 p(k).
4*(k - 1)*(k + 7)
Let l(h) = -8*h**5 - 4*h**4 + 12*h**3 + 20*h**2 + 8*h + 8. Let i(a) = -9*a**5 - 4*a**4 + 12*a**3 + 20*a**2 + 8*a + 10. Let x(v) = -4*i(v) + 5*l(v). Factor x(g).
-4*g*(g - 2)*(g + 1)**3
Suppose 5*r - 78 + 65 = b, 5*r - 9 = 3*b. Factor -1/5*x**5 + 0*x**4 + 0*x**b + 0 + 2/5*x**3 - 1/5*x.
-x*(x - 1)**2*(x + 1)**2/5
Suppose -5*j - 4*g = -48, -j - 2*g + 9 = -g. Determine y so that 12*y + j*y**2 + 10*y**2 + 6*y**5 - 15*y**4 - 6*y**3 - 3*y**3 + 2*y**2 = 0.
-1, -1/2, 0, 2
Find a, given that -3*a + 19/4*a**2 + 1/4*a**4 + 0 - 2*a**3 = 0.
0, 1, 3, 4
Let q(b) be the second derivative of 23/30*b**3 - 1/100*b**5 + 0 - 6/5*b**2 - 1/6*b**4 + 28*b. Factor q(y).
-(y - 1)**2*(y + 12)/5
Suppose -5*n + 7*n - 8 = 0. Let c(z) = -8*z**4 - 6*z**3 - 11*z. Let v(h) = -2 - 2*h**3 - 4*h - 3*h**4 + 2. Let j(g) = n*c(g) - 11*v(g). Let j(d) = 0. What is d?
0, 2
Let u(o) be the third derivative of o**8/1344 - o**7/60 + 53*o**6/480 - 19*o**5/60 + 3*o**4/8 + 169*o**2. Factor u(k).
k*(k - 9)*(k - 2)**2*(k - 1)/4
Solve 42*r**2 - 23*r**2 + 140 - 17*r**2 + 142*r = 0.
-70, -1
Let s be 4 + (-2)/1 + 17 + -19. What is t in -8*t + 4*t**4 - 16*t**3 + 12*t**2 + 8*t**2 + s*t**2 = 0?
0, 1, 2
Let m(o) be the third derivative of 1/840*o**7 + 0 + 3/80*o**5 - o - 7/96*o**4 - 1/96*o**6 + 1/12*o**3 - 7*o**2. Let m(x) = 0. What is x?
1, 2
Let p(n) be the first derivative of 0*n**3 + 6/25*n**5 + 0*n**2 - 30 - 1/3*n**6 + 0*n + 1/5*n**4. Solve p(l) = 0.
-2/5, 0, 1
Suppose 10*j = -1474 - 546. Let o = j - -1820/9. Factor -4/9*k - 2/9*k**2 - o.
-2*(k + 1)**2/9
Let b(z) = z**3 + 7*z**2 - 14*z + 42. Let l be b(-9). Let g(p) be the second derivative of 0 - 1/10*p**l + 0*p**2 + 7*p + 0*p**5 + 3/4*p**4 - p**3. Factor g(j).
-3*j*(j - 1)**2*(j + 2)
Let c be 312/20 + 2/20*4. Factor 25*t + 14 + c + 12*t**2 - 17*t**2.
-5*(t - 6)*(t + 1)
Let g(b) = b**2 + 2*b - 286. Let h be g(16). Factor -3*n**3 - 13/2*n**h - 2 - 1/2*n**4 - 6*n.
-(n + 1)**2*(n + 2)**2/2
Let h(r) be the first derivative of 9*r**5/5 - 11*r**4/3 - 32*r**3/3 + 8*r**2 + 14*r + 13. Let s(w) be the first derivative of h(w). Let s(k) = 0. Calculate k.
-1, 2/9, 2
Let j(x) = 8*x**4 + 13*x**3 + 2*x**2 - 3*x - 3. Let s(l) = 8*l**3 - 2*l + 7*l**3 + 7*l**4 - 3*l**3 - 2 + 3*l**2. Let k(c) = 2*j(c) - 3*s(c). Factor k(d).
-5*d**2*(d + 1)**2
What is u in 32 - 1/2*u**4 - 40*u + 6*u**2 + 5/2*u**3 = 0?
-4, 1, 4
Suppose -81 = 80*z - 100*z - 1. Factor 16/7*s**3 - 10/7*s**z - 8/7*s**2 + 0*s + 2/7*s**5 + 0.
2*s**2*(s - 2)**2*(s - 1)/7
Let 2*j**2 + 2/7*j**3 + 40/7 - 8*j = 0. What is j?
-10, 1, 2
Let p(o) = -32*o**2 + 23*o - 7*o - 7*o**3 + 29*o**2. Let i(y) = 6*y**3 + 2*y**2 - 16*y. Let s(n) = 3*i(n) + 2*p(n). Solve s(f) = 0.
