 3
Let w = 1199/7 + -171. Let z(p) be the first derivative of -1/14*p**2 - w*p - 1 + 1/7*p**3. Suppose z(c) = 0. What is c?
-2/3, 1
Suppose 53*x - 468 = -103*x. Factor -26/7*n + 52/7*n**2 - 12/7 - 2*n**x.
-2*(n - 3)*(n - 1)*(7*n + 2)/7
Suppose -4*h = g - 22, 5*h + 4 = -4*g + 37. Suppose 5 = g*o + 1. Let 0*b**4 + b**4 - 3*b**5 + o*b**5 = 0. What is b?
0, 1
Factor -355*g**3 + 350*g**3 + 10*g**2 + 0*g**2 - 15*g**4.
-5*g**2*(g + 1)*(3*g - 2)
Suppose 3*v + 0*v + 45 = 0. Let a be (-5)/(v/9) - 0. Find c such that -c**2 + 3*c**a + c**3 - 7*c**3 + 2*c**3 = 0.
-1, 0
Let p = 17501/27 - 648. Let m(t) be the second derivative of -1/90*t**5 + 2/9*t**2 + 2/27*t**4 + 0 + 3*t - p*t**3. Factor m(q).
-2*(q - 2)*(q - 1)**2/9
Let v(k) be the first derivative of -k**5/5 + 5*k**3/3 - 4*k - 104. Determine h so that v(h) = 0.
-2, -1, 1, 2
Factor -20*f - 26*f + 16*f**3 - 176 - 36*f + 18*f**2 + 18*f + 26*f**2.
4*(f - 2)*(f + 2)*(4*f + 11)
Let h = 2641/13 + -203. Factor 0*y + 0 + 6/13*y**3 - 4/13*y**2 - h*y**4.
-2*y**2*(y - 2)*(y - 1)/13
Factor 26/7*d**2 + 2/7*d**3 - 128/7*d + 136/7.
2*(d - 2)**2*(d + 17)/7
Let p(u) be the first derivative of u**7/105 - u**5/30 + 3*u**2/2 + 18. Let t(s) be the second derivative of p(s). Determine x, given that t(x) = 0.
-1, 0, 1
Let q(z) be the third derivative of 0*z + 5/12*z**4 + 0 + 14*z**2 - 5/6*z**3 - 1/12*z**5. Factor q(g).
-5*(g - 1)**2
Factor 0 + 2/5*r**2 + 2/5*r.
2*r*(r + 1)/5
Let y(t) = 6*t**3 + 81*t**2 - 69*t. Let q(p) = -3*p**3 - 40*p**2 + 35*p. Let x(g) = -9*q(g) - 4*y(g). Find l such that x(l) = 0.
-13, 0, 1
Factor 14/9*n - 2/3 + 2/9*n**3 - 10/9*n**2.
2*(n - 3)*(n - 1)**2/9
Factor 1/4*r**4 + 0 + 17/4*r**2 + 0*r - 9/2*r**3.
r**2*(r - 17)*(r - 1)/4
Let u(g) be the first derivative of g**5/5 - g**4/4 - g + 10. Let l(c) = -239*c**4 - 391*c**3 - 160*c**2 - 20*c - 6. Let f(q) = l(q) - 6*u(q). Factor f(i).
-5*i*(i + 1)*(7*i + 2)**2
Let a(q) = -5*q**3 + 8*q**2 + 35*q + 22. Let g(o) = -o**2 + 1. Let n(h) = a(h) - 2*g(h). Factor n(k).
-5*(k - 4)*(k + 1)**2
Let x(d) be the second derivative of -7*d**6/30 + 3*d**5/2 - 43*d**4/12 + 4*d**3 - 2*d**2 - 119*d. Find m such that x(m) = 0.
2/7, 1, 2
Let w(m) be the third derivative of m**6/96 + m**5/12 - 5*m**4/96 - 5*m**3/6 - 14*m**2. Factor w(b).
5*(b - 1)*(b + 1)*(b + 4)/4
Let w(l) = 41*l + 85. Let z be w(-2). Factor 21/2*p + 3*p**2 + 3 - 9/2*p**z.
-3*(p - 2)*(p + 1)*(3*p + 1)/2
Let t = 60 + -55. Suppose 0 = 4*p + 3*g - 17, -t*p + g = -2 - 5. Factor 1/4*v**p + 1/2*v + 0.
v*(v + 2)/4
What is p in -2/3*p**4 - 242/3 + 440/3*p - 40/3*p**3 - 52*p**2 = 0?
-11, 1
Let -51*l - 1/4*l**2 - 2601 = 0. What is l?
