*(m - 1)*(m + 1)/5
Suppose 11*a + 6 = 13*a. Find w such that -1/3*w**2 - a - 2*w = 0.
-3
Let a(d) = -105*d**3 - 66*d**2 + 195*d - 105. Let p(j) = -8*j**3 - 5*j**2 + 15*j - 8. Let r(k) = 2*a(k) - 27*p(k). Factor r(h).
3*(h - 1)*(h + 2)*(2*h - 1)
Solve 4/13*d**2 + 2/13*d - 2/13 = 0.
-1, 1/2
Let d(s) = 9*s**2 - 37*s + 44. Let l(o) = 3*o**2 - 12*o + 15. Let c(a) = 3*d(a) - 8*l(a). Factor c(x).
3*(x - 4)*(x - 1)
Let v(x) = -x**3 - x**2 - 1. Let j be v(-2). Factor -6 + i + 5*i**2 - i - 2*i**2 - j*i.
3*(i - 2)*(i + 1)
Solve 0 - 2/9*z - 2/9*z**4 + 2/9*z**3 + 2/9*z**2 = 0.
-1, 0, 1
Let l(o) = -9*o**2 + 3*o - 7. Let w(b) = -5*b**2 + 2*b - 4. Let i(q) = -4*l(q) + 7*w(q). Factor i(n).
n*(n + 2)
Let a be 1 - 10 - (3 - 3). Let w = a - -11. What is h in -1/2*h + 3/2*h**w - 1 = 0?
-2/3, 1
Determine n so that 1/6*n**2 + 7/6*n - 4/3 = 0.
-8, 1
Let m(d) be the third derivative of -d**6/120 - d**5/15 + d**4/8 + 3*d**3 + 4*d**2. Factor m(a).
-(a - 2)*(a + 3)**2
Let f(c) be the first derivative of -5*c**4 + 32*c**3/3 - 2*c**2 - 8*c - 1. Find d, given that f(d) = 0.
-2/5, 1
Let v(n) be the first derivative of 4*n**5/35 - 11. Factor v(a).
4*a**4/7
Let i be 0/(-1) + 4/6. Find q such that 2/3*q**2 - 2/3*q**4 + i*q - 2/3*q**3 + 0 = 0.
-1, 0, 1
Let x(a) be the first derivative of a**6/2 - 6*a**5 + 30*a**4 - 80*a**3 + 120*a**2 - 96*a + 12. Suppose x(k) = 0. Calculate k.
2
Factor -2 + 14 - 8 + 5*q**3 + 16*q - 19*q**2.
(q - 2)**2*(5*q + 1)
Suppose 5*v + 44 = -3*p + p, 4*v = 4*p - 24. Let q be (1/v)/((-1)/4). Let -1/4*z**2 + 0 + q*z**3 + 0*z - 1/4*z**4 = 0. What is z?
0, 1
Let p(n) be the third derivative of -1/360*n**6 + 0*n + 0*n**3 + 4*n**2 + 1/1008*n**8 + 0 + 0*n**4 - 1/180*n**5 + 1/630*n**7. Factor p(u).
u**2*(u - 1)*(u + 1)**2/3
Let c(g) be the third derivative of g**6/900 - g**4/180 - 3*g**2. Solve c(s) = 0.
-1, 0, 1
Let t(a) be the second derivative of a**8/6720 - a**6/240 + a**5/60 + a**4/6 - 3*a. Let u(d) be the third derivative of t(d). Suppose u(y) = 0. What is y?
-2, 1
Let d(x) be the second derivative of -x**8/1680 - x**7/840 - x**3/3 - x. Let y(k) be the second derivative of d(k). Factor y(z).
-z**3*(z + 1)
Let h(x) = -2*x**2 + 2. Let k(v) = -3*v**2 + v + 4. Let y(c) = -5*h(c) + 3*k(c). Factor y(s).
(s + 1)*(s + 2)
Let x be (-13)/(-2) - 6/(-12). Let g(r) = r**3 - 6*r**2 - 7*r. Let k be g(x). Determine a so that -2/9*a**3 - 4/9*a**2 + k - 2/9*a = 0.
-1, 0
Factor 27/4 - 1/4*l**3 - 27/4*l + 9/4*l**2.
-(l - 3)**3/4
Let a(m) be the first derivative of 9/2*m**2 + 3/4*m**4 - 3*m + 2 - 3*m**3. Let a(v) = 0. Calculate v.
1
Let u(z) be the second derivative of -z**7/105 + z**2 - 3*z. Let i(d) be the first derivative of u(d). Factor i(b).
-2*b**4
Suppose 0 = -4*c + 11 + 13. Determine v so that -6 + 3*v**2 - c*v + 6 = 0.
0, 2
Factor -8 - 4*r**2 - 3*r + 0*r**2 + 7*r + 12*r**2 - 4*r**3.
