7
Suppose -7*g + 488 = -401. Suppose g*d = 128*d. Factor v**4 + v**3 + 0 + 1/3*v**2 + d*v + 1/3*v**5.
v**2*(v + 1)**3/3
Factor -8 + 20*w + 5/2*w**4 - 5/2*w**3 - 25/2*w**2 + 1/2*w**5.
(w - 1)**3*(w + 4)**2/2
Let f be -11 + 17 + -9 + 5. Factor -f - 2/9*h**2 + 20/9*h.
-2*(h - 9)*(h - 1)/9
Let g be (-9)/(1*9/(-6)). Suppose 3 = -c - 5*m + 6, 5*m = 2*c - g. What is r in 9/5*r**5 - 3/5*r**2 + c*r**3 - 21/5*r**4 + 0 + 0*r = 0?
0, 1/3, 1
Suppose -21*f = -18*f - 12. Suppose 0 = -f*m + w + 11, -3*w = 4 + 5. What is j in 0*j**m + 0 - 2/3*j**3 + 2/3*j**5 + 0*j**4 + 0*j = 0?
-1, 0, 1
Let n(t) be the first derivative of -t**4/4 - t**3/2 - 2*t - 11. Let g(w) be the first derivative of n(w). Suppose g(p) = 0. Calculate p.
-1, 0
Factor 237*z**3 - 328*z**4 + 70*z**4 + 150*z**4 + 720*z**2 + 28 + 411*z**3 + 248*z.
-4*(z - 7)*(3*z + 1)**3
Let m(i) be the third derivative of 25/24*i**4 + 0*i - 2/21*i**7 - 5/336*i**8 - 1/6*i**6 - 7*i**2 + 5/3*i**3 + 0 + 1/6*i**5. Find z, given that m(z) = 0.
-2, -1, 1
Let i(a) = 4*a**2 - 8*a + 3. Let f(r) = r**2 - r + 1. Let v = -40 - -30. Let u(b) = v*f(b) + 2*i(b). Factor u(o).
-2*(o + 1)*(o + 2)
Let a(d) be the second derivative of 16*d**7/21 - 216*d**6/5 + 6721*d**5/10 - 540*d**4 + 400*d**3/3 + 2*d + 2. Factor a(r).
2*r*(r - 20)**2*(4*r - 1)**2
Let w be (-2 - 0)*6/63*-6. Factor -10/7*u + 4/7 - 2/7*u**3 + w*u**2.
-2*(u - 2)*(u - 1)**2/7
Let z(y) be the first derivative of y**6/180 - y**5/30 - 19*y**3/3 - 21. Let n(v) be the third derivative of z(v). Suppose n(b) = 0. Calculate b.
0, 2
Let f(z) = -1 + 9 - 3*z + 4*z + 8. Let p be f(-13). Find h, given that 10*h + 3*h + 8*h**2 - 6*h - 3*h + 4*h**p = 0.
-1, 0
Let n(k) be the first derivative of k**5/420 - 8*k**2 - 22. Let y(l) be the second derivative of n(l). Find r, given that y(r) = 0.
0
Let r(o) = 45*o**3 + 180*o**2 - 20*o - 155. Let l(f) = -2*f**3 + f**2 + f - 2. Let q(d) = 25*l(d) + r(d). Factor q(v).
-5*(v - 41)*(v - 1)*(v + 1)
Let b(v) = -4*v + 1. Let k be b(-1). Let h = k - 1. Factor 0*f**2 + 4*f + 0*f**3 + 3*f**2 + f**4 - h - 4*f**3.
(f - 2)**2*(f - 1)*(f + 1)
Let h be 28/(-14) + 3 + -1. Let c(v) be the third derivative of -v**2 + 0*v**4 + h*v + 1/20*v**5 + 0 - 1/2*v**3. Let c(d) = 0. What is d?
-1, 1
Let b(x) = -x**2 - 16*x - 20. Let a be b(-12). Let -6*m**5 - a*m**4 + 11*m**5 - 50*m**2 + 2*m**4 - 5 + m**4 + 50*m**3 + 25*m = 0. What is m?
1
Let w(y) = -2*y**4 + 12*y**3 + 41*y**2 + 24*y - 3. Let r(h) = -3*h**4 + 11*h**3 + 42*h**2 + 24*h - 4. Let m(f) = -3*r(f) + 4*w(f). Factor m(z).
z*(z + 1)*(z + 2)*(z + 12)
Let s(u) = -u**2 - 4*u - 3. Let b be s(-4). Let f = 1 - b. Determine l so that 6*l**3 - 2*l**4 - 4*l + 3 - 2*l - l**f = 0.
-1, 1
Let n(q) be the third derivative of q**8/6720 + q**7/840 + q**6/240 + q**5/60 + q**2. Let p(f) be the third derivative of n(f). Factor p(o).