-2, 0, 2
Suppose -3*u + 9*u = 48. Determine b, given that 6 - 6 - u*b**2 + 4*b**4 + 4 - 16*b + 32*b**3 - 13*b**5 - 3*b**5 = 0.
-1, 1/4, 1
Let x(r) = -3*r**4 - 5*r**3 + 56*r**2 + 113*r + 60. Let t(w) = -3*w**4 - 6*w**3 + 57*w**2 + 114*w + 60. Let n(o) = 5*t(o) - 6*x(o). Factor n(v).
3*(v - 5)*(v + 1)*(v + 2)**2
Let v(p) = -p**4 + p**3 + p - 1. Let j(m) = -8*m**4 + 12*m**3 + 9*m - 9. Suppose c + 7 = -11. Let x(o) = c*v(o) + 2*j(o). Factor x(w).
2*w**3*(w + 3)
Let t = -62810 - -62812. Suppose -2*l + 2 = 5*g - 0*l, 4*l - 4 = -2*g. Suppose 0 + g*z + 2/7*z**t = 0. Calculate z.
0
Factor -12/7 - 9/7*q**3 - 27/7*q**2 - 31/7*q - 1/7*q**4.
-(q + 1)**2*(q + 3)*(q + 4)/7
Let f(y) be the third derivative of 5/96*y**4 + 10*y**2 + 1/48*y**5 + 0*y**3 + 0*y + 0. Factor f(m).
5*m*(m + 1)/4
Factor 36 + 0*k**3 + 30*k**2 + 3/4*k**5 - 15/4*k**4 - 60*k.
3*(k - 2)**4*(k + 3)/4
Factor -7*g**3 + 1/3*g**2 - 10/3*g**5 + 9*g**4 + g + 0.
-g*(g - 1)**3*(10*g + 3)/3
Suppose -1/3*g**2 - 10/3*g + 25 = 0. What is g?
-15, 5
Suppose 0 = -4*y + 2*y. Let l be (540/88 + -6)/(12/16). What is w in 0*w + 0 + 0*w**2 + 2/11*w**5 - l*w**3 + y*w**4 = 0?
-1, 0, 1
Let l be 0 - (-3)/4 - (-4)/16. Let w be l + (-5)/3 - (-13)/15. Solve 1/5*z**2 + 0 + w*z = 0.
-1, 0
Let d(s) be the third derivative of -s**6/180 - 2*s**5/45 - 5*s**4/36 - 2*s**3/9 + s**2 + 36. Solve d(j) = 0 for j.
-2, -1
Let 200/13*m**4 + 34/13*m**5 + 356/13*m**2 - 16/13 + 418/13*m**3 + 88/13*m = 0. Calculate m.
-2, -1, 2/17
Let k(b) = -4*b - 24. Let z be k(-7). Let w = 3 - 3. Find c, given that 0*c**z + 2*c**5 + 2*c**4 + w*c**4 = 0.
-1, 0
Let x be (-314)/28*2 - -5. Let o = x - -422/21. Solve o - 2*h**2 - 2/3*h**4 - 8/3*h + 8/3*h**3 = 0 for h.
-1, 1, 2
Let s = 49 - 40. Factor 3*r**5 - r**4 - 11*r**4 + 0*r**4 + s*r**3.
3*r**3*(r - 3)*(r - 1)
Let c be (-96)/(-110) - 48/176. Factor -6/5*h + c*h**2 + 0.
3*h*(h - 2)/5
Let b(p) = p**3 + 8*p**2 - 10*p - 9. Let w be b(-9). Let c be w*2/(-8 - -4). Let 1/4*v**3 - 3/4*v**2 + c + 0*v = 0. What is v?
0, 3
Let r(s) be the third derivative of s**11/443520 - s**10/151200 + s**9/241920 + s**5/10 - 4*s**2. Let m(d) be the third derivative of r(d). Factor m(z).
z**3*(z - 1)*(3*z - 1)/4
Let a(q) be the first derivative of -2*q**5 - 7*q**4 + 2*q**3 + 20*q**2 - 8*q + 87. Suppose a(h) = 0. What is h?
-2, 1/5, 1
Suppose -9*t - 432 = -t. Let p be -1*(t/(-14) - 4). Factor -p*q**2 + 1/7*q + 0.
-q*(q - 1)/7
Let o(l) = l - 51. Let h be o(54). Let s(j) be the first derivative of -1/10*j**5 + 1/4*j**4 + 0*j - 3 + 0*j**h + 0*j**2. Factor s(r).
-r**3*(r - 2)/2
Let b(f) = -f**3 + 33*f**2 + 2. Let y be b(33). Let z(u) be the second derivative of 4*u + 0 + 6/5*u**y + 1/20*u**4 + 1/2*u**3. Factor z(s).
3*(s + 1)*(s + 4)/5
Factor 0*c + 6/7*c**2 + 26/7*c**3 + 0.
