y + 1/3*y**2 + 1/18*y**4 - 2/9*y**3 + z. Suppose p(r) = 0. What is r?
1
Let i(a) be the second derivative of 3*a**5/160 + 15*a**4/16 + 75*a**3/4 + 375*a**2/2 - 21*a. Let i(m) = 0. What is m?
-10
Let l(i) be the second derivative of i**4/22 + 4*i**3/33 - 4*i**2/11 + i + 9. Factor l(h).
2*(h + 2)*(3*h - 2)/11
Let s(v) be the third derivative of 0*v**3 - 2*v**2 + 0 - 1/420*v**7 + 0*v**4 + 0*v - 1/672*v**8 + 1/240*v**6 + 1/120*v**5. Factor s(o).
-o**2*(o - 1)*(o + 1)**2/2
Factor -138/7*p**2 - 75/7 - 180/7*p - 3/7*p**4 - 36/7*p**3.
-3*(p + 1)**2*(p + 5)**2/7
Let a(q) be the third derivative of q**8/672 - q**7/105 + q**6/60 + q**5/60 - 5*q**4/48 + q**3/6 - 11*q**2. Determine z, given that a(z) = 0.
-1, 1, 2
Let b be 108/(-135)*(-10)/28. Factor 2/7 + 4/7*v + b*v**2.
2*(v + 1)**2/7
Let r(o) = -5*o**2 - 4*o + 4. Let y(z) be the first derivative of z**3/3 + z**2/2 - z - 1. Let x(c) = -r(c) - 4*y(c). Determine d so that x(d) = 0.
0
Let m(i) be the second derivative of -20*i**6/3 - 9*i**5 + 13*i**4/3 + 6*i**3 + 2*i**2 - 31*i. Determine u, given that m(u) = 0.
-1, -1/5, 1/2
Let k(a) be the third derivative of -a**6/480 + a**5/240 + a**4/96 - a**3/24 - 4*a**2. Factor k(p).
-(p - 1)**2*(p + 1)/4
Suppose -2*m + 16 = 4*z, 3*m - 2*z + 8 = -0*z. Suppose -3*t - 2*h + 10 = 0, 5*t - 3*h - 23 = -m*h. Factor -4*j**4 - 3*j**3 + j**2 + 2*j**4 + 5*j**t - j**5.
-j**2*(j - 1)**3
Factor -1/4*r**4 - 1/2*r**3 + 0*r + 0 + 3/4*r**2.
-r**2*(r - 1)*(r + 3)/4
Let u(r) be the first derivative of r**5/120 + r**4/12 + r**3/3 - r**2 + 3. Let a(j) be the second derivative of u(j). Factor a(p).
(p + 2)**2/2
Let d(z) = -2*z**2 + 12*z - 2. Let s(y) = -y - 1. Let f(a) = d(a) + 4*s(a). Determine p so that f(p) = 0.
1, 3
Factor 88*y + 317*y + 3*y**3 - 90*y**2 + 5*y**3 - 3*y**3.
5*y*(y - 9)**2
Let f = 118 + -118. Let a(v) be the second derivative of 1/66*v**4 - 1/231*v**7 + 0*v**2 + 2*v + 0 + f*v**3 + 1/110*v**5 - 1/165*v**6. Solve a(b) = 0 for b.
-1, 0, 1
Suppose 4*i = 4*b, 3*i + 3*b = -0*i - 12. Let h be (i - -3) + (-1 - 0). Find n, given that h*n**2 + 6*n**2 - 2 - 4*n**2 = 0.
-1, 1
Find f, given that 14/3*f**2 + 2/3*f**3 - 14/3 - 2/3*f = 0.
-7, -1, 1
Let o(m) be the third derivative of m**6/300 - m**5/150 - m**4/12 - m**3/5 - 21*m**2. Factor o(r).
2*(r - 3)*(r + 1)**2/5
Let n(k) = -3*k**2 + 30*k. Let q(t) = t. Let a(z) = -n(z) + 15*q(z). Factor a(l).
3*l*(l - 5)
Let p(x) be the first derivative of 0*x**2 - 1 + 0*x + 2/3*x**3. Factor p(v).
2*v**2
Let x(p) be the first derivative of -3*p**4/8 + p**3 - 3*p**2/4 - 19. Suppose x(i) = 0. Calculate i.
0, 1
Let q(w) = w - 1. Let z(x) = -4*x**2 - 10*x + 2. Let d(v) = 8*q(v) - z(v). Factor d(y).
2*(y + 5)*(2*y - 1)
Let c(b) be the third derivative of -b**8/420 + b**6/90 - b**3/2 + 3*b**2. Let n(p) be the first derivative of c(p). Find x, given that n(x) = 0.
-1, 0, 1
Solve 5*v**4 - 16*v + 55*v**4 - 29*v - 10 + 95*v**3 = 0 for v.
-1, -1/4, 2/3
Let s(g) be the first derivative of g**6/3 - 4*g**5/5 + g**4/2 + 5. Factor s(k).