3*(o + 1)**2
Let t(i) be the first derivative of 25*i**6/9 + 6*i**5 - 7*i**4/6 - 82*i**3/9 - 2*i**2 + 16*i/3 + 114. Let t(x) = 0. What is x?
-1, 2/5, 4/5
Let k = -30 + 46. Suppose -2*r + 24 = 4*h, -3*h - h = -2*r + k. Solve -r*v**2 + 20*v + 2*v**2 - 22*v = 0.
-1/4, 0
Suppose 3*p = -2*p - 5*j + 30, -j - 3 = 0. Suppose 4*m - w = p, -3*w + 3 = 4*m + 2*w. Factor -1/2*f**3 + 1/2 - 3/2*f + 3/2*f**m.
-(f - 1)**3/2
Let q(s) = 3*s**4 + 9*s**3 + 9*s**2 + 3*s - 2. Let j(a) = a**3 - a + 2. Let z(h) = 4*j(h) + 4*q(h). Factor z(y).
4*y*(y + 1)*(y + 2)*(3*y + 1)
Let g = 5 + -7/2. Let j(y) be the first derivative of -27/2*y + 3 + 27/4*y**2 - g*y**3 + 1/8*y**4. Factor j(c).
(c - 3)**3/2
Let c(d) be the first derivative of 3*d**5/35 - 9*d**4/28 - 4*d**3/7 - 14. Factor c(w).
3*w**2*(w - 4)*(w + 1)/7
Let j(w) be the third derivative of w**6/120 - w**5/10 + 13*w**2 + 2. What is i in j(i) = 0?
0, 6
Let -539*p + 4*p**3 - 4*p**5 + 16*p**4 + 607*p - 4*p**3 - 56*p**2 - 24 = 0. Calculate p.
-2, 1, 3
Factor 14*t**2 + 18*t + 0*t**2 + 2*t**2 + 16 - 5*t**4 + 14*t - t**5 - 4*t**3.
-(t - 2)*(t + 1)*(t + 2)**3
Let v = -37 - -54. Suppose 0 = -5*z - 7 + v. Factor 0 - 2/5*g**4 + 2/5*g**z - 2/5*g + 2/5*g**3.
-2*g*(g - 1)**2*(g + 1)/5
Let v(g) be the first derivative of g**6/27 - 28*g**5/45 - 17*g**4/18 + 20*g**3/9 + 942. Solve v(c) = 0 for c.
-2, 0, 1, 15
Let f(j) be the first derivative of -j**6/120 - 9*j**5/40 + 5*j**4/4 + 29*j**3/3 + 41. Let c(x) be the third derivative of f(x). Let c(t) = 0. What is t?
-10, 1
Let t(i) be the second derivative of -i**4/12 + 31*i**3/2 + 47*i**2 + 11*i. Find q, given that t(q) = 0.
-1, 94
Let x(t) = -4*t**4 + 13*t**3 + 6*t**2 - 18*t. Let m(j) = -22*j**4 + 66*j**3 + 30*j**2 - 90*j. Let f(g) = -3*m(g) + 16*x(g). Factor f(c).
2*c*(c - 1)*(c + 3)**2
Let u(t) be the first derivative of t**3/15 - 17*t**2/10 - 12*t + 288. Suppose u(n) = 0. What is n?
-3, 20
Factor 1/4*d**2 - 5/2 + 3/4*d.
(d - 2)*(d + 5)/4
Let b(z) = -2*z**4 + 10*z**3 + 20*z**2 + 11*z + 3. Let p(j) = -9*j**4 + 40*j**3 + 81*j**2 + 45*j + 13. Let x(y) = 26*b(y) - 6*p(y). Find c, given that x(c) = 0.
-8, -1, 0
Let c be (((-56)/(-12))/(-7))/((-2)/6). Find w such that -75*w**4 + 32*w**2 + 8*w**c - 10*w + 110*w**5 + 35*w**2 - 100*w**3 = 0.
-1, 0, 2/11, 1/2, 1
Let l(j) be the first derivative of -j**4/6 + 10*j**3/9 - 4*j**2/3 + 60. Factor l(i).
-2*i*(i - 4)*(i - 1)/3
Factor -12/5*l**2 + 1/5*l**3 + 1/5*l**4 - 16/5 - 28/5*l.
(l - 4)*(l + 1)*(l + 2)**2/5
Let q(s) be the third derivative of -7*s**2 - 1/60*s**5 + 1/24*s**4 + 0*s + 1/3*s**3 + 0. Factor q(j).
-(j - 2)*(j + 1)
Let m be 1*-11*6/(-88). Let x(d) be the first derivative of -d**3 + 3/5*d**5 + 1/2*d**6 + 0*d + 4 - m*d**4 + 0*d**2. Factor x(o).
