16, 0
Let w(q) be the first derivative of 4/3*q**3 - 4*q + 1/2*q**4 - 20 - q**2. Factor w(m).
2*(m - 1)*(m + 1)*(m + 2)
Suppose 0 = -v + k + 4, 0 = -2*v - 23*k + 26*k + 12. Let n(f) be the first derivative of 1/6*f**2 + 2/15*f**5 + v*f - 1/4*f**4 + 0*f**3 - 2. Factor n(x).
x*(x - 1)**2*(2*x + 1)/3
Let s(j) be the third derivative of j**6/30 + 4*j**5/15 - j**4/6 - 8*j**3/3 + 37*j**2 + 2*j. Suppose s(n) = 0. What is n?
-4, -1, 1
Let i(q) = 7*q**3 + 17*q**2 + 12*q + 2. Let z(r) = 152*r**3 - 130*r**3 + 7 + 37*r - 2*r**2 + 54*r**2. Let y(b) = 7*i(b) - 2*z(b). Suppose y(n) = 0. What is n?
-2, -1, 0
Let t = -24 + 21. Let k be t*1/1 - -7. Let z(r) = -15*r**2 + 6*r. Let f(x) = -3*x**2 + x. Let w(l) = k*z(l) - 21*f(l). Solve w(n) = 0 for n.
-1, 0
Let o(g) be the first derivative of -g**5/5 + 2*g**4 - 17*g**3/3 + 5*g**2 + 187. Let o(n) = 0. What is n?
0, 1, 2, 5
Let b(o) = -o**2 + o - 2. Let i(s) = 10*s**2 - 11*s + 31. Let y(j) = 22*b(j) + 2*i(j). Determine a, given that y(a) = 0.
-3, 3
Let c be (-10)/(25/5) + 0. Let v(d) = -d**2 - 5*d - 3. Let y be v(c). Factor -64/5*m + 32/5 + 48/5*m**2 + 2/5*m**4 - 16/5*m**y.
2*(m - 2)**4/5
Let q = -30 - -33. Suppose q = 2*g - g. Factor -6 + 3*t**3 + 6 - g*t.
3*t*(t - 1)*(t + 1)
What is h in 1/8*h**2 - 1/4*h + 0 - 1/8*h**4 + 1/4*h**3 = 0?
-1, 0, 1, 2
Let b(z) = -3*z**5 - 6*z**4 + 3*z**2 + 3*z - 3. Let y(a) = 3*a**5 + 7*a**4 - 2*a**2 - 2*a + 2. Let l(g) = -2*b(g) - 3*y(g). Factor l(t).
-3*t**4*(t + 3)
Let f(j) be the second derivative of j**4/42 + 4*j**3 - 85*j**2/7 - 554*j. Suppose f(a) = 0. Calculate a.
-85, 1
Factor 175*u - 5*u**2 - 3645 + 198*u - 103*u.
-5*(u - 27)**2
Let h(p) be the second derivative of 11*p**4/16 - 3*p**3/2 + 3*p**2/8 + 20*p. Factor h(t).
3*(t - 1)*(11*t - 1)/4
Let c be 2*(-1 - (-12)/(-8))/(-1). Suppose -c*a - 10 = -10*a. Factor -3/4*w**a + 3/2*w + 9/4.
-3*(w - 3)*(w + 1)/4
Let h(f) be the first derivative of -5*f**6/72 + 13*f**5/24 + 5*f**4/4 - 35*f**3/3 + 22. Let r(a) be the third derivative of h(a). Factor r(n).
-5*(n - 3)*(5*n + 2)
Suppose 4 = 3*c - 2. Factor -q**3 + q**3 + c*q**3 - 10*q**2 + 3*q**3.
5*q**2*(q - 2)
Let v(g) be the third derivative of -g**5/105 - g**4/3 + 64*g**3/21 + 304*g**2. Let v(d) = 0. Calculate d.
-16, 2
Factor -30/7*p**2 + 48/7*p**3 + 4/7*p + 0 + 32/7*p**4.
2*p*(p + 2)*(4*p - 1)**2/7
Factor 3*h**2 + 0*h - 26*h + 4*h**3 - 18 - 6*h**3 + 17*h**2 - 30.
-2*(h - 8)*(h - 3)*(h + 1)
Suppose 0 = l + 3*p - 6*p + 8, 0 = l + 3*p - 16. Let g(s) be the second derivative of 0 + 0*s**2 + 1/3*s**3 - 7/20*s**5 + 5*s - 5/12*s**l. Factor g(w).
-w*(w + 1)*(7*w - 2)
Let -7/4*y - 5/4*y**3 + 1/2 + 9/4*y**2 + 1/4*y**4 = 0. What is y?