-4*(r - 2)*(r - 1)*(r + 1)
Let m be (-8 + 4)*(-7)/4. Let p = m + -27/4. Factor 1/4*b**3 - p*b + 1/4*b**2 - 1/4.
(b - 1)*(b + 1)**2/4
Let g(q) = -4*q**4 + 13*q**3 - 20*q**2 + 11*q - 3. Let n(m) = -4*m**4 + 12*m**3 - 20*m**2 + 12*m - 4. Let h(x) = 4*g(x) - 3*n(x). Suppose h(t) = 0. Calculate t.
0, 1, 2
Suppose 2*b - 8 = -2*b. Factor -3*w**3 + 0*w**3 + 6*w**2 + 4*w**b - 16*w + 8 + w**3.
-2*(w - 2)**2*(w - 1)
Let l(r) be the second derivative of 0 - 1/70*r**5 - r - 1/7*r**2 - 1/14*r**4 - 1/7*r**3. Factor l(y).
-2*(y + 1)**3/7
Let u(c) = c**3 + 5*c**2 + 4*c. Let x be u(-5). Let k be 0 + 0 + x/(-30). What is j in k*j**2 + 8/3*j + 8/3 = 0?
-2
Find g, given that 4/7*g**3 + 16/7*g**2 + 8/7 + 20/7*g = 0.
-2, -1
Let m(n) be the second derivative of -n**5/35 + n**4/21 + 2*n**3/21 - 2*n**2/7 - 2*n. Factor m(b).
-4*(b - 1)**2*(b + 1)/7
Let a = 2 - -1. Let b(t) = t - 4. Let c be b(a). Let v(j) = 4*j**2 + 3*j. Let u(d) = d. Let h(p) = c*v(p) + 5*u(p). Factor h(f).
-2*f*(2*f - 1)
Let h(q) be the first derivative of -q**3/9 + 16*q**2/3 - 256*q/3 + 8. Factor h(p).
-(p - 16)**2/3
Let g be 2/7 - (-14)/(-49). Factor g + k**3 + 2 + 3*k - 6*k.
(k - 1)**2*(k + 2)
Let q(f) be the first derivative of -3 + 2/3*f**3 + 1/2*f**4 + 0*f**2 + 0*f. Factor q(l).
2*l**2*(l + 1)
Let 20*d**2 + 16/3 + 24*d - 50/3*d**3 = 0. What is d?
-2/5, 2
Suppose -15 + 31 = 4*j. Suppose -1/2*i**3 + 0*i**2 - 1/2*i**j + 0 + 0*i = 0. Calculate i.
-1, 0
Factor -7*t**2 + 0*t - 6*t**4 - 6*t**3 - 2*t**5 + 0*t + 5*t**2.
-2*t**2*(t + 1)**3
Suppose 0*k**2 + 0 - 2*k**5 - 4/3*k**3 + 14/3*k**4 + 0*k = 0. Calculate k.
0, 1/3, 2
Let -8/17 + 26/17*w**2 - 24/17*w + 42/17*w**3 = 0. What is w?
-1, -2/7, 2/3
Let v(z) = -z**3 + 5*z**2 + 6*z - 4. Let y be v(6). Let b be y/(-6) - (-8)/(-48). Factor 0 - 1/2*i - b*i**2.
-i*(i + 1)/2
Determine h so that -1215*h + 68*h**3 - 73*h**3 + 99*h**2 + 36*h**2 + 3645 = 0.
9
Suppose -48 = 18*o - 102. Suppose 1/2*h**2 + 9/2 + o*h = 0. Calculate h.
-3
Factor 0*f**2 + 0*f**3 + 0 + 2/15*f**4 - 2/15*f**5 + 0*f.
-2*f**4*(f - 1)/15
Let s be 68/51*(-1)/(-4). Determine k, given that -k**2 + 0 - 4/3*k**5 + k**4 + 5/3*k**3 - s*k = 0.
-1, -1/4, 0, 1
Let b(n) be the first derivative of -n**5/20 + n**3/6 + 3*n + 1. Let d(z) be the first derivative of b(z). Factor d(v).
-v*(v - 1)*(v + 1)
Let k be (25/(-10))/(3/30). Let x be (10/k)/(4/(-5)). Determine r so that -1 + x*r**2 + 1/2*r = 0.
-2, 1
Let x(k) be the third derivative of -k**8/10080 - k**7/1260 - k**6/360 - k**5/30 - k**2. Let w(f) be the third derivative of x(f). Factor w(s).
-2*(s + 1)**2
Suppose 0 = -5*a - 6 + 1. Let o be -1 + a*3/(-3). Find c, given that 0*c**2 + 1/2*c**3 - 1/2*c + o = 0.