2*k**3*(k - 1)**2
Let d(h) = h**2 + 7*h + 6. Let u be d(-6). Suppose -4*r - 4*p = 16, 5*r + u*p + 16 = -4*p. Let -1/2*t**2 + 0*t + r = 0. Calculate t.
0
Factor 1/2*i - 1 + 3/2*i**2 - 1/2*i**4 - 1/2*i**3.
-(i - 1)**2*(i + 1)*(i + 2)/2
Factor 4*j + 0*j - 2*j - 6*j**3 + 4*j**3.
-2*j*(j - 1)*(j + 1)
Let f(c) be the second derivative of 2/65*c**5 - 1/195*c**6 + 0 + 2/39*c**3 + 0*c**2 - 5/78*c**4 + 3*c. Solve f(p) = 0.
0, 1, 2
Let z = 31 - 26. Let y(x) be the third derivative of 0*x + 0*x**3 + 0*x**z - 4*x**2 + 0 - 1/20*x**6 - 1/70*x**7 + 0*x**4. Factor y(a).
-3*a**3*(a + 2)
Let o(d) be the second derivative of d**4/36 - 2*d**3/9 - 3*d. Determine b so that o(b) = 0.
0, 4
Factor 16/3*v**2 - 2/3*v**3 + 0 - 32/3*v.
-2*v*(v - 4)**2/3
Let b(y) be the first derivative of 3*y + 3/2*y**2 - y**3 - 3/4*y**4 + 1. Factor b(c).
-3*(c - 1)*(c + 1)**2
Let v(g) be the first derivative of 2*g**3/15 + g**2/5 + 5. Factor v(q).
2*q*(q + 1)/5
Let r(x) be the second derivative of -x**5/60 - x**4/24 + x**3/3 + x**2/2 - 2*x. Let h(k) be the first derivative of r(k). Factor h(o).
-(o - 1)*(o + 2)
Let p = 484 - 481. Suppose 7/2*d**p + d**2 + 0*d + 5/2*d**4 + 0 = 0. What is d?
-1, -2/5, 0
Suppose 10 = 4*v + 2. Let l(i) be the first derivative of 0*i + 5/2*i**4 - 14/3*i**3 + v*i**2 + 2. Factor l(n).
2*n*(n - 1)*(5*n - 2)
Let p be (-2)/(-2)*3 + -5. Let m be 2/p*(-9 - -2). Factor 3*y**3 + 2*y + 3 + m*y + 6*y**2 + 3*y**2.
3*(y + 1)**3
Suppose 32 = 6*k + 20. Factor 2*l**k + 4/3 - 10/3*l.
2*(l - 1)*(3*l - 2)/3
Find b such that 3*b**2 - 3*b**3 + 34 - 16 - 18 = 0.
0, 1
Suppose -46*r**2 + r**3 + 4*r**4 + 38*r**2 + 3*r**3 = 0. What is r?
-2, 0, 1
Let i be (10/4)/((-8)/16). Let d(g) = -g**3 - 6*g**2 + g + 6. Let l(u) = -u**2 + 1. Let h be -1 + 0 + 1 + 1. Let c(v) = h*d(v) + i*l(v). Factor c(a).
-(a - 1)*(a + 1)**2
Factor -4/3*z + 0 + 10/3*z**2.
2*z*(5*z - 2)/3
Suppose -8/5*w**3 + 18/5 + 10*w**2 - 84/5*w = 0. Calculate w.
1/4, 3
Let h(q) = q**2 + 9*q + 3. Let t be h(-9). Suppose -t*a + 7 - 1 = 0. Determine b so that 4/5*b**a + 0 + 2/5*b + 2/5*b**3 = 0.
-1, 0
Let g(u) be the third derivative of -u**5/4 + 3*u**4/8 + u**3 - 7*u**2. Factor g(p).
-3*(p - 1)*(5*p + 2)
What is w in 18/5*w - 3 - 3/5*w**2 = 0?
1, 5
Let g(o) = 12*o**4 - o**3 - 27*o**2 + 11*o. Let w(d) = -6*d**4 + 14*d**2 - 6*d. Suppose 0 = -2*i - 3*i + 10. Let t(n) = i*g(n) + 5*w(n). Factor t(s).
-2*s*(s - 1)*(s + 2)*(3*s - 2)
Let r(s) = -s**5 + 6*s**4 - 2*s**2 + 5*s + 4. Let t(q) = q**4 + q + 1. Let k(o) = r(o) - 4*t(o). Suppose k(p) = 0. What is p?
-1, 0, 1
Determine m so that -11*m**2 + 0*m - 4*m**4 + 15*m**2 + 2*m**3 + 4*m - 6*m**3 = 0.
-1, 0, 1
Let g(l) be the first derivative of -5*l**7/63 - l**6/15 + l**5/15 + l + 1. Let n(j) be the first derivative of g(j). Factor n(p).
-2*p**3*(p + 1)*(5*p - 2)/3
Suppose -5*k - 5*a = -55, 3*a + 2 = 2*k - 5. What is u in 0*u - 4*u - 