1, 2
Let q(z) = -8*z**4 - 16*z**3 - 46*z**2 + 18*z + 50. Let j(u) = 3*u**4 - 2*u**3 - u**2 + u. Let h(f) = -2*j(f) - q(f). Suppose h(y) = 0. Calculate y.
-5, -1, 1
Let d(l) = -5*l**3 - 480*l**2 + 905*l - 350. Let s(a) = -a**3 - 80*a**2 + 151*a - 58. Let z(i) = -6*d(i) + 35*s(i). Let z(k) = 0. Calculate k.
1, 14
Suppose 3872/3*f**2 + 176/3*f + 2/3 = 0. Calculate f.
-1/44
Let x(m) be the third derivative of -9*m**2 - 1/240*m**5 - 1/4*m**3 - 7/96*m**4 + 0 + 0*m. Solve x(q) = 0.
-6, -1
Suppose 4*d - 5*d = 14. Let r = -9 - d. Solve -6*m**r + 3*m**2 - 2 + 15*m**4 + 2 - 12*m**3 = 0.
0, 1/2, 1
Let g(z) be the first derivative of -3/4*z**4 + 10*z**3 - 10 + 0*z - 75/2*z**2. Factor g(r).
-3*r*(r - 5)**2
Let r(b) = -15*b**3 - 790*b**2 - 14590*b - 87490. Let m(n) = -5*n**3 - 264*n**2 - 4863*n - 29163. Let s(w) = 10*m(w) - 3*r(w). Find i, given that s(i) = 0.
-18
Suppose 3*o + 9 = -4*n, -7*n + 12 = -2*n - 4*o. Determine m so that 1/4*m**2 + n - 1/4*m = 0.
0, 1
Let u be -4 - -3 - -6*(-10)/(-45). Let s(f) be the third derivative of 0 + u*f**4 + 9*f**2 + 0*f + 1/6*f**6 + 0*f**3 + 7/15*f**5. Find g such that s(g) = 0.
-1, -2/5, 0
Find l such that -l**3 + 4/3*l + 0 + 1/3*l**5 + 4/3*l**2 - 2/3*l**4 = 0.
-1, 0, 2
Let q be 0/((-1)/(-4) + (-1175)/188). Factor -3/5*p + q + 1/5*p**2.
p*(p - 3)/5
Let c = -1563 - -1574. Let u(s) be the third derivative of 0 + 0*s**4 + 0*s**3 + 0*s + 1/840*s**8 + c*s**2 - 4/525*s**7 + 1/60*s**6 - 1/75*s**5. Factor u(i).
2*i**2*(i - 2)*(i - 1)**2/5
Let x(q) be the first derivative of q**3/3 + 137. Solve x(j) = 0 for j.
0
Suppose -l = -12*c - 26, 8*l - 3*l = 4*c + 18. Let -1/4*i**l + 1/2*i + 0 = 0. Calculate i.
0, 2
Let v(w) be the third derivative of -w**6/30 + w**5 + 11*w**4/2 + 34*w**3/3 - 15*w**2. Suppose v(y) = 0. Calculate y.
-1, 17
Factor 12*g + 0 + 1/3*g**2.
g*(g + 36)/3
Let o be 38/133 - 138/(-7). Factor -30 - 115*y - 2 + 25*y**2 + o*y**3 + 2.
5*(y - 2)*(y + 3)*(4*y + 1)
Suppose -3*v - v + 16 = 0. Let -20*u**3 + 9*u**2 - 5*u**2 - v*u**2 + 4*u**4 = 0. Calculate u.
0, 5
Let g(m) = -3*m**3 - 19*m**2 + 7*m + 16. Let k be -2*1 - (-4)/20*-5. Let a(f) = f**3 + 9*f**2 - 3*f - 8. Let o(h) = k*g(h) - 7*a(h). Factor o(b).
2*(b - 2)**2*(b + 1)
Let y(r) be the third derivative of r**7/1260 - r**6/720 - r**5/360 + r**4/144 - 49*r**2. What is s in y(s) = 0?
-1, 0, 1
Factor 8/5*b**3 + 136/5*b - 72/5 + 2/5*b**4 - 74/5*b**2.
2*(b - 2)**2*(b - 1)*(b + 9)/5
Suppose 5*z - 15 = -0*z. Find p such that p + p**2 - 65*p**4 + 64*p**4 + p**3 - 2*p**z = 0.
-1, 0, 1
Suppose 4*y + k + 4*k - 137 = 0, -4*k = -y + 8. Let j be y/10 - ((-32)/20)/(-2). Factor -2/11*q**j + 4/11 - 2/11*q.
-2*(q - 1)*(q + 2)/11
Let m(b) be the third derivative of b**8/84 + 2*b**7/21 - b**6/30 - b**5/3 + 266*b**2. Factor m(x).