-1, 0, 1
Let n be 6 - 32/6 - (-16)/30. Let -n*k**2 + 2/5 - 2*k**3 - 4/5*k**4 + 2/5*k = 0. Calculate k.
-1, 1/2
Let l(k) = k + 9. Let r be l(-9). Factor -1/2*w + 0 + 1/2*w**3 + r*w**2.
w*(w - 1)*(w + 1)/2
Let j(l) = l**2 - l + 25. Let r(t) = -12. Let b(x) = 4*j(x) + 9*r(x). Factor b(v).
4*(v - 2)*(v + 1)
Suppose -8 = -3*g - 2. Factor g*r**4 + 0*r**5 - 3*r**5 + 5*r**5.
2*r**4*(r + 1)
Let b(a) = 2*a**3 - 3*a. Let o(p) be the first derivative of -3*p**4/4 + 2*p**2 - 1. Let m(f) = -4*b(f) - 3*o(f). What is g in m(g) = 0?
0
Let c(x) be the first derivative of 9*x**5/5 + 11*x**4/4 + 2*x**3/3 - 10. Factor c(a).
a**2*(a + 1)*(9*a + 2)
Let x = -21 - -25. Factor -2/11*j - 6/11*j**3 + 6/11*j**2 + 2/11*j**x + 0.
2*j*(j - 1)**3/11
Let b(t) = 7*t - 54. Let p be b(8). Let v(g) be the first derivative of g - 1/6*g**3 - p - 1/4*g**2. Determine d so that v(d) = 0.
-2, 1
Let p(n) be the first derivative of -3 + 0*n - 1/8*n**4 + 0*n**2 - 1/10*n**5 + 0*n**3. What is y in p(y) = 0?
-1, 0
Find o, given that -1/3*o + 0 + 1/3*o**5 + 2/3*o**4 + 0*o**3 - 2/3*o**2 = 0.
-1, 0, 1
Let b = -15 - -3. Let f be (-9)/(-6)*b/(-63). Factor -f*i**5 + 0*i + 2/7*i**3 + 0 + 0*i**2 + 0*i**4.
-2*i**3*(i - 1)*(i + 1)/7
Let j(b) be the third derivative of b**7/210 + b**6/60 + b**5/60 - 2*b**2. Factor j(z).
z**2*(z + 1)**2
Suppose -11 = -4*g + 5*d, -2*d + 24 = 5*g + 2*d. Suppose -17 = -g*n - 1. Factor 0 + 0*l**2 - 1/4*l**5 + 0*l + 1/4*l**3 + 0*l**n.
-l**3*(l - 1)*(l + 1)/4
Let g(a) be the second derivative of 0 - 2/3*a**3 - 2*a**2 - 1/12*a**4 + 3*a. Factor g(l).
-(l + 2)**2
Let x be (-33)/9*(0 - -3). Let t be 2*x/((-165)/18). Let -18/5*w**3 - t*w**2 - 2/5*w + 0 = 0. Calculate w.
-1/3, 0
Let z(a) be the first derivative of 0*a**4 - 1 + 1/90*a**5 + 0*a - a**2 - 1/9*a**3. Let d(q) be the second derivative of z(q). Let d(o) = 0. What is o?
-1, 1
Let f = -8 - 0. Let u be (6/f)/(2/(-8)). Factor 3 - 4*z**2 - u*z - 1 + 5*z**2.
(z - 2)*(z - 1)
Let j be 5/2*40/25. Let -j*b**2 + 0*b**2 + 0*b**2 + 2*b**3 - 2*b - 4*b**3 = 0. Calculate b.
-1, 0
Factor -648/13 - 72/13*o - 2/13*o**2.
-2*(o + 18)**2/13
Let s(x) = x**2 - x + 1. Let p(o) = -4*o**4 - 12*o**2 + 20*o - 24. Let t(c) = p(c) + 20*s(c). Find k such that t(k) = 0.
-1, 1
Let g(t) be the third derivative of t**8/840 - t**7/105 + t**6/50 + 2*t**5/75 - 2*t**4/15 - t**2. Factor g(v).
2*v*(v - 2)**3*(v + 1)/5
Let n(u) = 6*u**2 - 2*u - 3*u**2 - u. Let k be n(2). Let -4*b + k*b**2 + 8*b + 0*b**2 + 4*b**3 + 1 + b**4 = 0. Calculate b.
-1
Let l = -84 - -84. Factor 2/9*z**3 + l*z + 0 + 2/9*z**2.
2*z**2*(z + 1)/9
Let j be (-378)/(-204) + (-36)/24. Factor 10/17*t**2 - j*t**3 - 2/17*t - 2/17.
-2*(t - 1)**2*(3*t + 1)/17
Factor -1/4 - 1/4*p**4 + 0*p + 0*p**3 + 1/2*p**2.
-(p - 1)**2*(p + 1)**2/4
Let k = -73 + 73. Let s(r