2*c**2*(13*c + 3)/7
Factor 5/4*v**4 + 10*v + 0 + 15*v**2 + 15/2*v**3.
5*v*(v + 2)**3/4
Let m be (-76)/(-133)*42/4. Let l(n) be the third derivative of 0*n + 13/15*n**5 - 2*n**2 - 2*n**4 + 8/3*n**3 + 0 + 2/105*n**7 - 1/5*n**m. Factor l(p).
4*(p - 2)**2*(p - 1)**2
Let g(m) be the first derivative of m**4/28 + 2*m**3/21 - m**2/2 + 4*m/7 + 143. Find u, given that g(u) = 0.
-4, 1
Suppose 26 = 5*l + r, 0 = -3*l - l - 4*r + 24. Let 0*m**4 + 0*m - 2/11*m**l + 0*m**2 + 0 + 2/11*m**3 = 0. Calculate m.
-1, 0, 1
Let x(m) be the third derivative of -m**8/840 + m**6/90 - m**4/12 + 5*m**3/6 - 11*m**2. Let s(v) be the first derivative of x(v). Find p, given that s(p) = 0.
-1, 1
Suppose 0 = -3*u - 4*h - 20, 2*u + 3*h + 124 - 109 = 0. Factor 0*f + u + 36/5*f**3 + 0*f**2 + 3/5*f**4.
3*f**3*(f + 12)/5
Let r = -2580 - -2582. Suppose -1/6*n**4 + 0 + 1/3*n**3 + 0*n + 0*n**r - 1/6*n**5 = 0. What is n?
-2, 0, 1
Suppose 77 = 44*a - 11. Let m(q) be the third derivative of 1/21*q**3 - 1/735*q**7 + 0*q + 0 + 0*q**5 - 1/42*q**4 - q**a + 1/210*q**6. Factor m(s).
-2*(s - 1)**3*(s + 1)/7
Let x(r) = -195*r**3 - 85*r**2 + 175*r + 85. Let n(u) = -28*u**3 - 12*u**2 + 25*u + 12. Let f(k) = 20*n(k) - 3*x(k). Factor f(j).
5*(j - 1)*(j + 1)*(5*j + 3)
Let s = -4723 + 4725. Let 0 - o - 1/2*o**3 + 3/2*o**s = 0. What is o?
0, 1, 2
Let f(r) = -23*r + 146*r**3 - 33*r**2 - 15*r**2 + 60 - 143*r**3 + 5*r**4. Let n(g) = -g**3 + g**2 + g. Let b(h) = f(h) + 3*n(h). Suppose b(y) = 0. What is y?
-2, 1, 3
Factor -2 + 2/7*o**2 + 12/7*o.
2*(o - 1)*(o + 7)/7
Let l(q) = -2*q**2 - q + 2. Let s(r) = -4*r**2 - 58*r + 33. Let i(h) = -3*l(h) + s(h). Find k, given that i(k) = 0.
1/2, 27
Let z = 2197/5712 - 1/272. Let j(m) be the third derivative of 0*m - 1/420*m**6 - 1/7*m**4 - 3*m**2 + 0 + 1/35*m**5 + z*m**3. Find q, given that j(q) = 0.
2
Let z be (-243)/(-54) + (-44)/16. Solve -z*t**3 - 1/2 + 7/4*t + 1/2*t**2 = 0.
-1, 2/7, 1
Find i such that -3*i**2 - 43/3*i + 10/3 = 0.
-5, 2/9
Suppose 69/7*n - 66/7 - 3/7*n**2 = 0. What is n?
1, 22
Find m such that -214*m**3 + 97*m**3 + 4*m**5 - 8*m**2 + 105*m**3 = 0.
-1, 0, 2
Factor 1/3*d**4 - 224*d - 384 + 47/3*d**3 + 526/3*d**2.
(d - 2)*(d + 1)*(d + 24)**2/3
Let i(g) be the first derivative of 3*g**4/14 - 4*g**3/21 - g**2/7 - 28. Factor i(j).
2*j*(j - 1)*(3*j + 1)/7
Let v(o) be the second derivative of 5*o**7/42 - o**6/2 + o**5/2 + 8*o - 3. Factor v(w).
5*w**3*(w - 2)*(w - 1)
Let v(m) = -5*m**4 + 15*m**3 - 4*m**2 - 4*m + 2. Let f(s) = 17*s**2 + 20*s - 11 + 3*s**2 - 76*s**3 + 0 + 25*s**4. Let x(t) = 2*f(t) + 11*v(t). Factor x(w).
-w*(w - 2)*(w - 1)*(5*w + 2)
Let o(r) be the third derivative of r**7/1365 - r**6/65 + r**5/13 - 7*r**4/39 + 3*r**3/13 + 5*r**2. Factor o(s).
2*(s - 9)*(s - 1)**3/13
Let p(t) = t**3 + t + 1. Let n(l) = -2*l**3 + 8*l + 3. Let k be (-2)/(2 + -1