3*o**2*(o - 1)*(o + 1)**2
Let o(y) = y**3 + 8*y**2 + 58*y + 359. Let a be o(-7). Factor 0*z - 2/5*z**a - 1/5*z**3 + 1/5*z**4 + 0.
z**2*(z - 2)*(z + 1)/5
Let s = -19 - -24. Suppose 3*b = -5*c - s, b - 11 = 2*c + 4*b. Factor -7/5*v**c + 2/5 + v.
-(v - 1)*(7*v + 2)/5
Let c = 113 - 3952/35. Let m(s) be the first derivative of 0*s**2 + 0*s + 3/7*s**4 + c*s**5 + 4/7*s**3 + 1. Factor m(w).
3*w**2*(w + 2)**2/7
Suppose -2*y - 4*y = -42. Factor 26*p + 17*p - y*p - 108 - 3*p**2 + 0*p**2.
-3*(p - 6)**2
Let l(q) be the third derivative of 0 + 13/105*q**5 + 0*q**3 - 2/735*q**7 + 0*q - 1/6*q**4 + 22*q**2 - 1/42*q**6. Determine t, given that l(t) = 0.
-7, 0, 1
Let g be ((7533/216)/(-31))/((-5)/2 + 2). Factor -g - 21/8*t - 3/8*t**2.
-3*(t + 1)*(t + 6)/8
Let t(z) = 5*z**3 - 10*z. Let n(l) = 12*l**3 - 8*l**3 - 9*l**3 + l**2 + 10*l. Let j(h) = 5*n(h) + 6*t(h). Factor j(g).
5*g*(g - 1)*(g + 2)
Let m(g) be the second derivative of 20*g + 0*g**5 + 0*g**2 + 0*g**3 - 1/168*g**7 + 0 - 1/120*g**6 + 0*g**4. What is n in m(n) = 0?
-1, 0
Let b(j) be the second derivative of 2*j**7/147 + 2*j**6 - 86*j**5/7 + 650*j**4/21 - 290*j**3/7 + 218*j**2/7 + 408*j. Let b(t) = 0. Calculate t.
-109, 1
Let b(r) be the first derivative of 1/3*r**3 - 2*r + 6 - 1/2*r**2. Find f such that b(f) = 0.
-1, 2
Let f = 6 - 4. Let q be ((-1785)/14)/17 - -8. Suppose -q*n + 0 + 1/4*n**f = 0. What is n?
0, 2
Let 4/7*n**3 - 2/7*n**5 - 2/7*n + 0 + 0*n**4 + 0*n**2 = 0. What is n?
-1, 0, 1
Let j(u) = -38*u**5 + 30*u**4 + 2*u**3 - 30*u**2 - 18*u. Let h(o) = 2*o**5 - o**4 + o**2 + o. Let d(p) = 36*h(p) + 2*j(p). Find t, given that d(t) = 0.
-1, 0, 1, 6
Let w be ((-2289)/(-12))/(2/(-8)*-5). Let i = -152 + w. Solve 1/5*p**3 - i*p**2 - 1/5 + 3/5*p = 0.
1
Let f(s) be the first derivative of -s**6/120 + 31*s**2/2 + 3. Let b(u) be the second derivative of f(u). Solve b(x) = 0 for x.
0
Let b(g) = 2*g**4 - 104*g**3 - 1338*g**2 + 3024*g - 1564. Let p(i) = 3*i**4 - 103*i**3 - 1336*i**2 + 3024*i - 1563. Let u(m) = -5*b(m) + 4*p(m). Factor u(f).
2*(f - 1)**2*(f + 28)**2
Let j(g) be the first derivative of -50 - g**4 + 2*g**2 + 2/5*g**5 - 8/3*g**3 + 6*g. Factor j(u).
2*(u - 3)*(u - 1)*(u + 1)**2
Suppose 5*o - 36 = -26. Let k(r) be the second derivative of 1/54*r**4 + 3*r + 0*r**o + 0 - 1/27*r**3. Factor k(f).
2*f*(f - 1)/9
Let -170/3*k + 1/3*k**2 + 7225/3 = 0. Calculate k.
85
Let x(k) be the third derivative of 1/120*k**5 - 1/160*k**6 + 0*k**3 + 12*k**2 + 0*k + 1/840*k**7 + 0 + 0*k**4. Let x(o) = 0. What is o?
0, 1, 2
Let a(b) = b**4 - 12*b**3 + 57*b**2 - 108*b + 81. Let o(p) = -143 + 34*p - 19 + 182*p - 115*p**2 + 24*p**3 - 2*p**4. Let n(l) = 7*a(l) + 3*o(l). Factor n(y).
(y - 3)**4
Let q(p) = 2*p**3 + 83*p**2 + 290*p + 254. Let v(y) =