-102
Suppose -5*i + 322 = -293. Let y = 985/8 - i. Factor 0 + 0*p**2 + y*p + 0*p**4 + 1/8*p**5 - 1/4*p**3.
p*(p - 1)**2*(p + 1)**2/8
Let b = -28 - -31. Let y(p) be the second derivative of -3/20*p**5 + 19/18*p**4 + 4/3*p**2 - 22/9*p**b + 2*p + 0. Factor y(j).
-(j - 2)**2*(9*j - 2)/3
Suppose 0 = -5*y - 0*t + t + 352, 5*y = -5*t + 340. Let m be 360/y + (-3 - 2). Find c such that -3/7*c - m*c**2 + 4/7 = 0.
-4, 1
Let b be (-5)/(-20) - 2/8. Suppose -o + 3 = -b. Determine z, given that -9*z**2 - 24/5*z - 4/5 - 5*z**o = 0.
-1, -2/5
Factor 17/2*i - 1/4*i**3 + 10 - 7/4*i**2.
-(i - 4)*(i + 1)*(i + 10)/4
Let n = -5024 + 5026. Solve -2/3*a + 4/3*a**5 + 2*a**4 - n*a**2 + 0 - 2/3*a**3 = 0 for a.
-1, -1/2, 0, 1
Let b = 23011 + -23007. Suppose 0 + 66/5*y**3 + 27/5*y - 72/5*y**2 - 24/5*y**b + 3/5*y**5 = 0. Calculate y.
0, 1, 3
Let l(z) be the third derivative of z**7/175 + z**6/25 + z**5/25 - z**4/5 - 3*z**3/5 + 152*z**2. Factor l(r).
6*(r - 1)*(r + 1)**2*(r + 3)/5
Suppose 5*d = -4*n, 4*n = 6*n - 5*d. Suppose n = -j - j. Suppose 0*x**3 + 3/5*x**4 + 6/5*x - 9/5*x**2 + j = 0. Calculate x.
-2, 0, 1
Suppose -15*k = -14*k - 150. Let t = 152 - k. Let 4/5*x**4 - 4/5 + 0*x**t + 8/5*x**3 - 8/5*x = 0. What is x?
-1, 1
Let o be 5/((-2025)/(-72)) - 4/(-18). Solve -o*j**2 + 2/5*j + 0 - 2/5*j**3 + 2/5*j**4 = 0 for j.
-1, 0, 1
Determine t so that -2/3*t - 2*t**5 + 4/3*t**2 - 4/3*t**4 + 0 + 8/3*t**3 = 0.
-1, 0, 1/3, 1
Let z(r) be the third derivative of r**6/60 + 16*r**5/3 + 2*r**2 - 86*r. Find g such that z(g) = 0.
-160, 0
Suppose w - j - 6 = 0, -w - 12 = 4*j + 2. Factor w*l**2 - 2*l + 15072 - 15072.
2*l*(l - 1)
Determine a so that 4/9*a**2 - 403/9*a - 101/9 = 0.
-1/4, 101
Let y = -11419 - -11419. Solve y + 2/5*h**2 + 2/5*h = 0.
-1, 0
Let r be 3/(1*3/2). Let b(d) = -d**2 + 16*d - 15. Let z be b(15). Factor -3/5*k + z + 3/5*k**r.
3*k*(k - 1)/5
Let a(s) = -s**3 + 11*s**2 - 10*s + 10. Let f be a(7). Factor 4*l**4 + 4*l - f*l**2 + 132*l**2 + 2*l**3 - 6*l**3.
4*l*(l - 1)**2*(l + 1)
Suppose 0 = -2*c + 3*f + 20, -f + 1 = 3*c - 7. Suppose c*o + 4 = 3*o, 26 = 2*u - 5*o. Factor -1 + 6*b**u + 17*b**3 + 3 + 32*b**4 + 20*b + 57*b**3 + 66*b**2.
2*(b + 1)**2*(4*b + 1)**2
Let t(i) be the second derivative of -i**7/3780 - i**6/1080 + i**5/90 - 11*i**4/3 + 34*i. Let n(k) be the third derivative of t(k). Factor n(u).
-2*(u - 1)*(u + 2)/3
Let p(v) be the second derivative of -v**5/100 + 8*v**3/15 + 130*v. Determine h, given that p(h) = 0.
-4, 0, 4
Solve -4/3*a**3 + 100/3*a**2 - 748/3*a + 484 = 0.
3, 11
Let b(x) be the second derivative of -20*x**7/147 + 13*x**6/105 + 9*x**5/35 - 13*x**4/42 + 2*x**3/21 + 15*x + 1. Solve b(o) = 0.
-1, 0, 1/4, 2/5, 1
Solve 5*f**3 + 133*f**2 - 9*f**3 - 129*f**2 - 4*f**4 + 4*f + 0*f**3 = 0.
-1, 0, 1
Suppose 29 - 22 = -f. Let b be (f/21)/(3/(-6)). Suppose b*a + 2/9*a**4 - 2/9*a**2 + 0 - 2/3*a**3 = 0. Calculate a.