4*x**2*(x - 1)*(x + 1)*(x + 5)
Let o be (5/(-11*(-28)/385))/((-10)/(-4)). Factor o*j - j**2 - 5/2*j**3 + 1.
-(j - 1)*(j + 1)*(5*j + 2)/2
Let b(l) be the second derivative of l**8/210 - l**7/420 - 7*l**3 - 22*l. Let n(i) be the second derivative of b(i). Factor n(w).
2*w**3*(4*w - 1)
Let g(p) be the third derivative of -p**8/84 - 2*p**7/105 + 3*p**6/10 - 11*p**5/15 + 2*p**4/3 - 144*p**2. Suppose g(c) = 0. What is c?
-4, 0, 1
Let h(p) be the second derivative of p**9/12096 - p**8/6720 - p**7/560 + 29*p**3/6 - 9*p. Let i(d) be the second derivative of h(d). Solve i(y) = 0 for y.
-2, 0, 3
Let r be (-1140)/(-589) + (-6)/(-93). Factor 2/5*j**r + 6/5*j - 8/5.
2*(j - 1)*(j + 4)/5
Let o = -268 - -268. Factor 0 + o*x - 1/3*x**5 + 0*x**4 + 4/3*x**3 + 0*x**2.
-x**3*(x - 2)*(x + 2)/3
Let l = -242 + 245. Let j(z) be the second derivative of 1/30*z**3 - 1/5*z**2 + 0 + 1/30*z**4 - l*z - 1/100*z**5. Find b, given that j(b) = 0.
-1, 1, 2
Suppose 0 = 5*g, -5*g = -d - d - 150. Let p = -69 - d. Let -p*l - 12 - 3/4*l**2 = 0. What is l?
-4
Suppose -48*s = -45*s - 9. Factor -12*a + 10 + 0*a**3 + 37*a + 2*a**3 + s*a**3 + 20*a**2.
5*(a + 1)**2*(a + 2)
Let w(n) be the third derivative of 1/27*n**3 + 0 + 1/540*n**5 + 0*n + 1/72*n**4 + 8*n**2. Find b such that w(b) = 0.
-2, -1
Let r(g) be the first derivative of -16 + g**2 + 3/2*g**4 - 2*g**3 - 2/9*g. Factor r(u).
2*(3*u - 1)**3/9
Let y be 3*5/((-75)/(-10)). Suppose x + 30 = -h + y*h, 3*h + 4*x - 97 = 0. Find f, given that -f**2 - h + 0*f**2 + 32 = 0.
-1, 1
Let f(j) be the second derivative of -j**8/33600 + j**6/1200 - j**5/300 - j**4/3 + 2*j. Let k(v) be the third derivative of f(v). Suppose k(n) = 0. What is n?
-2, 1
Let j(c) = 9 + 5 - 8 + 0*c - c. Let l be j(6). Factor -2/5*y**4 + 2/5*y**3 - 2/5*y + l + 2/5*y**2.
-2*y*(y - 1)**2*(y + 1)/5
Let v = -72 + 74. Let i(t) be the first derivative of 3/2*t**v - 9/16*t**4 + 1/8*t**6 - 2 + 0*t - 3/10*t**5 + t**3. Factor i(l).
3*l*(l - 2)**2*(l + 1)**2/4
Let u(i) = 7*i**2 - 10*i + 7. Let b(j) = -6*j**2 + 10*j - 8. Let z(k) = 5*b(k) + 4*u(k). Factor z(l).
-2*(l - 3)*(l - 2)
Let s = 56/65 - 38/195. Let m(t) be the second derivative of -12*t - s*t**4 + 16*t**2 - 8/3*t**3 + 1/5*t**5 + 0. Factor m(y).
4*(y - 2)**2*(y + 2)
Let o = -4852 + 4854. Find s such that -9/7*s + 12/7 - 3/7*s**o = 0.
-4, 1
Factor 27/4*u**4 + 0 + 1/4*u**5 + 0*u**2 - 7*u**3 + 0*u.
u**3*(u - 1)*(u + 28)/4
Let t be ((40/(-24))/(27/(-9)))/((-5)/(-6)). Factor 0 + 8/3*g + t*g**2.
2*g*(g + 4)/3
Let y be ((-4)/(-300))/(-4*(-6)/40). Let m(r) be the second derivative of -5*r - 27*r**2 - 2/5*r**5 - 12*r**3 - y*r**6 + 0 - 3*r**4. Factor m(d).
-2*(d + 3)**4/3
Let d(g) be the third derivative of -g**6/40 + 3*g**5/10 - 9*g**4/8 - 152*g**2. Factor d(y).
-3*y*(y - 3)**2
Let h(d) be the third derivative of 0*d - 27*d**2 - 1/14*d**3 + 0 - 3/140*d**5 - 3/56*d**4 - 1/280*