-1, 0, 1, 3
Let x(z) = 9*z**2 + 138*z + 121. Let n(d) = 17*d**2 + 274*d + 243. Let s(t) = 4*n(t) - 7*x(t). Suppose s(w) = 0. What is w?
-25, -1
Let h be (1/4 - (-1)/(-4))*474/948. Let -3/7*n - 3/7*n**2 + h = 0. Calculate n.
-1, 0
Suppose -3*h + 7 = 19, 5*u + h - 11 = 0. Factor 2/7*k**2 + 0 - 2/7*k**u + 4/7*k.
-2*k*(k - 2)*(k + 1)/7
Let a(x) be the third derivative of x**6/40 - 2*x**5 + 50*x**4 - 5*x**2 - 47*x. Determine w so that a(w) = 0.
0, 20
Factor -34/3 + 2/3*r - 2/3*r**3 + 34/3*r**2.
-2*(r - 17)*(r - 1)*(r + 1)/3
Suppose -2166/11*a + 114/11*a**2 - 2/11*a**3 + 13718/11 = 0. What is a?
19
Let y(j) be the first derivative of -12/5*j**5 - 64/3*j - 15 - 64/3*j**2 + 8*j**4 + 32/9*j**3. Factor y(d).
-4*(d - 2)**2*(3*d + 2)**2/3
Let q(y) be the first derivative of y**4/2 - 30*y**3/7 + 81*y**2/7 - 54*y/7 + 53. Determine i, given that q(i) = 0.
3/7, 3
Solve 9*m - 3*m**2 + 8*m**2 - 10*m - 3*m - 2*m + 2*m**3 - m**4 = 0.
-2, 0, 1, 3
Let g be (2 - 6)/(16 - 19). Let x(s) be the first derivative of -4*s - 1/2*s**4 + g*s**3 + 5 + s**2. Find w such that x(w) = 0.
-1, 1, 2
Suppose 0 = l + 4 - 6. Suppose 8*d - 28 = 4. Determine i so that 4*i - 2*i**2 - 6*i**3 + 2*i**3 - l*i**2 + 4*i**d = 0.
-1, 0, 1
Let z be 6/(-11) + 195/55. Let g(i) be the third derivative of 1/180*i**5 + 0 - 1/36*i**4 - 4*i**2 + 0*i + 0*i**z. Suppose g(s) = 0. What is s?
0, 2
Let h be 6/(-4) + ((-3)/18)/((-6)/72). Let 0 - 1/2*w**4 - 3/2*w**3 + w + h*w**2 + 1/2*w**5 = 0. What is w?
-1, 0, 1, 2
Determine n so that 10602 + 3072*n + 192*n**2 - 5316 + 11098 + 4*n**3 = 0.
-16
Factor 205*d + 462*d + 136 + 152 + 176*d + 1080*d**3 + 469*d + 54*d**4 + 2016*d**2.
2*(d + 18)*(3*d + 2)**3
Let y(i) = 2*i**2 - 9. Let l(h) = -4*h**2. Let p(k) = -3 - 1 + 3 + k**2. Let q(f) = l(f) + 5*p(f). Let n(m) = -7*q(m) + 4*y(m). Factor n(d).
(d - 1)*(d + 1)
Suppose 2*l = 6*l - 9*l + 15. Determine s so that 2/7*s**l + 8/7*s**2 + 4/7 + 10/7*s = 0.
-2, -1
Let y(c) be the third derivative of -c**8/2184 + 3*c**7/455 - c**6/30 + 17*c**5/195 - 7*c**4/52 + 5*c**3/39 + 252*c**2. Suppose y(s) = 0. What is s?
1, 5
Let k(x) be the first derivative of x**5/25 + 13*x**4/2 + 845*x**3/3 + 247. Suppose k(f) = 0. What is f?
-65, 0
Factor 564*u - 4*u**4 + 13*u**2 - 188*u - 187*u - 185*u - 13*u**3.
-u*(u - 1)*(u + 4)*(4*u + 1)
Let h(b) be the third derivative of b**8/168 - 29*b**7/105 + 163*b**6/60 + 673*b**5/30 + 184*b**4/3 + 256*b**3/3 - 3*b**2 + 14. What is z in h(z) = 0?
-1, 16
Suppose 4*k = -k + 15. Find z, given that -4*z - k*z**2 + 3*z + 3*z**3 - 5*z = 0.
-1, 0, 2
Let x(m) = -3*m + 14. Let r be x(4). Suppose -8 = -4*g + 4. Let 3*w**3 + 0*w**g - 4*w**r + w - 4*w**4 + w**5 + 3*w**3 = 0. What is w?
0, 1
Let p(y) be the second derivative of y**7/630 - y**6/180 - y**5/90 + 5*y**3/2 + 17*y. Let 